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Florida State University Libraries
Electronic Theses, Treatises and Dissertations The Graduate School
2012
A Study on Charter School Effects onStudent Achievement and on Segregation inFlorida Public SchoolsSeungbok Choi
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THE FLORIDA STATE UNIVERSITY
COLLEGE OF SOCIAL SCIENCES AND PUBLIC POLICY
A STUDY ON CHARTER SCHOOL EFFECTS ON STUDENT ACHIEVEMENT AND ON
SEGREGATION IN FLORIDA PUBLIC SCHOOLS
By
SEUNGBOK CHOI
A Dissertation submitted to the Department of Public Administration and Policy
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
Degree Awarded: Spring Semester, 2012
ii
Seungbok Choi defended this dissertation on March 20, 2012.
The members of the supervisory committee were:
Frances Stokes Berry Professor Directing Dissertation
Betsy Jane Becker University Representative
Ralph Brower Committee Member
Lance deHaven-Smith Committee Member
The Graduate School has verified and approved the above-named committee members, and certifies that the dissertation has been approved in accordance with university requirements.
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To my parents whose lives have been dedicated to educating their children and who have inspired me to be a learned man
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ACKNOWLEDGEMENTS
I could not thank my parents too much who have dedicated their lives to educating
children and have always inspired me to be a learned man. I really appreciate my wife having
been with me. She has always helped, encouraged and trusted me in any case and at any cost. My
daughters always respect me, and they make me happy and work hard. Thanks, Byul and Saem!
Without Dr. Berry’s help, I could not finish my study in FSU. She has always been kind,
helpful, and considerate to me. She has always encouraged me, which made me be confident and
keep at it. My family and I are in debt a lot to Dr. Becker. At the very start of our lives in FSU,
she helped my wife and me in studying, researching, and living. We could not forget those
parties in her house. Dr. Brower has been generous and ready-to-help and gave me sociological
insights for public policy analysis. Dr. deHaven-Smith taught me the importance of
comprehensive and critical perspectives in public policy analysis through his impressive book. I
could not thank them enough with any word. I really appreciate Dr. Eger’s kindness to give me
an opportunity to teach undergraduate classes for two semesters, which helped me educationally
and financially as well.
My friends, especially Boktae Kim, Cheongeun Choi, Insoo Shin, Seungjin Lee, and
Raesun Kim, have helped me at the every corner where I met problems and difficulties in my
research for dissertation and in my life in FSU. Other many Korean friends and some of
international students have been available helpers and guides academically, emotionally and
financially during my stay in Tallahassee. So do my colleagues from the Ministry of Education,
Technology and Science. Thank you so much, Friends and Colleagues!
I have always been indebted to the invisible hands, or the history and the society in which
I have been raised, educated, and supported in every aspect of my life. I could not find any word
to express my indebtedness to them. Korean government funded my study in FSU for 22 months
from January 2009 and allowed me to have an official leave for overseas study from October,
2010, which made this dissertation possible from start to finish. I am so grateful to Korean
government and my Ministry.
I hope that everyone would be blessed by the great Nature, by the Heaven and the Earth!
At the beginning of spring of 2012 In Tallahassee, Florida, USA
Seungbok Choi
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TABLE OF CONTENTS
LIST OF TABLES ....................................................................................................................... VII
ABSTRACT ................................................................................................................................. XII
CHAPTER ONE
INTRODUCTION .......................................................................................................................... 1
1.1 Charter Schools in the U.S. and Florida ............................................................................1
1.2 Problem Statement .............................................................................................................2
1.3 School Effectiveness Theory: Autonomy and Accountability ..........................................4
1.4 Market Competition Theory ..............................................................................................5
1.5 Social Inequality Theory ...................................................................................................6
1.6 Significance of the Study ...................................................................................................8
1.7 Dissertation Plan ................................................................................................................9
CHAPTER TWO
LITERATURE REVIEW ............................................................................................................. 11
2.1 Studies on School Effects on Charter School Students .................................................. 11
2.1.1 Nation-wide studies on student achievement in charter schools ......................... 11
2.1.2 Studies on student achievement in Florida charter schools ................................. 13
2.1.3 Limitations of the previous studies on student achievement comparison............ 14
2.2 Studies on Market Competition from Charter Schools ................................................... 15
2.2.1 Review of the previous studies on competition effects ....................................... 15
2.2.2 Limitations of the previous studies on competition effects ................................. 19
2.3 Studies on Social Impacts of Charter Schools ................................................................ 20
2.3.1 Studies on racial/ethnic composition in charter schools ...................................... 20
2.3.2 Studies on charter school impacts on racial/ethnic composition in TPSs ............ 22
2.3.3 Limitations of the previous studies on segregation effects .................................. 23
CHAPTER THREE
RESEARCH DESIGN AND METHODOLOGY ........................................................................ 25
3.1 Research Questions ......................................................................................................... 25
3.1.1 School effectiveness thesis .................................................................................. 25
3.1.2 Market competition thesis .................................................................................... 26
3.1.3. Segregation effect thesis ..................................................................................... 26
3.2 Units of Analysis............................................................................................................. 27
3.3 Data Collection ............................................................................................................. 288
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3.4 Measurement in the Study ............................................................................................ 299
3.4.1 Student achievement .......................................................................................... 299
3.4.2 Market competition pressure from charter schools .............................................. 29
3.4.3 The Degree of segregation in public schools ....................................................... 30
3.5 Methodology ................................................................................................................... 32
3.6 Analytic Strategy ............................................................................................................ 34
3.6.1 Stage 1: Checking the distribution of variance .................................................... 34
3.6.2 Stage 2: Examining charter school effects (without-control models) .................. 34
3.6.3 Stage 3: Testing the robustness of charter school effects (with-control models) 34
3.6.4 Stage 4: Checking the similarity or dissimilarity of charter school effect sizes .. 34
3.7 Analytic Models ............................................................................................................ 355
3.7.1 Model I: Multilevel models for univariate change ............................................ 355
3.7.2 Model II: Multilevel models for multivariate change .......................................... 37
CHAPTER FOUR
CHARTER SCHOOL EFFECTS ON STUDENT ACHIEVEMENT ......................................... 38
4.1 Characteristics of Public Schools and Counties in Florida ............................................. 38
4.2 Analysis of Variance and Yearly Changes in the FCAT Scores of Public Schools ....... 42
4.3 Testing the School Effectiveness Theory ....................................................................... 50
4.4 Testing the Market Competition Theory at the School level ........................................ 588
4.5 Testing Social Equality Theory ...................................................................................... 71
4.6 Chapter Conclusion ..................................................................................................... 7980
CHAPTER FIVE
SOCIAL IMPACTS OF CHARTER SCHOOLS ....................................................................... 844
5.1 Preliminary Analyses of the Distribution of Demographic Compositions ................... 844
5.2 Analyses of the DIs of Charter Schools .......................................................................... 90
5.3 Analysis of Variance in the DIs of Traditional Public Schools ...................................... 98
5.4 Analyses of Charter School Effects on the DIs of Traditional Public Schools ............ 103
5.5 Multivariate Analyses of the DIs among Traditional Public Schools........................... 111
5.6 Chapter Conclusion ....................................................................................................... 121
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CHAPTER SIX
CONCLUSION AND DISCUSSION ........................................................................................ 125
6.1 Research Design and Framework ............................................................................... 1255
6.2 Primary Findings and Conclusions ............................................................................... 126
6.3 Contributions of This Study .......................................................................................... 130
6.4 Limitations of This Study ............................................................................................. 132
6.5 Concluding Remark ...................................................................................................... 133
APPENDIX 1
CHARTER SCHOOL GROWTH IN FLORIDA ....................................................................... 135
APPENDIX 2
DESCRIPTIVE STATISTICS OF FLORIDIAN PUBLIC SCHOOLS ..................................... 136
APPENDIX 3
RESULTS FROM THE YEARLY CHANGE MODELS .......................................................... 141
APPENDIX 4
RESULTS FROM THE CHARTER SCHOOL EFFECT MODELS......................................... 148
APPENDIX 5
RESULTS FROM THE MARKET COMPETITION MODELS ............................................... 160
APPENDIX 6
RESULTS FROM CS MODELS AND SOCIAL INEQUALITY MODELS............................ 184
APPENDIX 7
RESULTS FROM ANALYSES OF CHARTER SCHOOL DIS ............................................. 2011
APPENDIX 8
RESULTS FROM THE ONE-WAY ANOVA HMLM MODELS ............................................ 205
APPENDIX 9
DEFINITIONS OF THE VARIABLES USED THE ANALYSES IN THIS STUDY .............. 208
APPENDIX 10
STUDIES ON THE CS COMPETITION IMPACTS ................................................................ 211
REFERENCES ........................................................................................................................... 216
BIOGRAPHICAL SKETCH ...................................................................................................... 223
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LIST OF TABLES
1-1 A FRAMEWORK FOR CHARTER SCHOOL POLICY EVALUATION ............................ 4
4-1 NUMBER OF CHARTER SCHOOLS AND TPSS IN THE DATASETS BY YEAR AND
SCHOOL LEVEL ................................................................................................................... 39
4-2 YEARS OF OPERATION OF CHARTER SCHOOLS BY SCHOOL LEVEL (2009) ....... 40
4-3 DISTRIBUTION OF CHARTER SCHOOLS AND TPSS BY LOCATION (1998-2009) .. 40
4-4 CHARACTERISTICS OF PUBLIC SCHOOLS IN FLORIDA BY SCHOOL LEVEL ...... 41
4-5 RESULTS FROM THE ONE-WAY ANOVA MODELS FOR THE FCAT MATH SCORES
................................................................................................................................................. 44
4-6 RESULTS FROM THE ONE-WAY ANOVA MODELS FOR THE FCAT READING
SCORES ................................................................................................................................. 45
4-7 RESULTS FROM THE YEARLY CHANGE MODELS FOR THE FCAT MATH SCORES
................................................................................................................................................. 47
4-8 RESULTS FROM THE YEARLY CHANGE MODELS FOR THE FCAT READING
SCORES ................................................................................................................................. 47
4-9 CORRELATIONS BETWEEN THE INITIAL STATUS AND THE ANNUAL CHANGE
RATES .................................................................................................................................... 48
4-10 REDUCTIONS OF VARIANCE IN YEAR EFFECTS BY THE YEARLY CHANGE
MODELS ................................................................................................................................ 49
4-11 RESULTS FROM THE SCHOOL EFFECTIVENESS MODELS FOR THE FCAT MATH
SCORES ................................................................................................................................. 52
4-12 RESULTS FROM THE SCHOOL EFFECTIVENESS MODELS FOR THE FCAT
READING SCORES .............................................................................................................. 53
4-13 RESULTS FROM THE CHARTER POLICY MODELS FOR THE FCAT MATH
SCORES ................................................................................................................................. 56
4-14 RESULTS FROM THE CHARTER POLICY MODELS FOR THE FCAT READING
SCORES ................................................................................................................................. 57
4-15 DESCRIPTION OF CHARTER COMPETITION MEASURES ........................................ 60
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4-16 FIXED EFFECTS RESULTS FROM THE MODELS WITH CHARTER PRESENCE
VARIABLE (MATH) ............................................................................................................. 62
4-17 FIXED EFFECTS RESULTS FROM THE MODELS WITH CHARTER PRESENCE
VARIABLE (READING) ....................................................................................................... 63
4-18 PEARSON CORRELATIONS BETWEEN THE FCAT SCORES AND CHARTER
COMPETITION VARIABLES .............................................................................................. 64
4-19 FIXED EFFECTS RESULTS FROM THE MODELS WITH CHARTER NUMBERS
(MATH) .................................................................................................................................. 64
4-20 FIXED EFFECTS RESULTS FROM THE MODELS WITH CHARTER NUMBERS
(READING) ............................................................................................................................ 65
4-21 DISTRIBUTION OF COUNTY LEVEL COMPETITION VARIABLES ......................... 67
4-22 FIXED EFFECT RESULTS FROM THE MODELS WITH SCHOOL CHOICE IN LEVEL
3 (MATH) ............................................................................................................................... 69
4-23 FIXED EFFECT RESULTS FROM THE MODELS WITH SCHOOL CHOICE IN LEVEL
3 (READING) ......................................................................................................................... 70
4-24 RESULTS FROM BASE MODEL AND SOCIAL INEQUALITY MODEL (5TH GRADE;
MATH) ................................................................................................................................... 73
4-25 RESULTS FROM BASE MODEL AND SOCIAL EQUALITY MODEL (8TH GRADE;
MATH) ................................................................................................................................... 74
4-26 RESULTS FROM BASE MODEL AND SOCIAL EQUALITY MODEL (10TH GRADE;
MATH) ................................................................................................................................... 75
4-27 RESULTS FROM BASE MODEL AND SOCIAL INEQUALITY MODEL (5TH GRADE;
READING) ............................................................................................................................. 77
4-28 RESULTS FROM BASE MODEL AND SOCIAL EQUALITY MODEL (8TH GRADE;
READING) ............................................................................................................................. 78
4-29 RESULTS FROM BASE MODEL AND SOCIAL EQUALITY MODEL (10TH GRADE;
READING) ............................................................................................................................. 79
4-30 RANDOM EFFECT RESULTS FROM CHARTER SCHOOL MODELS AND SOCIAL
EQUALITY MODELS (MATH) ........................................................................................... 82
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4-31 RANDOM EFFECT RESULTS FROM CHARTER SCHOOL MODELS AND SOCIAL EQUALITY MODELS (READING) ..................................................................................... 83
5-1 MEAN PERCENTAGE COMPARISONS OF DEMOGRAPHIC CHARACTERISTICS
(1998-2009)............................................................................................................................. 86
5-2 COUNTY DESCRIPTIVE STATISTICS IN DEMOGRAPHIC COMPOSITIONS (1998-
2009) ....................................................................................................................................... 87
5-3 PAIRED MEAN COMPARISON OF THE PERCENTAGES OF DEMOGRAPHIC
GROUPS (2009) ..................................................................................................................... 89
5-4 DESCRIPTIVE STATISTICS OF CHARTER SCHOOL VARIABLES ............................. 91
5-5 FIXED EFFECT RESULTS FROM YEARLY CHANGE MODELS FOR CHARTER
SCHOOL DIS ......................................................................................................................... 92
5-6 RANDOM EFFECT RESULTS FROM YEARLY CHANGE MODELS FOR CHARTER
SCHOOL DIS ......................................................................................................................... 93
5-7 FIXED EFFECT RESULTS FROM MODELS FOR CHARTER SCHOOL DIS ................ 95
5-8 CORRELATIONS AMONG VARIABLES AND DISTRIBUTIONS OF CHARTER
SCHOOLS .............................................................................................................................. 96
5-9 COMPARISONS OF THE VARIANCE EXPLAINED BY MODELS ................................ 97
5-10 RESULTS FROM ONE-WAY ANOVA MODELS BY SCHOOL LEVEL .................... 100
5-11 ANNUAL CHANGE RATES FROM YEARLY CHANGE MODELS FOR THE DIS .. 103
5-12 FIXED EFFECT RESULTS FROM CHARTER SCHOOL EFFECT MODELS
(ELEMENTARY SCHOOL) ................................................................................................ 107
5-13 FIXED EFFECT RESULTS FROM CHARTER SCHOOL EFFECT MODELS (MIDDLE
SCHOOL) ............................................................................................................................. 108
5-14 FIXED EFFECT RESULTS FROM CHARTER SCHOOL EFFECT MODELS (HIGH
SCHOOL) ............................................................................................................................. 109
5-15 COMPARISON OF THE VARIANCE EXPLAINED BY MODELS IN LEVEL 2 ...... 1111
5-16 CORRELATIONS BETWEEN THE DIFFERENCES IN DIS OF TPSS AND THE
DEMOGRAPHIC COMPOSI-TIONS IN NEARBY CSS................................................... 115 5-17 RESULTS FROM TWO-LEVEL HMLM MODELS (ELEMENTARY SCHOOL) ........ 117
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5-18 RESULTS FROM TWO-LEVEL HMLM MODELS (MIDDLE SCHOOL) ................. 1188
5-19 RESULTS FROM TWO-LEVEL HMLM MODELS (HIGH SCHOOL) ......................... 119
5-20 COMPARISONS OF THE EXPLAINED PROPORTIONS IN SCHOOL VARIANCE . 121
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ABSTRACT
Charter schools have now been in operation for two decades in the U.S., and for 15 years
in Florida. Florida was third in the U.S. in the number of charter schools operated and in student
enrollment in 2010. This study examined the assumed effects of charter school policy on the
public school system: charter school effects on student achievement in charter schools and in
TPSs, and segregation effects and stratification effects on charter schools and traditional public
schools (TPSs). I applied three perspectives to investigate charter school effect on student
achievement: School effectiveness theory, market competition theory, and social inequality
theory. The racial/ethnic segregation effect and the socio-economic stratification effect were
examined longitudinally and cross-sectionally. Datasets of primary and secondary public schools
and county educational and demographic information covering 1998 to 2010 were obtained from
multiple sources: the Common Core of Data from NCES, the Florida School Indicator Report,
the Florida Department of Education, Florida Statistics Abstract, and the U.S. Census Bureau.
Hierarchical linear modeling was utilized to explore charter school effects in different
organizational levels and hierarchical multivariate linear modeling was used to take into account
the closely correlated relationships of the demographic compositions in public schools.
The analyses of student achievement in charter schools and traditional schools indicated
that charter schools and traditional public schools are significantly different from each other, and
that the school characteristics were more influential on school performance than county
characteristics or year effects, especially in the higher grades. Some charter schools achieved
better in some subjects and grades, in that they started at lower scores than TPSs but grew faster
during the period 1998-2010. However, the charter school effectiveness turned out to be
insignificant or even negative when control variables such as educational factors and
demographic composition were introduced. Market competition theory could not explain the
variation in schools’ FCAT scores, while social inequality theory explained it better. The
findings of this study did not support the School Effectiveness Theory nor the Market
Competition Theory in charter school movement. Instead, Social Inequality Theory was
confirmed to be relevant to understand variation in public school academic achievement.
The analyses of segregation and stratification effects showed that charter schools were
more racially and socio-economically segregated, and that they exacerbated the segregation and
stratification in traditional public schools. Analyses of the Dissimilarity Index (DI) distribution
xiii
among charter schools and TPSs revealed that the demographic compositions in charter schools
deviated more from the county means than did TPSs during the period 1998 through 2009.
Charter schools had much lower proportions of free/reduced price lunch program students than
TPSs in every school level, which was negatively related to the percentage of white students but
positively to the percentage of black students. The years of charter school policy adoption in a
county have similar effects on both groups: the longer it was since a county introduced a charter
school policy, the fewer black students and the more white students were enrolled in charter
schools. Overall, charter schools were likely used as pockets for white flight and self-isolation,
and exacerbated socio-economic stratification in public schools. The analyses of charter school
DIs supported the warnings of white flight, self-isolation, and socio-economic stratification
(Carnoy, 2000; Frankenberg, Lee, & Orfield, 2003; Rivkin, 1994).
The findings of this study suggested that increasing proportions of black students and
free/reduced price lunch program recipients have enrolled in TPSs at all school levels along the
years during 1998-2009. However the percentages of white students in TPSs have decreased year
by year even though the rates of decrease are small. The analyses implied that charter schools
were likely to locate around TPSs that had a higher proportion of a certain demographic group;
and the higher proportion of certain demographic group in the area would induce charter schools
to target these groups.
Hierarchical multivariate linear models (HMLM) were introduced to detect the relative
relationships between demographic groups. The multivariate analyses suggested that middle
school charters were likely to locate around the TPSs with more white students and fewer
Hispanic students, while more elementary charter schools opened around the TPSs with fewer
black students. The location and targeting strategies of charter schools also affected the
racial/ethnic distributions in high TPSs, even though the relationship in high TPSs got weaker
than in elementary and middle TPSs. The proportions of free/reduced lunch program students in
TPSs had a consistently and significantly negative relationship with the proportions of white
students and a positive relationship to the percentages of black and Hispanic students in TPSs.
The academic performance of TPSs were highly and negatively related to the proportion of black
students, while the relationship was much weaker to the percentage of white students and neutral
to that of Hispanic students. The cross-sectional multivariate analyses suggested that charter
schools created more racially segregated educational institutes in public education in Florida.
xiv
The racial/ethnic compositions of TPSs were closely interrelated to the issues of the socio-
economic stratification and residential division (Carnoy, 2000; Frankenberg, et al., 2003; Rivkin,
1994). The comparisons of the proportions of variance explained by HMLM models and by other
models revealed that the percentages of white students were much more sensitive to socio-
economic and residential factors than the proportions of black students were, while the
proportions of Hispanic students were much more sensitive to the charter-school factors.
The findings of this study highlighted the critical role of social context in public
educational policies and the importance of policy design. This study rediscovered the old but
important principle: Charter school policy makers need to take into account the expectable but
ignored consequences of the policy in public education system and the impacts of the policy on
those students left behind in TPSs as well.
1
CHAPTER ONE
INTRODUCTION
1.1 Charter schools in the U.S. and Florida
Since the 1980s, many politicians, scholars, organizations and the mass media frequently have
contended that American public education is ineffective, out-dated, bureaucratic, unsatisfactory, and far
behind other countries’ educational achievement, and that this has undercut the economic
competitiveness of the United States in the global market. Some scholars have charged that education is
the most inefficient and slow changing area! For instance, Milton Friedman (1997) said that “there is
enormous room for improvement in our educational system. Hardly any activity in the U.S. is
technically more backward. We essentially teach children in the same way as we did 200 years ago” (p.
343).
The climax of these campaigns was perhaps the report of The National Commission of
Excellence in Education in 1984.
Our nation is at risk. Our once unchallenged preeminence in commerce, industry, science, and
technological innovation is being overtaken by competitors throughout the world. … it is the
one that undergirds American prosperity, security, and civility. … the educational foundations
of our society are presently being eroded by a rising tide of mediocrity that threatens our very
future as a nation and a people (p. 5).
One of the suggested solutions to the failings of public schools in the U.S. was the charter
school, one of several school options in the universe of school choice and a recent phenomenon in the
last two decades in the U.S. Charter schools have created a new mechanism for the delivery of public
education services. The financial resources come from the government, but groups of people or
agencies in the non-governmental sector are responsible for the design and the operation of the charter
school itself. In this regard, a charter school can be considered a new institution in the public education
system. Traditionally, school choice had been provided "(a) between public and private schools, (b)
among public school districts, and (c) among public schools in a given district " (Belfield & Levin,
2002, p. 281), although the government has typically only paid for public school education in the
school district in which one lives. But charter schools have given parents and students choices across
school districts among public schools run by agencies different from their own district's school boards.
Minnesota (MN) was the first state to adopt charter schools as an educational institution by
passing the MN charter school law in 1991. California was the second in 1992, and Florida passed a
2
charter school law in 1996. As of 2011, 40 states and the District of Columbia have adopted charter
school laws. Across the U.S., the total number of charter schools grew to 4,694 in 2008 from 1,993 in
2000, and the number of students in charter schools rapidly increased to 1,433,116 in 2008 from
448,343 in 20001.
Since the enactment of the charter school law in Florida in 1996, charter schools have grown
rapidly reaching 459 charter schools in 2010-11. During the same period, student enrollment in charter
schools has reached 154,780 (5.86% of elementary and secondary public school students) in 43
districts. Florida ranked third in the nation both in the number of charter schools and in charter school
enrollment in 2010-11 (See Appendix 1).2
1.2 Problem Statement
Charter school policy has multiple goals: to enhance the quality of public schooling, to satisfy
the expectations of parents, and to improve the efficiency of public school administration. The
advocates argue that it will create a market for education, that is, stimulate new “supply” by various
educational service providers and new demand from parents, students and communities. This market
for education will crowd out bureaucratic inefficiency, and lead to better performance in public schools
through competition for customers. However, the opponents of school choice, especially those against
charter school policy, have argued that it would exacerbate racial and residential segregation
(Clotfelter, 2001; C. Lubienski, 2001, 2005a; Renzulli, 2006; Renzulli & Evans, 2005), result in
creaming and cropping (Henig, 1996; Lacireno-Paquet, Holyoke, Moser, & Henig, 2002), and drain
financial and human resources from public schools.
As shown in Appendix 1 and by national statistics from the National Center for Education
Statistics (NCES), even though the number of charter schools in Florida and in the nation is still
growing, charter schools seem to have passed their rapid growth period and entered into a stable stage.
Also, they have now been in operation for almost two decades in the U.S., and for 15 years in Florida.
Therefore, it is time for a critical evaluation of charter school academic performance and other
educational and socio-cultural influences (Buckley & Schneider, 2007). This study will examine the
assumed effects of charter school policy on the public school system: school effects on student
1 SOURCE: U.S. Department of Education, National Center for Education Statistics, Common Core of Data (CCD),
"Public Elementary/Secondary School Universe Survey," 1990-91 through 2008-09.
2 From http://www.floridaschoolchoice.org/default.asp and http://www.fldoe.org/eias/eiaspubs/default.asp visited on Oct
13th, 2011.
3
achievement in charter schools, market competition effects on academic achievement in traditional
public schools (hereafter TPSs), segregation effects and stratification effects on demographic
composition of traditional public schools. I will also check whether those effects, if any, are really
caused by the charter school policy or by the impact of other socio-cultural and educational factors.
Other issues such as cream-skimming, cropping off, and the absorption of low performing students
from traditional public schools by charter schools will be explored. This study will shed light on the
issue of what the policy makers and educational authorities should focus on to improve the
performance of public school system.
To evaluate the academic effects of charter schools and analyze their social consequences, “the
evaluator should actively search for and construct a theoretically justified model of the social problem
in order to understand and capture what a program really can do for a social problem – social science
knowledge and theory become crucial in the evaluation process” (Chen & Rossi, 1980, p. 111)
Buckley and Schneider (2007) classified rationales for charter schools into three theories: 1) systemic
reform, 2) local autonomy and 3) the market for schools. They then suggested five criteria for charter-
school-policy evaluation: competition, choice, community, accountability and achievement (pp. 4 – 18).
Levin (2009) suggested three criteria to be attended to when the school choice policy design is
evaluated: productive efficiency, equity, and social cohesion (p. 27).
In this study, I suggest three theories or rationales for and against charter school policy on
which this evaluation research will be based: 1) school effectiveness theory, 2) market competition
theory in education, and 3) social inequality theory. School effectiveness theory assumes that those
schools with more autonomy, less political control, and more sensitivity to parental preferences would
create more effective instructional programs, administrate schools more efficiently, and be more
accountable for improving student achievement. As a result, those schools would outperform the other
schools (Budde, 1988; Bulkley & Fisler, 2003; Chubb & Moe, 1990; Friedman, 1997). Market
competition theory assumes that public choice would produce the Pareto optimum in the educational
policy area, which will lead to an efficient public school system (Chubb, 2006; Friedman, 1955;
Tiebout, 1956). “Once the government’s monopoly on public schooling is broken and parents and
students become consumers, a host of new suppliers of education will enter the market and compete
with existing schools and among themselves to provide educational programs that better meet the
demands of parents and students than does the current monopoly provision of education” (Buckley &
Schneider, 2007, p. 7). On the other hand, social inequality theory argues that such a quasi-market
approach would produce unintended and pernicious consequences such as racial segregation and socio-
4
economic stratification, cream-skimming of high performing students, and further weakening of public
schools financially and academically.
Table 1 summarizes these theories and what impacts they predict.
Table 1-1 A framework for charter school policy evaluation
Academic effect Socio-cultural effect
School Effectiveness
Theory
Better student achievement
in charter schools
Cream skimming of high
performing student, or cropping off
low performing students
Market Competition
Theory
Better student achievement
in TPSs
Increase of stratification in
demographic composition
Social Inequality
Theory
Widening of achievement
gap between blacker TPSs
and whiter TPSs
White flight and self-isolation of
minorities
1.3 School Effectiveness Theory: Autonomy and Accountability
One of the most important goals of the charter school movement is to create academically
effective public schools. In his proposal for restructuring public school districts by introducing charter
schools, Budde (1988) assumed that education by charter would “give teachers responsibility for and
control over instruction”, and encourage pupils to “assume responsibility for their own learning and
behavior” (p. 30). After their long analyses of ineffectiveness of American public schools and pointing
out the democratic control and dysfunction of bureaucracy as the main causes of the failures in public
school system, Chubb and Moe (1990) suggested:
“the key to effective education … rests with granting them the autonomy to do what they do
best. As our study of American high schools documents, the freer schools are from external
control – the more autonomous, the less subject to bureaucratic constraint – the more likely they
are to have effective organizations” (p. 187)
Charter school proponents hope that the new combination of autonomy and accountability will produce
better learning programs than local public alternatives, and thus lead to better student achievement in
charter schools (Buckley & Schneider, 2007; Bulkley & Fisler, 2003; Kolderie, 1990).
Florida charter school law reflects this hope in its provisions. The Florida Student and Parental
Rights and Educational Choices Act of 1995 depicts the academic purpose of charter school policy as
follows: 1. Improve student learning and academic achievement, 2. Increase learning opportunities for
5
all students, with special emphasis on low-performing students and reading, 3. Encourage the use of
innovative learning methods, 4. Require the measurement of learning outcomes (s. 98, ch 1002.33 (2)
(b)).
This study will explore the practicality of the school effectiveness theory in the charter school
movement. If students in charter schools outperform their peers in TPSs in terms of yearly change rates
and achieved academic levels, charter schools could prove to be more effective in academic
performance.
1.4 Market Competition Theory
Chubb and Moe (1990) were among the researchers to emphasize the importance of
institutional settings in education. They argued that the bureaucracy and direct democratic control in
public school systems has stifled innovation and prevented educational enhancements. They
recommended that the public school system should be restructured by introducing market-like
competition to save it from bureaucratic inefficiency and inertia. Milton Friedman (1997) contended
that “… the only way to make a major improvement in our educational system is through privatization
… nothing else will provide the public schools with the competition that will force them to improve in
order to hold their clientele” (p. 343). Budde (1988) wrote “Education by Charter: Restructuring school
districts as the key reform to long-term continuing improvement in American public schools”. He
suggested charter schools as the remedy for the ineffective American public school system.
One of the most influential and persuasive contentions about charter schools has been the
market choice and competition effect. Kolderie (1990) argued that the exclusive franchise or monopoly
held by district school boards is the heart of the problem, and that “choice and new public schools
would go to the heart of the problem” (p. 10) Market approach advocates have contended that a market
in education would provide parents and students with choice and bring competition into the public
school system. This would increase productive behavior in the education process, because of the threat
that charter schools will pull out the students and financial resources that go with them from the
traditional public schools (Belfield & Levin, 2002; Chubb & Moe, 1990; Hoxby, 2002b). Charter
school advocates expected that charter schools would affect the public school system, and, as a result,
districts and schools would change in response to market competition. “The theory was that markets,
and specifically competitive pressure to win and hold consumers, would generate efficiencies, stimulate
innovation, better engage families, and weed out nonperformers. It was the link between charter
schools and the general theory of markets” (Henig, 2008, p. 56) that made charter schools attractive.
6
However, there are opposing arguments about the effect of charter schools on student's
achievement. If charter schools draw higher performing students away from traditional public schools,
student achievement in nearby public schools would become lower (resulting in a “creaming” effect).
Or, to the contrary, if the charter schools serve those students with performance problems relatively
more than traditional public schools do, the student achievement in traditional public schools would
increase due to adverse selection by charter schools without "competition or market effect".
1.5 Social Inequality Theory
Other scholars such as Carnoy (2000) opposed the introduction of school choice, pointing out
that school choice is one kind of privatization of education, and that “a privatization reform would
likely increase educational inequality without improving educational effectiveness. … privatization
could also leave the educational system worse off than it actually is, despite all its flaws” (p. 19).
Since the landmark report: Equality of Educational Opportunity (Coleman, et al., 1966),
segregation effects on student achievement in public schools have been one of the most important
issues in American public education. Coleman et al. (1966) found that black students were ‘largely and
unequally segregated,’ that minority students in public schools achieved less than their white
counterparts, and that “the social composition of the student body is more highly related to
achievement, independently of the student's own social background, than is any school factor” (p. 325).
Then they concluded:
That schools bring little influence to bear on a child's achievement that is independent of his
background and general social context; and that this very lack of an independent effect means
that the inequalities imposed on children by their home, neighborhood, and peer environment
are carried along to become the inequalities with which they confront adult life at the end of
school. (Coleman, et al., 1966, p. 325)
Rumberger and Palardy (2005) argued that segregation still matters. They found that the effects
of socioeconomic segregation can largely be explained by its association with such school
characteristics as academic climate and teacher expectations, and that “students attending the most
affluent schools (those with the highest socioeconomic composition) receive the greatest academic
benefits, which raises questions about the political and individual will to integrate schools in order to
achieve equality of educational opportunity” (p. 2003).
7
On the other hand, recent studies have reported that desegregation trends have lost momentum
and continue to have negative effects on black student academic achievement. When we consider the
stable resegregation trends across the nation and a strong relationship of segregation by race and
poverty to educational inequality, the intensified resegregation through the 1990s in which “most of the
progress of the previous two decades in increasing integration … was lost (Orfield, 2001, p. 1)” would
bring serious consequences for the society as a whole and for minority students themselves as well
(Frankenberg, et al., 2003).
Frankenberg, Lee, and Orfield (2003) examined the changes in the demographic composition in
American public schools and found that after the major three Supreme Court decisions in the 1990’s,
the desegregation trends have “clearly reversed in the South, where the movement had by far its
greatest success” (p.6). The proportion of black students attending majority white schools decreased by
13 percentage points, to the lowest level since 1968. Rivkin (1994) also found that despite some
improvements in desegregation, blacks across the country attended schools with far lower white student
shares than the overall regional white student share. He argued that the geographic concentration and
district’s allocation causes this racial segregation, and that only the inter-district integration programs
to move students across districts could reduce the racial isolation of black students.
Racial segregation is likely to broaden achievement gaps between the minority students and
white students, and among the students from poor families and affluent families. Borman et al. (2004)
explored the relationship of racial segregation to student achievement in Florida. They found that “the
racial composition of the student body is an important predictor of the percentage of students passing
the Florida Comprehensive Assessment Test (hereafter FCAT) math and reading tests” (p.625), and
that the racial balance of schools significantly influences the passing rates in the FCAT reading and
math tests.
Hanushek, Kain, and Rivkin (2009) investigated the achievement gap between black students
and white students in Texas. They concluded that the test score gap among black and white students in
the seventh grade could be reduced over 10 % through eliminating the differences in the black
enrollment share in Texas public schools. Hanushek and Rivkin (2006) identified the racial
composition in schools as one of the factors that increases the achievement gap between black and
white students with age, and found that “the majority of expansion in achievement gap occurs between
rather than within schools” (p. 4).
This issue of inequality in educational opportunity becomes more important when the parents’
preferences for cultural familiarity and particularistic forms of socialization are considered in the
establishment of school choice schemes (Fuller, Elmore, & Orfield, 1996):
8
Parents report … that they are attracted to the familiarity and proximity of the local school and
that they want their children to feel comfortable. These are the same things that white middle-
class parents seek in a “nice neighborhood”: cultural familiarity, a sense that fellow parents
share their values, beliefs, and customs. … … many parents in pluralistic America seem to want
both assimilation and particularistic forms of socialization. … These parents move into
neighboring communities that have safer streets and higher-quality schools. Left behind are
families that typically have less education and fewer job options. Nouveau middle-class black
parents essentially vote with their feet. (p. 13-14)
1.6 Significance of the Study
This study puts a focus on the impacts of institutional change due to the introduction of charter
school on student achievement vis-à-vis the established public educational system. “Institutions define
and limit the set of choices of individuals” (North, 1990, p. 4), and “the persistence of inefficient
institutions” induces poor performance (North, 1990, p. 7). When institutions are changed by
introduction of a new public policy, the actors in a society should adapt their actions and strategies to
get the most benefits from the new settings. This study will give some insights on the behaviors of
actors such as educators, administrators, parents and students when they are given new choices in
public educational system. This study will evaluate the charter school policy from multiple
perspectives.
Policy analysts made a serious mistake when they omitted comprehensive theory from their
enterprise. … policy analysis without broad, philosophical frames of reference is blind to the
most important policy impacts (deHaven-Smith, 1988, p. 1).
The previous studies on charter school effects focused on one or two issues. For example,
studies examined student achievement in charter schools, the competition effects on student
achievement in TPSs, or the segregation effects in charter schools and TPSs. Most previous studies
tested hypotheses from one perspective and tried to find evidence to falsify or verify it. However, as
deHaven-Smith (1988) emphasized, in a perspectival analysis, “the possibility that conflicting
perspectives might conceptualize the subject matter of policy analysis in entirely different ways was
overlooked” (p. 120). I will investigate the charter school effects on student achievement in TPSs as
well as in charter schools, and competition effects on student achievement in TPSs from the market
9
approach and from the socio-cultural approach as well. I will also explore the unintended consequences
of charter school policy in communities, such as racial segregation and socio-economic stratification
effects. Florida is one of the southern states where the desegregation policy brought the most dramatic
transformation “from virtually total apartheid to the most integrated region in the U.S. between 1964
and 1970” (p. 8). However, in 1998, Florida fell behind the level of integration in 1970 and is still
moving towards resegregation (Frankenberg, et al., 2003).
This study will be the first research using Hierarchical Linear Modeling (hereafter HLM) to
investigate the charter school effects on student achievement from competition impacts and on student
racial/socio-economic composition in traditional public schools. Most of the previous studies used
traditional OLS regression analysis and put different levels of information into the same level of
analysis. However, educational data are usually nested. When data are combined into the same level, it
introduces aggregation bias, because student data from the same school, for example, would have
similarities to some degree. HLM enables researchers to disaggregate the effects from different levels
into separate parts. In this study, those effects will be classified into three kinds of effects from
different levels specifically the year level, school level, and county level. In addition, HLM enables us
to examine from what level the variance in the dependent variables of interest mainly comes and to
explain those variation with appropriate level predictors. I will examine the school differences in
student achievement and racial/socio-economic composition by partitioning the effects into 3 levels
such as year effects, school effects and county effects.
This study will give policy makers and public administrators useful guidelines regarding what
they should focus on and where they can put more emphasis to enhance the public education system.
This study could advise policy makers about how to prioritize among the policy instruments. For
instance, in order to improve public school effectiveness, policy makers can promote more competition
among schools, or introduce some compensatory courses for the disadvantaged or poor students, or
adopt mandatory balancing policy of racial composition in accordance with that of county. This study
will give some practical advice regarding these issues to the policy makers and educational
administrators.
1.7 Dissertation Plan
The dissertation will be composed of 5 chapters: Introduction, Literature review, Research
design, Analyses, and Discussion.
10
The first chapter will discuss a brief history of charter school policy in the U.S. and Florida, and
then introduce a theoretical framework which this study will use to investigate comprehensive
consequences from charter school policy adoption in counties in Florida. The previous studies will be
reviewed in the second chapter. This literature review includes those studies that examined the charter
school effects on the student achievement in charter schools (focusing on the studies using Florida
data), the charter school competition effects on student achievement in TPSs, and the segregation
effects of charter schools by charter schools themselves and in TPSs.
In the third chapter, I will suggest research questions, and formulate investigation strategies to
examine charter school effects from various perspectives. The data used in the analyses and their
descriptive characteristics will be shown in this chapter. Then I will build analytic models to answer the
research questions, and address the methodological issues by comparing the methods used by the
previous studies with multivariate hierarchical linear modeling which I will apply in this study.
In the fourth and fifth chapters, I will present the results from the analytic models for the three
primary research questions I am studying and discuss the meaning of the results. Finally, in the
conclusion I will discuss the implications of my study and the limitations, and then suggest further
research my work has inspired regarding charter school policy effects.
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CHAPTER TWO
LITERATURE REVIEW
2.1 Studies on school effects on charter school students
Numerous studies have been done on this issue in most states that have charter schools and at
the national level. See the National Alliance for Public Charter Schools (hereafter NAPCS, 2009) for
the research designs and the key findings in detail. According to NAPCS, more than 200 studies have
been done on charter school achievement in the U.S. (NAPCS, 2009).
In this section I will review those studies that investigated student achievement in charter
schools at the national level and in Florida. Nationwide studies will show the big picture for this work,
and the research using Florida data will provide a good comparison for this study. Since the analyses in
this study focus on charter school effects in Florida, I will use only Florida school and county data sets.
I found 12 national studies and 10 studies on Florida’s charter schools conducted through 2010 which
will be reviewed in this section.
2.1.1 Nation-wide studies on student achievement in charter schools
Loveless (2002) compared the 1999-2001 state standardized test scores of charter schools to
those of TPSs in 10 states including Florida. The results showed that charter schools’ achievement
scores were significantly lower than the scores of TPSs in all ten states, and that charter school students
display relatively better performance in reading than in math, and in the middle and high school grades
than in 4th grade. Nelson, Rosenberg, and Meter (2004) analyzed the 2003 NAEP results and the 2003
NAEP charter school report. Their analyses suggested that the students in charter schools scored
substantially below traditional public school student NAEP scale scores in both 4th and 8th grades and
in both math and reading regardless of eligibility status for the free and reduced price lunch program.
Also the achievement score gaps between charter schools and TPSs were larger in central cities than in
suburban or rural areas. Braun, Jenkins, and Grigg (2006) examined the mean difference in reading and
math NAEP scores for 4th graders between all charter schools and all traditional public schools using
the 2003 NAEP data. They found that charter schools achieved significantly lower NAEP scores in
reading and math than traditional public schools. CREDO (2009) collected student-level data and
compared the test scores of students who exited to charter schools with those of students in TPS they
attended in 16 states. The national pooled analysis of charter school effects showed that charter school
12
students had significantly lower growth in reading and math scores (p. 22), and that black and Hispanic
students in charter schools had significantly lower growth rates than their twins in TPSs (p. 26).
Chung, Shin, and Lee (2009) analyzed the student achievement differences between charter
schools and TPSs through quantitative meta-analysis of standardized mean-changes using 395 effect
sizes from 13 studies from 1994 to 2008. Their meta-analysis revealed that the student achievement of
charter schools was higher than that of TPSs, even though the effect size was very small, but
significantly positive (effect size: 0.06, SE: 0.02) (p. 69). Betts and Tang (2011) synthesized charter
school achievement studies using quantitative meta-analysis methods, and concluded that “overall
charter schools look to be serving students well, at least in elementary and middle schools, and
probably better in math than in reading” (p. 44)
Greene, Forster, and Winters (2003) compared the non-targeted charter schools achievement
scores to regular non-charter public schools in eleven states including Florida. They found from
national data analysis that non-targeted charter schools achieved significantly better on test scores than
traditional public schools did, even though the effect sizes were modest. Hoxby (2004) conducted a
study comparing student achievement in charter schools and neighboring traditional public schools in
36 states and Washington, D.C. using matching methods3 and the National Assessment of Educational
Progress (NAEP) data in 2002-03. She concluded that charter school students were more likely to be
proficient on reading and math examinations than the matched traditional public school students (p. 13),
and that the longer charter schools had been in operation, the more proficient their students were. But
Roy and Mishel (2005) replicated the Hoxby’s 2004 study using the same datasets but introducing race
and poverty variables as controls, and found that the positive effects of charter schools on student
achievement disappeared or became insignificant at the national level and in most states.
The U.S. Department of Education (2004a) published the 2003 NAEP report for charter schools.
It suggested that there were no measurable differences in achievement scores for reading among fourth
grade students in American charter schools and TPSs, and it was true for math only when the student
racial/ethnic and economic backgrounds were considered. Gleason, Clark, Tuttle, and Dwoyer (2010)
designed a quasi-experimental study to compare student achievement in charter schools with that of
TPSs. They recruited 36 participating schools that apply lotteries to admission and 2,330 participating
students who won the lotteries and attended charter schools and who lost the lotteries and attended
TPSs during the 2004-2005 and 2005-2006 from 15 states. Their comparisons showed that on average,
3 “Each school address in the United States is translated into a latitude and longitude. The distance between each charter
school and each regular public school is calculated and the nearest regular public schools are identified” ((Hoxby, 2004, p.
7) and matched as comparison groups.
13
charter schools had no statistically significant effects on student achievement, and that the higher
income students and the incoming students of the higher achievement scores were affected negatively
in their achievement levels, while other student subgroups were statistically similar in charter school
impacts. Lubienski and Lubienski (2006) also used the 2003 NAEP math data for 4th and 8th grades to
investigate whether charter schools and private schools perform better than traditional public schools.
Their results from HLM models with demographic controls showed that “no charter or private school
means were higher than public school means to any statistically significant degree, particularly at
Grade 4” (p. 680).
2.1.2 Studies on student achievement in Florida charter schools
Crew and Anderson (2003) compared the 1999 FCAT scores of charter schools to those of
TPSs and argued that charter schools underperformed compared toTPSs in math, reading, and writing
in grade four, eight and ten. Hassel, Terrell, and Kowal (2006) reported that students enrolled in Florida
charter schools in 2003-2004 typically were “further behind academically than their peers in districts
schools” (p. 18) and “charter students were less likely to meet grade-level expectations in math and
reading than their district school peers” (p. 17). The aforementioned 2009 CREDO report showed that
charter school students in Florida demonstrated lower growth than their counterparts in TPSs. In their
meta-analysis, the effect size of Florida was -0.04(SE 0.008), which means that charter school student
achievement was significantly below student achievement in TPSs in Florida (Chung, et al., 2009).
Greene, Forster, and Winters (2003) compared non-targeted charter school to TPSs. In their
analyses, non-targeted charter schools showed greater gains in SAT-9 math and FCAT reading scores
than did neighboring TPSs (p. 9). Hoxby (2004) also found that the fourth graders in Florida non-
targeted charter schools achieved better in reading exams. The longer charter schools had been in
operation, the more proficient their students were. However, in the replication of Hoxby’s study, Roy
and Mishel (2005) found significant negative effects on student achievement in charter schools by
introducing race and poverty variables as controls that Hoxby (2004) didn’t include in her analyses.
Sass (2006) used student level FCAT Norm Referenced Test data to examine charter school student
achievement during the period 1999 through 2002. He found that student achievement in math and in
reading in newly opened charter schools was below student achievement in TPSs, but as charter
schools operated five years or longer, math scores became similar to those of TPS students and reading
scores were higher than those of TPS counterparts.
14
Loveless (2002) used the 1999-2000 FCAT scores to compare student achievement in non-at-
risk charter schools to student achievement in TPSs, and concluded that non-at-risk charter schools
performed about at the state average. The Florida Department of Education (FLDOE) issued student
achievement reports in 2004, 2006, 2009, and 2010. In the 2004 and 2006 reports, Florida’s charter
schools underperformed traditional public schools in many comparisons in reading and math in grade 3
to 10, but in the 2009 and 2010 reports, Florida’s charter schools started to outperform TPSs in 73 out
of the 86 comparisons and in 83 out of 95 comparisons respectively, covering three measurements
(FCAT proficiency percentages, achievement gaps, and learning gains) that were broken down into
many subcategories such as grade, race, sex, subjects, poverty, and so on (FLDOE, 2004, 2006, 2009,
2010).
2.1.3 Limitations of the previous studies on student achievement comparison
The conclusions of studies on student achievement in charter schools when compared with
studies conducted on TPSs are contradictory and inconclusive both in national studies and in Florida
studies. More precise and rigorous research designs need to be applied to charter school achievement
evaluation. Most of the studies applied very simple research design and compared mean differences or
percentages. Crew and Anderson (Crew & Anderson, 2003) used the percentages of schools that
received grade of “D” or “F” and overall mean scores of students to compare student achievement of
charter schools to that of TPSs. The reports of the Florida Department of Education (FLDOE, 2004,
2006, 2009, 2010) employed simple methods of percentage comparison between the FCAT proficiency
pass rate of charter schools and those of TPSs in Florida. These studies didn’t test the statistical
significances of the differences in means and percentages at all, and did not use controls for
demographic background variables. Loveless (2002) also compared the mean z-score differences
between charter schools and TPSs.
Similar with Greene et al. (2003), Hoxby (2004) used matching methods that compared non-
targeted charter schools to the geographically nearest traditional public school. But there is no
guarantee for those matching schools to have similar demographic characteristics. As Roy and Mishel
(2005) pointed out, in Hoxby’s (2004) study “the data do not include any other characteristics of the
student body, including race and free or reduced-price lunch eligibility” (p. 4). Even though Sass (2006)
used student level data for three years to compare student achievement among charter schools and
TPSs, he didn’t control the socio-economic and demographic characteristics to control for these factors
on student achievement.
15
All of the previous studies except the U.S. Department of Education report (2004) didn’t take
the nested nature of educational data into account, which will introduce aggregation biases into their
analysis. The analyses of these studies didn’t reflect the variation in racial compositions, economic
status and educational factors among schools and communities Another issue regarding the previous
studies on student achievement comparison is the examination of student achievement change. Most
national and Floridian studies captured a snapshot of charter school effects on student achievement at a
single point in time. To answer the question whether the superiority or inferiority of the charter school
student achievement to the achievement of TPSs are real effects from charter school’s merits or
demerits, or a statistical aberration from “new year effects” or “attraction effects”, more sophisticated
research design and careful analyses of longitudinal data are needed.
2.2 Studies on market competition from charter schools
2.2.1 Review of the previous studies on competition effects
In this section, I will review studies that have investigated the charter school competition
impacts on student achievement in traditional public schools. The characteristics and the key findings
of the studies are shown in Appendix 2.
California: Zimmer and Buddin (2009) and Zimmer et al. (2009) investigated charter school
competition impacts on TPSs in six California school districts using student level longitudinal data for
the 1997-98 through 2001-02 school years. They computed the distances to, the numbers of, and the
share of charter schools or other alternatives, and the percentage of students lost to other schools within
2.5 miles as competition measures “based on the presence of nearby schools in each district” (p. 837)
and regressed student test scores on those measures with student, school and year fixed effects. They
concluded that most measures of charter competition have no statistically significant impacts on
student achievement in nearby TPSs across all school levels.
Florida: Crew and Anderson (2003) surveyed the charter school liaison in the local school
districts to evaluate the effects of charter schools on TPSs and to test the school choice hypothesis that
“charter schools will force traditional public schools to adapt their behavior and improve their
performance in order to keep their students from migrating to the charter schools” (p. 198). They found
no evidence suggesting that the presence of charter schools affects the performance of TPSs and their
16
educational programs. They concluded that “the hypothesized impact of charter schools on the
educational performance of public schools had failed to materialize in Florida” (p. 198).
Sass (2006) utilized longitudinal student achievement data in Florida to investigate the
competitive impact on student achievement in TPSs. He used a geographic information systems (GIS)
database to measure competitive impacts by determining the presence, the numbers and the enrollment
shares of charter schools within 2.5-mile, 5-mile, and 10-mile radius of each traditional public school,
and examined the achievement changes of traditional public schools. The regression results in his study
showed that all three measures within 2.5-mile radius, the presence of charter schools within 5 miles
radius, and the market share within 10 miles radius had positive competition effects only on math
scores, but the measures with other sizes of the geographic market didn’t have any effects on math
scores or on reading scores. However, he concluded that “the existence of charter schools does not
harm students who remain in traditional public schools and likely produces some net positive impacts”
even though he mentioned the possibility of disproportionate withdrawal of disruptive or below-
average students by charter schools (p. 119). Ertas (2007) examined charter school competition impacts
using Florida Writing Assessment Program data at grade 4 and grade 10 from 1995 through 2000. He
utilized the presence of charter schools within 5-mile radius and in a county, and the dummy variable
for a county with more than median charter school enrollment of the state as the competition measures.
He found some positive impacts on 4th graders writing scores only for those schools in counties with at
or above median charter school enrollment. Other measures for 4th graders’ scores and all measures for
10th graders’ scores showed all insignificant impacts on schools’ writing scores.
Michigan: Eberts and Hollenbeck (2001) tested the charter school competition hypothesis using
student level data from Michigan and the presence of charter schools in a district as a charter school
competition measure. They found little evidence for charter school competition effects on student test
scores in TPSs. Hoxby (2003) used the share of charter school students in districts as a competition
measure. She set 6 percent of charter school share as a critical level that is likely to affect school staffs
and principals and used a dummy variable of 6 percent or more share to test charter school competition
impacts on student’s achievement in Michigan. She found that the traditional public schools in the
districts with more than 6 % charter students showed significantly higher gains both in productivity
indices and in achievement scores. Lee (2009) reexamined Michigan data for 1994-1995 and 1999-
2000 school years to verify the charter school competition impacts on TPSs. He compared the
productivity changes and student achievement changes in charter hosting districts and in non-charter-
hosting districts only to find no significant difference in both measures between them. He also used the
17
same methodologies (difference-in-difference estimation and first differencing regression analysis) as
Hoxby (2003) did, but he found no significant improvement in district productivity and in student
achievement. Bettinger (2005) investigated charter school impacts on TPSs achievement changes using
Michigan school data from 1996 to 1998. He employed a difference-in-difference estimator to compare
the treatment effects and instrumental variable estimation to address the problem of endogeneity of
charter school location, and he concluded that “there is no robust, significant evidence that test scores
increase or decrease in neighboring public schools as the number of charter schools increases” (p. 145).
Another study that examined charter school impacts on TPSs in Michigan was performed by Ni (2009)
who measured charter competition faced by a district as “the percentage of students that each district
lost to charter schools” (p. 575). He created three dummy variables such as short-run, medium-run, and
long-run indicating how fast a district lost 6 percent of students to charter schools. He used pooled OLS
with school fixed effects and first-differenced estimation and found modest negative effects on 4th and
7th grade student’s math and reading scores in TPSs.
Milwaukee: Lavertu and Witte (2008), Zimmer et al. (2009), and Greene and Forster (2002)
studied the charter school competition impacts on student achievement in TPSs in Milwaukee. The
former two studies used the number of charter schools in 2.5-mile radius from a TPS and the distance
to the nearest charter schools as the competition indicator from charter schools, while the latter made a
distance index between the school and the three nearest charter schools. None of three studies found
significant relationship between charter school competition pressure and traditional public school test
scores except a positive effect in 10th grade in Greene and Forster’s report.
North Carolina: Two studies investigated the charter competition impacts in North Carolina.
Holmes et al. (2003) examined charter school competition impacts on student achievement in TPSs
using cross-sectional models with instrumental variable estimators and found that the distance to the
nearest charter schools and the number of charter schools in a certain miles radius from a TPS had
positively related with the increases in the student’s achievement in TPSs. Bifulco and Ladd (2006a)
used the distance to the charter schools and the number of charter schools within an n-mile radius as a
competition measure and employed OLS estimation and first-differencing strategy with student-,
school- and year-fixed effect. They found “no statistically significant effects on the achievement of the
traditional public school students in North Carolina” (p. 85).
18
Ohio: Ertas (2007) investigated charter school competition impacts using Ohio schools’
standardized test pass rate data from 1995 to 2001, and his results showed negative effects on student
achievement in math and reading of 4th and 10th graders in TPSs for all competition measures including
the presence of charter school in a county and within 5 mile-radius, and a dummy variable for charter
school student share in a county. Carr and Ritter (2007) examined the charter school competition
impact on TPSs in Ohio utilizing district level competition measures such as the presence of charter
schools, the number of charter schools, and the share of charter school students. They found negative
effects on the proficiency passage rates of traditional public schools attributable to cream-skimming or
resource withdrawal by charter schools. Zimmer et al. (2009) found no impacts on student achievement
gains in TPSs in Ohio.
Texas: All studies examining charter school competition impacts on TPSs in Texas reported
positive effects on students’ achievement. Bohte (2004) found positive effects of charter schools on
county pass rates on the Texas Assessment of Academic Skills (hereafter TAAS) exam. All the charter
school predictors like the number, the percentage and the presence of charter school students showed
positive effects on the TASS exam pass rate after controlling educational (class size, teacher
experience, teacher turnover, attendance, and percent of staff bureaucracy), racial (percent of African
American and Hispanic students), and socio-economic (percent of low-income student) factors.
Grosskopf, Hayes, and Taylor (2004) examined efficiency changes in school districts in Texas using
the percentage of charter school students as predictors and concluded that “districts that have charter
competitors within 30 miles have shown substantially more progress than districts without the
competitive spur” (p. 14). Booker et al. (2008) used school level and district level competition
measures and found that “the positive effect is consistent across both math and reading tests, both
district and campus level penetration measures, and across a variety of specifications” (p. 143). Zimmer
et al. (2009) examined whether the changes in student’s achievement in TPSs were affected by the
distance to the nearest charter schools and the number of charter schools within 2.5 miles radius in
eight geographical locations, and found that “only Texas shows evidence that charter schools are
creating any competitive effects for TPSs” even though the estimated effects were small (p. 80). Ertas
(2007) tested the charter school competition hypothesis using Texas public schools’ TAAS data from
1995 through 2001. He found positive effects on TPSs’ pass rates in all subjects in all grades after
controlling schools’ demographic changes and private school enrollment.
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Other states and cities: Hoxby (2003) examined Arizona student achievement data to test the
charter school competition impacts with the same research design as she applied to Michigan data, and
found positive impacts on student achievement in TPSs in Arizona. Winters (2009) found no effects on
TPSs’ student achievement from charter competition except some positive impacts on lower
performing students in New York City. Zimmer et al. (2009) examined the charter school impacts on
student achievement in TPSs in Philadelphia, Denver and Chicago using student level data from 2000
through 2006 and utilizing the distance to the nearest charter school and the number of charter schools
within 2.5 miles radius from a TPS, only to find no evidence of positive nor negative impacts “across
all of the jurisdictions examined, despite variation in funding mechanisms and the extent of funding
transfers from TPSs to charter schools” (p. 82). Imberman (2009) used the share of charter school
students within a certain distance in a certain grade as competition measures, and employed student
fixed effects and instrument variable strategy to address selection bias of choosers for charter schools
and the problem of endogeneity in charter school location. His results showed that charter schools had
negative impacts on the students’ math and reading test scores in traditional public schools in an
anonymous large urban school district in the southwest.
2.2.2 Limitations of the previous studies on competition effects
As reviewed in this section and shown in Appendix 2, many studies reported no competition
impacts from charter schools on TPSs, or some negative impacts are reported, while studies from Texas
and Arizona reported positive effects. On the other hand, studies investigating charter school
competition impacts in Florida, Michigan, Milwaukee, and North Carolina showed contradictory
results. Due to these contradictory and inconclusive research results, Bulkley and Fisler (2003) argued
that, overall, little evidence of district change in response to competition from charter schools was
found, and that “it is critical to investigate these impacts for a full understanding of the effects of this
approach to education reform” (p. 338). Hoxby (2004) also emphasized that “the key evidence we need
to establish is whether public schools raise their productivity when they are faced with conditions that
economists would recognize as market-like. By saying ‘market-like’, I refer to choice programs that
allow schools to enter, expand, contract, and exit” (p. 222).
The previous studies primarily relied on the conventional regression models to investigate the
charter school impacts on student achievement in traditional public schools. These studies ignored the
nested nature of educational data. However, students are nested within schools, and schools are nested
within school districts. Therefore the conventional regression models using data sets with nested
20
structures are subject to such biases as aggregation bias, estimation bias and the regression
heterogeneity. Aggregation bias can occur if we treat data nested in different levels (therefore having
different meanings and effects) as if they were in the same levels. Misestimated standard errors occur
with hierarchical data if the model fails to take into consideration the dependence which arises due to
the common characteristics shared by the individuals within the organization.
Many studies of charter school competition impacts have assumed student/school/district/year
fixed effects (Bettinger, 2005; Bifulco & Ladd, 2006a; 2008; Hoxby, 2002a; Imberman, 2009; Ni,
2009; Sass, 2006; Zimmer & Buddin, 2009), but the relationship between the characteristics of
student/school/district/year and the student achievement varies across schools and among districts
through the time. To investigate the charter school competition impacts on student achievement in
TPSs, we need to estimate “a separate set of regression coefficients for each organizational unit, and
then to model variation among the organizations in their sets of coefficients as multivariate outcomes to
be explained by organizational factors” (Raudenbush & Bryk, 2002, p. 100).
2.3 Studies on social impacts of charter schools
2.3.1 Studies on racial/ethnic composition in charter schools
Sector level studies: Horn and Miron (1999) evaluated Michigan charter school policy. They
suggested that charter schools were serving more minority students when compared to the overall state
student enrollment, but fewer minority students when compared to their host districts. They reported “a
very mixed picture”, with many traditional public schools enrolling more minorities than their host
districts, as well as many TPSs having fewer minorities than their host districts. Miron and Horn (2002)
surveyed Connecticut charter schools and compared their racial composition with statewide student
enrollment data. They concluded that minorities are much more represented in Connecticut charter
schools.
NAEP (2003) surveyed and compared the population comparison between charter schools and
traditional public schools. The results show that the charter schools are serving significantly fewer
white students and more black students, but have similar student cohorts in free and reduced-price
lunch status as the traditional public schools, so family income levels of students in charter and public
schools are similar. In its charter school report, Florida Department of Education (2006) compared the
demographic composition of charter schools and TPSs by aggregated percentage of minorities. It
suggested that charter schools served an “increasingly diverse student population” (p. 6) reporting the
21
minorities in charter schools and TPSs changed from 56% and 43% in 1996 to 57% and 52% in 2005,
respectively. The U.S. Department of Education (2004b) evaluated the public charter schools program
and reported that charter schools enrolled more African American students and a higher proportion of
free and reduced price lunch program students, but fewer white students and a lower proportion of
special education students (p. 24-25).
In Massachusetts, charter schools served more African Americans and fewer low-income
students than the host districts did. But when the areas were divided by three categories such as Boston,
urban, and suburban, charter schools in suburban areas had fewer African Americans and more white
students than the feeder districts (Reville, Coggins, & Candon, 2004).
On the other hand, Miron et al. (2010) compared the demographic compositions of charter
schools operated by ‘education management organizations’ (EMOs) with those of traditional public
schools of the sending districts at the national level. They found that EMO charter schools are strongly
racially segregated for both minority and majority students and for economically challenged students.
School level studies: Crockett (1999) analyzed California charter schools’ demographic
composition in terms of racial/ethnic distinctness from sponsoring districts and ethnic concentration in
charter schools. She found that “over 63 percent of charter schools were whiter than their sponsoring
districts” (p. 37), and that charter schools operating for 5 years or longer had “a higher average
distinctness from their sponsoring districts than newer charter schools” (p. 38).
Cobb et al. (2000) used the mapping techniques to avoid misrepresentation accrued from
aggregated data at the nation, state and local level, and found that “Arizona’s charter schools
contributed to ethnic/racial separation during 1998-99. (p. 10)” Then they argued that the situation
would get worse with the increase in the number of charter schools and students. They reanalyzed the
Horn and Miron (1999) report and argued that because most charter schools are located in urban areas
in Michigan, “charter schools are actually serving disproportionately fewer minorities in diverse areas.
(p. 13)”
Crew and Anderson (2003) investigated whether charter schools were more racially and
economically segregated than TPSs in Florida, and they concluded that charter schools in Florida in
1999-2000 were more segregated in both race and socio-economic status than TPSs. Frankenberg and
Lee (2003) also examined the racial/ethnic composition in charter schools and then compared them
with that of public schools “by aggregating the school level data to the state level” (p. 16). They found
strong evidence of ‘white flight’ and ‘black self-isolation’ at the same time. Eighty-three percent (or 22
%) of white charter school students attend majority white charter schools whose student bodies are
22
more than 50 % (or 90 %), while eighty-nine percent (or 70 %) of black students are in schools where
50 % (or 90%) of the student bodies were minorities.
Student Level studies: Weiher and Tedin (2001) surveyed the parents whose children
transferred from public schools into charter schools and gathered school information of both before-
and-after choices. They found that the parents’ actual choices didn’t agree with their stated preferences.
In spite of their claim that they put more value on the academic performance of schools, their real
choices indicate that all ethnic groups sorted themselves out from other racial groups indicating white
flight or self-isolation. Bifulco and Ladd (2006b) used student level panel data from 1996 to 2000 and
found that charter schools in North Carolina increased the self-isolation of both black and white
students which leads to a wider achievement gap between them.
Garcia (2008) used a student level dataset to track the school attendance patterns of the students
who exited from public schools and entered charter schools from 1997 to 2000 in Arizona. He found
the following facts: White charter school choosers enter more segregated charter schools exiting from
still racially segregated public schools (white flight). Black elementary school students isolate
themselves by choosing charter schools with a higher percentage of black students (self-isolation). Both
white flight and self-isolation were salient especially at the elementary level.
2.3.2 Studies on charter school impacts on racial/ethnic composition in TPSs
Ertas (2007) investigated the charter school impacts on racial composition and socio-economic
stratification in traditional public schools using four states datasets of 1995 and 2001: Texas, Florida,
New Jersey, and Ohio. Most of the results from difference-in-difference analyses and regression
analyses showed that the presence of charter schools in a county and within 5-mile radius and the share
of charter school enrollment significantly affect the decrease of non-Hispanic white students proportion
and the increase of free or reduced price lunch eligible students percentage in nearby TPSs in all four
states.
Dee and Fu (2004)investigated the changes in the proportion of non-Hispanic white students in
nearby TPSs in Arizona using the CCD dataset of 1994 and 1999. They employed difference-in-
difference estimation and controlled some community-level variables such as the non-Hispanic white
population, household median income and the poverty level. Their results suggested that the
introduction of charter schools in Arizona reduced the proportion of non-Hispanic white students in
TPSs.
23
2.3.3 Limitations of the previous studies on segregation effects
Charter schools are operating under various conditions. For example, charter schools in most
states have to reflect the racial/ethnic composition of the sponsoring districts by the law, and the
counties and districts where they nested are quite different in the demography, educational resources,
and economic status. Charter schools also vary a lot in location, in conversion status, in the initiators or
management entities and so on. This is why Cobb et al. (2000) and Garcia (2008) criticized that the
aggregated “state and national data are incapable of showing between-school ethnic/racial separation
… (and) such comparison between charters and “all public schools” are inappropriate” (Cobb et al.,
2000, p. 4). The sector level studies aggregated school level data to the state level or national level
(Frankenberg, et al., 2003; Horn & Miron, 1999; Gary Miron & Horn, 2002; G. Miron, et al., 2010;
NAEP, 2003) could “mask underlying disparities at regional and local levels” (Cobb, et al., 2000, p.
12). On the other hand, school level studies just examined the racial/ethnic composition of charter
schools compared to those of neighboring (Cobb, et al., 2000) or within-district public schools
(Crockett, 1999), while student level studies compared the demographic composition of before-public
schools with that of after-choice charter schools (Bifulco & Ladd, 2006b; Garcia, 2008; Weiher &
Tedin, 2001). These school level and student level studies did not take into account the characteristics
of counties and school districts.
Most of the previous sector, school, and student level studies used datasets only at one time
point and compared the racial/ethnic characteristics of charter schools with those of traditional public
schools (Crockett, 1999; Frankenberg, et al., 2003; Horn & Miron, 1999; Gary Miron & Horn, 2002;
NAEP, 2003). Some researchers (Dee & Fu, 2004; Ertas, 2007; G. Miron, et al., 2010) collected two or
three time points datasets and analyzed the mean difference changes in the demographic compositions.
These cross-sectional analyses do not allow one to investigate the trends of the racial composition
changes in charter schools and TPSs.
Therefore, the evaluation of the charter school effects on segregation requires a more vigorous
and carefully constructed research design. First, we need to investigate the longitudinal trends of
demographic compositions of charter schools taking into account the educational, social, economic
contexts where charter schools are nested. Second, few studies have been done on the impact of charter
school policy on the racial/ethnic integration or segregation of the left-behinders/non-choosers in public
school systems. To measure the racial/ethnic segregative/integrative impact of charter school policy on
the public school systems, the trend of demographic composition changes needs to be examined
utilizing longitudinal data and the methodology to parse out the differences between-schools and
24
within- and between-districts. Dee and Fu (2004) and Ertas (2007) used datasets with only two time
points and compared the differences between the two datasets.
In many ways, the investigation of charter school effects on segregation both in charter schools
and in TPSs in Florida is important in public policy making as well as in educational effectiveness and
equality. First, Florida is one of the leading states in the charter school movement. Second, the racial
integration in Florida’s public schools achieved in 1970s and 1980s has been dismantled since the
1990s (Frankenberg, et al., 2003; Orfield, 2001). Third, Florida, one of the southern states where the
desegregation policy brought the most dramatic transformation “from virtually total apartheid to the
most integrated region in the U.S. between 1964 and 1970” (p. 8), yet by 1998, fell behind the level of
integration in 1970 and is still moving backward (Frankenberg, et al., 2003). Fourth, the resegregation
and segregation negatively affect the student achievement in public schools (Allen, Consoletti, &
Kerwin, 2009; Borman, et al., 2004; Coleman, et al., 1966; Hanushek, et al., 2009; Hanushek & Rivkin,
2006; Rumberger & Palardy, 2005). However, only one study by Ertas (2007) has been done to
examine the demographic distribution in charter schools and its effects on demographic integration in
TPSs in Florida.
25
CHAPTER THREE
RESEARCH DESIGN AND METHODOLOGY
3.1 Research Questions
In this section, I will suggest research questions based on my theoretical frameworks and the
literature reviews in the previous chapter. Three main theories for or against charter schools frame three
main groups of research questions regarding school effectiveness, market and competition effects, and
segregation effects of charter schools.
3.1.1 School effectiveness thesis
School effectiveness refers to the performance of schools as organizational units. School
performance varies across schools. The questions about schools’ effectiveness concern how much they
differ from each other in terms of effectiveness, and what factors determine their effectiveness.
Generally speaking, educational economists emphasize the ratio of instructional and administrative
input to educational output such as test scores, and educational psychologists focus on instructional
strategies and techniques, while educational sociologists have more interests in organizational aspects
such as leadership style, the composition of the student body, and socio-cultural environments.
Rationales for charter schools suggest that charter schools should be more effective, because they
would be more autonomous in the exchange of accountability, more innovative in their curriculum and
instruction, freer from bureaucratic regulations and political controls, and more congruent to parental
needs (Chubb & Moe, 1990; Clark, 2005; Teske, Schneider, Buckley, & Clark, 2000). However, the
opponents of charter-school policy argue that charter schools would cream-skim better performing
students or students with more potential and draw financial resources from TPSs. They suggest that
charter school effects on student achievement, if any, would not be true improvements.
Therefore, the research questions I will address in this dissertation regarding the school
effectiveness thesis are the following:
1-a. Is student achievement in charter schools higher than that of TPSs in 1998 (the first year
that the FCAT data are available)?
1-b. How much do charter schools vary in student achievement among themselves?
1-c. Are the annual change rates of student achievement in charter schools and in TPSs
26
different from each other?
1-d. Is the student achievement in charter schools still higher when educational, socio-
economic, and demographic factors are taken into account?
3.1.2 Market competition thesis
Another influential argument for charter schools is the possible market competition effect on
TPSs and on the public education system. Charter schools are expected to introduce competition into
the educational market and to pressure TPSs to be more effective, more innovative, and more focused
on the needs of students and parents (Belfield & Levin, 2002; Chubb & Moe, 1990; Friedman, 1955;
Tiebout, 1956). To test this thesis, I formulated several research questions.
2-a. Does the competitive pressure on TPSs from charter schools, measured by the presence
and number of charter schools within a certain radius and distance to the nearest charter
school (school level competition), raise the student achievement in nearby TPSs?
2-b. Does the competitive pressure on TPSs from charter schools measured by adoption of a
charter school policy, years since its adoption, and the percentage of a county’s students in
charter schools (county level competition) raise the student achievement in TPSs?
2-c. Are these competition effects from charter schools, if any, robust when educational,
socio-economic, and demographic factors are taken into account?
3.1.3. Segregation effect thesis
Perhaps the most persuasive argument against charter school policy is the possibility of
segregation effects in demographic composition and socio-economic status of schools. Historically,
school choice was used by those who wanted to avoid the racial desegregation mandate of public
schools, especially in the southern states. Parents’ preferences for cultural similarity and pluralistic
forms of socialization (Fuller, et al., 1996) seem likely to result in ‘self-isolation’ or ‘white flight’ and
socio-economic stratification in school choice schemes (Cobb, et al., 2000; Crew & Anderson, 2003;
Crockett, 1999; Frankenberg & Lee, 2003; Garcia, 2008; Horn & Miron, 1999; Renzulli, 2006;
Renzulli & Evans, 2005; USDOE, 2004a; Weiher & Tedin, 2001).
To explore these issues, I will answer these research questions:
3-a. Do charter schools serve more students from a certain racial/ethnic group or a certain
socio-economic stratum? In other words, are they used as pockets for self-isolation, white
flight, or as socialization venues for the rich?
27
3-b. Do charter schools affect the demographic composition of students in nearby TPSs?
3-c. Are TPSs in counties that have adopted a charter school policy (or have more charter
school students) more (or less) similar racially and socio-economically than TPSs in
counties without charter schools?
3-d. Are these effects, if any, robust when school and county characteristics are controlled?
3-e. Is the size of the segregation effect the same across all three major racial/ethnic groups -
black, white, and Hispanic students?
3.2 Units of Analysis
Three types of units of analysis could be applied in charter-school effects studies: the student
level, school level, and county level. Researchers prefer using student-level achievement data, if
available, because the students in charter schools may differ systemically from the students remaining
in TPSs. Studies using student-level data can analyze the charter-school effects at the micro-level by
examining individual changes in achievement and student preferences to enroll in charter schools. They
can compare the charter-school effects on students in charter schools to those for students in TPSs as
well.
However, since this study puts more focus on the organizational and institutional impacts of
charter schools both on student achievement in charter schools and in TPSs, and on the demographic
changes in charter schools and in TPSs, school level and county level of analyses are more appropriate.
Schools are the key entities that devise strategies for, respond to, and arrange the management tools for
educational policy changes. Booker, Gilpatric, Gronberg, and Jansen argued that “competitive effects
are felt and, importantly, responded to, more at the campus level” (p. 137). Counties are the decision-
makers in educational policies which will be the critical environment for public schools. Bohte argued
that “changes … in traditional public schools are a logical consequence of policy changes … and other
educational reforms implemented when public school officials respond to the presence of charter
schools” (p. 504).
The main units of analysis in this study will be the school and the county, focusing on
organizational outcomes and their reactions to the charter-school policy. Most studies employ only one
unit of analysis such as the student, school, or county, due to their uses of conventional regression
analyses or comparisons in percentages and in differences. In their analyses, most previous studies put
data from different levels into the same level of analysis, ignoring the nested nature of educational data.
28
This may lead to aggregation bias and estimation problems. To avoid expected biases and integrate two
levels of analysis into my models, I use Hierarchical Linear Modeling (hereafter HLM).
3.3 Data Collection
I will use three types of data sets: data on student achievement, data on Florida’s public school
characteristics, and data on county characteristics. Student achievement data include the 5th, 8th and 10th
graders’ FCAT scores in math and reading from 1998 through 2010. These data are provided by the
Florida Department of Education through its web pages.
The school level data comes from U.S. Department of Education’s National Center for
Education Statistics (NCES) Common Core of Data (CCD). It provides the school types and school
level, the charter-school status, racial/ethnic composition, school location, the numbers of students
eligible for free or reduced price lunch programs, and so on. Another source for school information is
the Florida Department of Education (FLDOE), which collects such educational information as the
number of staff, the percentage of teachers with advanced degrees, the teachers’ average years of
experience, the percentage of disabled students, per pupil expenditure, the percentage of English
language learners, the number of students, and so on. The CCD classifies public schools into four
categories: regular school, special education school, vocational school, and other/alternative school.
Since this study focuses on the academic achievement and on public schools’ demographic changes by
charter-school choice, only the data on regular public schools4 will be analyzed.
County level data are provided by FLDOE and Florida Statistical Abstract published by The
Bureau of Economic and Business Research in the University of Florida. FLDOE data contains the
same educational information as the school level data. The Florida Statistical Abstract includes
economic and demographic data of counties like household median income, the percentage of children
in poverty and the percentage of minorities, and county level educational information such as dropout
rate, the percentage of private school and home education students. Some county level data such as
educational attainments of adults come from the U.S. Census Bureau.
4 The NCES CCD classification of public schools added one more category – reportable program starting in 2007. Regular
public schools include charter schools and traditional public schools.
29
3.4 Measurement in the Study
3.4.1 Student achievement
This study will use the FCAT scores as proxies for student achievement, even though they are
not the best or only measure for student achievement in schools. The FCAT math and reading scores of
schools for grade 5, 8 and 10 will be used to explore the school effectiveness of charter schools and to
investigate the competition effects on TPSs from charter schools.
Test scores have many preferable properties for educational research. They are measured and
presented as numbers which are very malleable to quantitative operations. They are one of the
outcomes of schooling of most concern to parents, politicians, and school administrators as well as
students themselves. They are ready for comparisons among schools and counties because they can be
standardized and normalized.
3.4.2 Market competition pressure from charter schools
What proxies will be utilized to measure the competition pressure from charter schools is one of the
most critical issues in the competition related literature. Four types of measures of competitive market
pressures have been used the most: the number of charter schools within a certain mile-radius or in a
county, the distance to the nearest charter school from a TPS, the percentage of charter-school students
in a n-mile radius or in a county, and the presence of any charter school in a certain mile-radius or in a
county. For example, Bohte (2004) used the number, the percentage, and the presence of charter-school
students in a county as the proxies for competitive pressure on the traditional public schools. Hoxby
(2003) and Lee (2009) used the share of charter-school students and dummy variables for a certain
percentage of charter-school students in school districts. Zimmer and Buddin (2009) used all three
measures. First, they calculated the distance to the nearest charter school to measure the strength of the
competition pressure. They presumed “the closer a traditional public school is to a charter school, the
more likely it is that the school will feel competitive pressure” (p. 78). They examined whether the
level of charter-school competitive pressure within a local educational market affects student
achievement of TPSs also by employing the number of charter schools and the share of charter students
within 2.5 miles of a TPS as competition measures.
Since this study will employ two levels of units of analysis, each level will have its own
measures for the competition pressure. At the school level, I will use the aforementioned four measures.
30
At the county level, I will use the number of charter schools and the percentage of charter-school
students in a county. In addition, I will introduce other proxies such as the charter-school policy
adoption (dummy variable), the years of charter-school adoption, a dummy variable for higher
percentage of county median percentage of charter-school students, and the student percentage in other
school alternatives such as private schools and home education.
3.4.3 The degree of segregation in public schools
Zoloth suggested three measures to gauge the degree of segregation in schools and districts: the
dissimilarity index (“based on the absolute deviation of the racial composition of a school from that of
the school district”), the segregation index (“based on the squared deviation”), and the information
theory index (“derives from information theory and has been suggested for this use by Theil and
Finizza [1971 ])” (Zoloth, 1974, 1976, p. 278). Rivkin (1994) and Clotfelter (1999) developed the
exposure index as the measure of racial segregation using the degree of interracial contacts. Renzulli
and Evans (2005) examined the white enrollment in charter school in districts to investigate the “white
flight without residential mobility” (p. 400) using a district-level contact index and an integration index.
Since these indexes are intended to measure the district level integration, they are not appropriate for
school-level models in this study.
In order to detect whether charter schools are utilized as pockets for ‘white flight’ or ‘self-
isolation’, and whether charter schools affect the demographic compositions in nearby TPSs, I will
analyze the demographic composition of charter schools and traditional public schools and their trends
regarding demographic composition changes. Then the results will be contrasted against those of the
county public school system. To investigate the segregation effects both in charter schools and in
traditional public schools, I will formulate a dissimilarity index, which is calculated by subtracting the
student percentage of a certain racial group or a certain socio-economic stratum in a given county from
that in a given school. The possible range of the dissimilarity index will be from 99.99 % to negative
99.99%.
DI(X) = (the percentage of X students in a school) – (the percentage of X students in the
county),
where X refers to racial/ethnic and socio-economic categories.
Examination of the trends in the changes of the dissimilarity indexes in charter schools and in
TPSs will show whether charter schools exacerbate or improve the integration of different racial/ethnic
groups and socio-economic strata, and whether charter schools are utilized as pockets for white flight
31
or self-isolation. The dissimilarity index has some merits. It is simple and intuitive. Every value
represents how much the percentage of X students of a given school is different from that of the county,
which the absolute value of dissimilarity index (Zoloth, 1974) does not provide. While most indexes
for integration and segregation mentioned above are supposed to measure county- or district-level
segregation, this index can be used at the school level and thus is more appropriate to examine school
level segregation than the segregation index (Zoloth, 1974) and the exposure index (Rivkin, 1994).
However, to check how much farther away TPSs and CSs are from the county means I will
calculate the absolute dissimilarity index, exposure rates of white students to non- withes, and
segregation index. The absolute dissimilarity index, which takes the absolute value of the differences
calculated by subtracting the student percentage of a certain racial group or a certain socio-economic
stratum in a given county from that in a given school. The possible range of the absolute dissimilarity
index is from 0 % to 99.99%.
ADI(X) = |(the percentage of X students in a school) – (the percentage of X students in the
county)|,
where X refers to racial/ethnic and socio-economic categories.
Every value represents how far the percentage of X students of a given school is from the mean
percentage of X students in the county public schools. The exposure index and segregation index
(Clotfelter, 1999; Rivkin, 1994) that will be used to examine the county’s degree of segregation. The
exposure rate or interracial contact rate is “the exposure rate of whites to non-whites” in county i that is
calculated by:
E� = (1
W�)�W��[N��/(W�� + N��)�� ],
where Wi is the total number of whites in a county i, Wti and Nti are the number of whites and non-
whites in a school t in a county i. And the segregation index of county i represents the gap between the
distribution of whites and non-whites students across schools and the distribution of them in the county
in which the schools are nested:
Si = [(Ni / (Wi + Ni) – Ei) ] / [ Ni / (Wi+Ni) ]
where (Ni / (Wi + Ni)) means the percentage of non-whites in a county i (Clotfelter, 2001).
32
3.5 Methodology
To test the differences in student initial status (at the year of 1998) and yearly change rates, a
Hierarchical Linear Modeling (hereafter HLM) is most appropriate. In the past, researchers have relied
primarily on two-time-point designs to study exposure effects, where “the adequacy of such measures
for distinguishing differences in rates of change among individuals is rarely considered” (Raudenbush
& Bryk, 2002, p. 161). This research will use multiple-time-point standardized state test results and the
changes of demographic composition in schools from 1998 to 2009, which requires the formulation of
individual school and district change trajectories based on periodical test results and the demographic
changes. “The development of hierarchical linear models has created a powerful set of techniques for
research on individual change. When applied with valid measurements from a multiple-time-point
design, these models afford an integrated approach for studying the structure and predictors of
individual growth” (Raudenbush & Bryk, 2002, p. 161). In my hierarchical linear model, at level 1,
each individual school’s development is represented by an individual school’s change trajectory that
depends on a unique set of parameters. These school change parameters become the outcome variables
of level 2 or the school-level models, where they may depend on level 3 or the district-level
characteristics.
The conventional regression models that most of the previous studies used to investigate the
charter-school impacts on the traditional public schools ignore the nested nature of educational data.
However, students are nested within schools, and schools are nested within school districts. Therefore
the conventional regression models using data sets with nested structures are subject to such biases as
aggregation bias, estimation bias, and regression heterogeneity. Aggregation bias can occur when we
treat data nested in different levels (therefore having different meanings and effects) as if they were in
the same levels. For example, the number of charter-school students may have different effects at the
school level and at the district level. “Hierarchical linear models help resolve this confounding by
facilitating a decomposition of any observed relationship between variables” (Raudenbush & Bryk,
2002, p. 100) into components due to separate levels. Misestimated standard errors occur with
hierarchical data if the model fails to take into consideration the dependence which arises due to the
common characteristics shared by the individuals within the organization. Hierarchical linear models
help address this problem by integrating a unique random effect for each organizational unit, which
enables the statistical model to take into account the variability of these random effects in calculating
standard errors.
Many studies on school effectiveness, and charter-school competition impacts on student
achievement and segregation have assumed student/school/district/year fixed effects (Bettinger, 2005;
33
Bifulco & Ladd, 2006a; Booker, Gilpatric, Gronberg, & Jansen, 2008; Hoxby 2002a; Imberman, 2009;
Ni, 2009; Sass, 2006; Zimmer & Budding, 2009), but the relationship between the characteristics of
student/school/district/year and student achievement varies across schools and among districts over
time. “Hierarchical linear models enable the investigator to estimate a separate set of regression
coefficients for each organizational unit, and then to model variation among the organizations in their
sets of coefficients as multivariate outcomes to be explained by organizational factors” (Raudenbush &
Bryk, 2002, p. 100)
This study will use repeated measurement data within individual schools from 1998 through
2010, which are generally correlated. There are other correlation called intra-class correlation and
considered as a special case of nested data. HLM is very useful to analyze these types of data which are
nested in different levels. Another merit of using HLM is that it doesn’t require balanced and regular
measurements. The data sets that this study will use have many cases without a complete set of the 13
years of FCAT scores and demographic compositions. Some charter schools and TPSs opened or
closed since 1998, and some schools did not administer the FCAT or report their information due to
various reasons such as too small enrollment or the lack of staff, etc. HLM is flexible enough to
analyze data collected at irregular intervals and with missing data for which the classical models such
as ANOVA and MANOVA are inappropriate. “Multilevel models can be effectively used almost
without regard to the patterns of missingness, provided data are missing at random” (Baumler, Harrist,
& Carvajal, 2003, p. 141).
Another question to be addressed is whether charter-school variables relate to the proportion of
blacks, whites and Hispanics in charter schools and in TPSs with the same strength or not. To answer
these questions, multilevel multivariate models will be formulated.
An obvious advantage of the multivariate approach is that we can incorporate the correlations
between outcomes into the analysis, as well as information about the measurement quality of
the items (or subtests) being used to define the multivariate outcome. … This is considered a
more efficient technique, since it has the advantage of cutting down on Type I error rates (Heck,
Thomas, & Tabata, 2010, p. 223)
34
3.6 Analytic Strategy
3.6.1 Stage 1: Checking the distribution of variance
The analyses will start with a check on the proportions of variation of student achievement and
demographic compositions in charter schools and TPSs found at the different levels. These analyses
will utilize the fully unconditional model which is “equivalent to a one-way ANOVA with random
effects” (Raudenbush & Bryk, 2002, p. 23). These analyses will show us the overall mean, within-
school variability (variation between repeated measurements), between-school variability (variation
across schools within counties), and between-county variability (variation across counties), and the
intra-class correlation coefficients which estimate the proportion of variance in each level.
3.6.2 Stage 2: Examining charter-school effects (without-control models)
Second, I will examine charter-school effects on student achievement in charter schools and in
TPSs and on demographic compositions in charter schools and in TPSs. I will use only charter schools
predictors such as the number and the presence of charter schools within a radius of a certain mile
range, and the distance to the nearest charter school. These analyses will present the charter-school
effects without taking various environmental factors influencing school performance into account such
as socio-economic, cultural factors and educational factors.
3.6.3 Stage 3: Testing the robustness of charter-school effects (with-control models)
In this stage, I will explore the robustness of charter-school predictors in school- and county-
level by introducing socio-economic, demographic and educational controls. Charter-school effects on
student achievement and demographic composition could be affected by the school’s socio-economic
status, racial/ethnic composition, educational investment and resources available to schools and
counties, and educational policies. Analyses with various controls will test whether charter-school
effects exist separate and independent from socio-economic and demographic factors.
3.6.4 Stage 4: Checking the similarity or dissimilarity of charter-school effect sizes
Generally speaking, student achievements in subjects are highly correlated. Therefore we need
to consider the correlations between the multiple outcome measures. To investigate this issue, I will
35
apply a hierarchical multivariate linear model which takes into account the correlation among the
multiple outcome measures.
Another issue is whether charter schools affect similarly the proportion changes of black
students, white students and Hispanic students in charter schools and in TPSs. This question of whether
the size of the charter-school effect, if any, is the same across subjects and across different racial/ethnic
groups can be tested by the multivariate hierarchical linear model.
3.7 Analytic Models
3.7.1 Model I: Multilevel models for univariate change
Model I will address those research questions related to examining the initial status and change
rate, i.e., research questions 1-a, 1-b, 1-c, 1-d, 2-a, 2-b, 2-c, 3-a, 3-b, 3-c, and 3-d. This model focuses
on univariate change with repeated measures. In this model, the main interest is in a single outcome
variable measured at each year for each school, for example, the FCAT math or reading scores in 5th,
8th, and 10th grades, or the dissimilarity index (DI) for white, black, and Hispanic students from 1998
through 2010. In this model, the outcome variable yk is represented as a function of year and a random
year effect. They will show the initial status levels and the yearly change rates of individual schools in
counties, and the variance of school outcomes across years. If a linear change rate is assumed, the
polynomial degree would be 1. Otherwise, it would be equal to or larger than 2. I assume non-linear
change rates in this study, because I found that the outcomes were not a linear function of years in the
preliminary analyses of the Florida data. The model is
ymti = ψ0ti + ����������� + ������������ + εmti
where
ymti is the FCAT scores, or DIs of Florida schools at year m for school t in county i;
ψ0ti is the initial status of school ti, that is, the expected FCAT score or DI for
school ti in 1998 (coded as zero);
ψ1ti is the yearly mean change rate for school ti over the time period from 1998 to
2010;
ψ2ti is the acceleration or deceleration rate for school ti over the time period;
36
εmti is a level 1 random effect that represents the deviation of school ti’s FCAT
scores or DIs in YEAR m from the scores predicted by the change model. These residual
year effects are assumed normally distributed with a mean of 0 and variance σ2.
The level 2 model will capture the effects of the school-level characteristics including the
charter status, the market competition pressures from the charter school, and so on. The intercept (ψ0ti)
and slopes (����) in level 1 model can be modeled as fixed, non-randomly varying, or random. The
level 2 model has three equations, because every level-1 coefficient will have its own equation whose
random effects are assumed to be correlated.
ψ0ti = π00i + ∑ ������������ + e0ti
ψ1ti = π10i + ∑ ������������ + e1ti
ψ2ti = π20i + ∑ ������������ + e2ti
where
π00i represents the mean initial FCAT scores of schools within county i for Xqti =
0, or the ���� equal to mean value of a centered variable;
π10i represents the mean yearly change rate of schools within county i for Xqti = 0
or the mean value of centered variable;
π20i represents the mean acceleration or deceleration rate of schools within a county
i for Xqti = 0 or equals to the mean value of centered variable;
Xqti is a school characteristic used as a predictor of the school effect ψpti ;
epti is a random “school effect”, that is, the deviation of school ti’s mean score or
DI, yearly change rate, or acceleration rate from the county mean value of them.
These effects are assumed to be multivariate normally distributed each with a
mean of 0 and some variance гψ and some covariance.
Each level 3 dependent variable would be each level-2 coefficient. These are modeled as a
function of county-level characteristics Wsi, specifically
πpqi = βpq0 + ∑ ������� ������ + rpqi,
where
β000 is the overall mean score, β100 is the overall mean yearly change rate, and β200
is the overall mean acceleration rate of the FCAT scores or DIs for all counties;
37
Wsi is a county level characteristic adopted as a predictor for school effect, πpqi;
βpqs is the level 3 coefficient corresponding to the relationship between county
characteristic Wsi and the school effect, πpqi;
rpqi is a random “county effect”, that is, the deviation of county i’s mean score,
yearly change rate, or acceleration rate from the overall mean. These effects are
assumed multivariate normally distributed with a mean of 0, some variance гπ and
covariance.
3.7.2 Model II: Multilevel models for multivariate change
Model II will address the research question related to research question 3-e. Since the analyses
of segregation effects of charter school use three outcome variables related to each other, that is, the
dissimilarity index for white, black, and Hispanic students, it is important to examine whether the
charter-school effects, if any, are statistically similar among the dissimilarity indexes for white, black
and Hispanic students. Model II will investigate this question.
To specify a multivariate multilevel model, let ymtik be a outcome variable for an individual
school t in county i at time m on outcome variable k (k=1 for DI of white students, k=2 for DI for black
students, and k=3 for DI for Hispanic students). Then the model defines dummy variables, δk which
would be 1 for the given measure on ymtik and δk = 0 otherwise. Then, a multilevel model for
multivariate change could be given as
ymtik = ∑ δ�(����� + ������������ + ������ )
The level 2 and level 3 models are the same as those in Model I in the section 3.7.1, except that
they include an additional set of equations representing three outcome variables. The main focus of the
analyses by Model II is the “covariance between random parameters representing corresponding
aspects of change on different outcome variables. … Relationships between patterns of change on
different variables are represented in terms of covariance between parameters of the change functions
for different variables” (MacCallum & Kim, 2000, p. 59).
This chapter talked about the data and outlined the research questions based on my theoretical
framework. Then I discussed the methodological issues, analytic strategies, and models to be utilized in
this study. My dissertation will show the results from each model and discuss the meanings and
implications of the results from each analysis.
38
CHAPTER FOUR
CHARTER-SCHOOL EFFECTS ON STUDENT ACHIEVEMENT
This chapter will examine the characteristics of public schools in Florida in the datasets that
will be used in the analyses of the following chapters. The descriptive statistics for charter schools and
traditional public schools will be compared within the school level. The preliminary analysis of
variance among schools and across counties will come next. This analysis will provide the information
about the mean scores and where the most variation are involved, at the school level or county level.
Then analysis of variance and the natural annual mean change rates in the FCAT scores of public
schools will be performed, which will be the basis for the more sophisticated analyses in the next
chapters.
4.1 Characteristics of Public Schools and Counties in Florida
The number of charter schools has been growing steadily, even though the change rates at each
school level have decreased. Table 4-1 shows the number of regular5 charter schools and regular
traditional public schools by year and school level included in the datasets of this study. Table 4-2
provides the information about the years of operation of charter schools by school level. Most of the
charter schools at every school level have been in operation for less than four years: 53.5 percent of
elementary schools, 64.0 percent of middle schools, and 70.5 percent of high schools. Greater
proportions of charter schools are located in suburban areas; this is similar to the distribution of TPSs
as shown in Table 4-3.
Table 4-4 provides the public school characteristics in Florida for both charter schools and
traditional public schools by school level (See Appendix 2 for the details). The datasets used in the
tables were analyzed by school level. This will show different pictures from such descriptive analyses
of the sector level as in Sass (2006) and in the FDOE reports (2002, 2006, 2010). They described the
student characteristics served by charter schools to be similar largely to those enrolled in traditional
public schools in Florida. For example, Sass (2006) said that “a somewhat lower proportion of students
from low-income households (as indicated by free/reduced-price lunch receipt) and gifted students” (p.
5 As mentioned in the data collection section, this study uses only the regular school data among the four categories in the
CCD: regular school, special education school, vocational school, and other/alternative school.
39
102) were served by charter schools. But as shown in Appendix 2, Sass’s statement is true for
elementary and middle schools, but not true for high schools in Florida. The same logic applies to the
charter school accountability reports by the Florida Department of Education. The greater proportions
of minority students and lower numbers of white students have enrolled in middle and high charter
schools than in traditional public schools, but no differences in the racial/ethnic compositions are
shown for in elementary schools. There is little difference in the proportion of disabled students, and
smaller proportions of the English language learners (ELL) are served by elementary and middle
charter schools.
Table 4-1 Number of Charter Schools and TPSs in the Datasets by Year and School Level
Year Elementary School Middle School High School
CS TPSs CS TPSs CS TPSs
1998 4 1,532 5 584 3 451
1999 10 1,558 13 576 6 427
2000 28 1,603 28 634 17 459
2001 48 1,651 35 684 20 496
2002 73 1,697 43 727 25 533
2003 86 1,740 53 726 33 535
2004 102 1,769 67 746 40 531
2005 103 1,797 70 782 27 558
2006 118 1,841 74 799 32 580
2007 126 1,880 87 816 35 581
2008 140 1,916 97 823 40 587
2009 150 1,952 110 852 48 616
Total 988 20,936 682 8,749 326 6,354
The other special features of charter schools involve educational factors. The class sizes of
charter schools and TPSs are similar, but the teacher characteristics are quite different from each other.
The percentages of teachers with advanced degrees are much higher in traditional public schools, while
the proportions of classes taught by out-of-field teachers are quite lower in TPSs than in charter schools.
Charter schools employ a much lower proportion of the instructional staff than TPSs do.
40
Table 4-2 Years of Operation of Charter Schools by School Level (2009)
Years Elementary Schools Middle Schools High Schools
N Percent N Percent N Percent
1 35 16.7 38 23.6 20 22.7
2 26 12.4 24 14.9 21 23.9
3 30 14.4 22 13.7 10 11.4
4 21 10.0 19 11.8 11 12.5
5 12 5.7 13 8.1 5 5.7
6 20 9.6 10 6.2 5 5.7
7 19 9.1 5 3.1 7 8.0
8 18 8.6 4 2.5 3 3.4
9 15 7.2 11 6.8 2 2.3
10 9 4.3 6 3.7 1 1.1
11 3 1.4 5 3.1 2 2.3
12 1 .5 4 2.5 1 1.1
Total6 209 100.0 161 100.0 88 100.0
Mean 3.15 - 2.98 - 2.77 -
Table 4-3 Distribution of Charter Schools and TPSs by Location (1998-2009)
Elementary Middle High
TPSs CSs TPSs CSs TPSs CSs
Urban 5351 277 1593 240 1231 83
27.4% 28.0% 23.8% 35.2% 25.3% 25.5%
Suburban 10283 457 3179 294 2128 169
52.7% 46.3% 47.5% 43.1% 43.7% 51.8%
Town 783 38 435 13 335 10
4.0% 3.8% 6.5% 1.9% 6.9% 3.1%
Rural 3102 216 1482 135 1173 64
15.9% 21.9% 22.2% 19.8% 24.1% 19.6%
Total 19519 988 6689 682 4867 326
100.0% 100.0% 100.0% 100.0% 100.0% 100.0%
6 The total numbers of charter school in Table 4-2 does not match with the numbers in Table 4-1, because some charter
schools were closed in a certain year and in a certain age between 1998 and 2009.
41
Table 4-4 Characteristics of Public Schools in Florida by School Level
Level/Features Traditional Public Charter Sig. of Mean
Difference N Mean N Mean
Elem
entary
Sch
ools
Free Lunch (%) 19,519 47.11 988 33.97 .000
Reduced Price Lunch (%) 19,519 10.06 988 8.63 .000
Free/Reduced Price Lunch (%) 19,519 57.17 988 42.60 .000
Gifted Student (%) 12,928 12.34 379 22.03 .000
Disabled Student (%) 12,644 15.93 434 14.44 .053
English Language Learner (%) 13,894 20.90 476 17.23 .014
Class Size 7,833 20.95 110 25.09 .351
Teacher with Advanced Degree
(%)
14,314 31.24 555 12.25 .000
Classes Taught by Out-of-Field
Teachers (%)
8,155 19.10 473 23.51 .003
Instructional Staff (%) 12,641 64.58 439 37.18 .000
Mid
dle S
cho
ols
Free Lunch (%) 6,689 39.75 682 33.77 .000
Reduced Price Lunch (%) 6,689 9.80 682 8.55 .000
Free/Reduced Price Lunch (%) 6,689 49.55 682 42.32 .000
Gifted Student (%) 4,553 6.99 242 8.27 .009
Disabled Student (%) 4,843 15.76 379 14.86 .267
English Language Learner (%) 4,602 4.69 278 3.48 .000
Class Size (Language Art) 2,032 24.39 80 25.77 .384
Class Size (Math) 2,032 25.12 80 24.34 .621
Teacher with Advanced Degree
(%)
4,862 32.22 388 13.77 .000
Classes Taught by Out-of-Field
Teachers (%)
2,830 7.95 307 11.95 .001
Instructional Staff (%) 4,862 66.86 388 39.58 .000
Hig
h S
choo
ls
Free Lunch (%) 4,867 27.78 326 27.23 .619
Reduced Price Lunch (%) 4,867 6.89 326 6.83 .853
Free/Reduced Price Lunch (%) 4,867 34.67 326 34.06 .624
Gifted Student (%) 2,556 4.39 102 3.88 .295
Disabled Student (%) 3,404 13.12 167 14.08 .396
English Language Learner (%) 3,256 4.02 138 4.72 .288
Class Size (Language Art) 1,426 24.65 24 26.28 .723
Class Size (Math) 1,426 25.02 24 24.62 .895
Teacher with Advanced Degree
(%)
3,427 37.48 168 17.25 .000
Classes Taught by Out-of-Field
Teachers (%)
1,995 6.83 144 14.69 .000
Instructional Staff (%) 3,427 68.52 168 42.33 .000
42
Tables in Appendix 2 describe the county characteristics. The counties in Florida differ very
much from each other in the educational environment, demographic and socio-economic situations, and
educational institutions during the period of 1998 to 2009. Forty nine percent of counties in Florida
have at least one elementary charter school through the period, and 46% and 33% of the 67 counties
have more than one middle and high charter school, respectively. The average class sizes of elementary
schools vary from 16.4 to 31.3 with a mean of 22.09. The median household incomes range from
$23,852 to $67,238 with mean of $37510.
The demographic compositions among counties vary considerably. For instances, the
population density ranges from 8.4 to 3384.1 persons per square mile with a mean of 308.6 persons.
The percentages of black, Hispanic, and white people also differ from one another. Those percentages
are less than 3% in some counties, while more than 60 percent in other counties (See Appendix 2 for
the details and other characteristics of the counties). The influence of these variation in the county
characteristics will be investigated in the following chapters.
4.2 Analysis of Variance and Yearly Changes in the FCAT Scores of Public Schools
Before getting into the comparisons of charter-school achievement levels with those of TPSs, I
will examine how the variation in student achievement is distributed among the different levels. One
merit of using HLM is that it will examine the influence of different organizational levels and the
variation caused by the multiple levels of institutional characteristics is partitioned into components for
each separate level. These analyses will reveal how much variation in the FCAT scores of schools exist
within and between counties. For this purpose, I formulated One-Way ANOVA HLM Models, or fully
unconditional HLM models for the 5th, 8th, and 10th grade FCAT math and reading scores:
Level-1 Model
MSSmti = ψ0ti + εmti
Level-2 Model
ψ0ti = π00i + e0ti
Level-3 Model
π00i = β000 + r00i
43
where
MSSmti is the FCAT score of a regular public school as the outcome at year m for school t
in county i;
ψ0ti is the mean FCAT score of school ti, across the years 1998-2010;
π00i represents the mean FCAT score within county i, while β000 is the overall mean
FCAT score for all counties across all years;
εmti is a level-1 random ‘year effect’ that represents the deviation of school ti’s FCAT
score in year m from the school’s mean scores. These effects are assumed normally
distributed with a mean of 0 and variance σ2ε;
e0ti is a random “school effect”, that is, the deviation of school ti’s mean from the county
mean. These effects are assumed normally distributed with a mean of 0 and variance σ2e;
r00i is a random “county effect”, that is, the deviation of county i’s mean from the overall
state mean. These effects are assumed normally distributed with a mean of 0 and
variance τπ.
First, I ran One-Way ANOVA models for the 5th, 8th, and 10th grade FCAT math scores, and
then for the 5th, 8th, and 10th grade FCAT reading scores. These simple three-level models partition the
total variability in the FCAT scores into the three components: variation over the years (σ2ε) in level 1;
variation among schools within a county (σ2e) in level 2; and variation between counties (τπ) in level 3.
The results from these models are shown in Table 4-5 for the FCAT math scores and in Table 4-6 for
the FCAT reading scores.
The intra-class correlation (ICC), which represents the portions of variance in the FCAT scores
between schools and among counties over the time period, can be calculated by using the estimated
variance components for their respective parameters in Table 4-5 and Table 4-6. For example, the
proportions of variance for the 5th grade FCAT math scores are,
The proportion of variance over the years: σ2ε / (σ2
ε+σ2e+τπ) = 212.34 / (212.34 + 402.68
+ 49.12) =0.3197, which means that 31.97% of total variance in the 5th grade FCAT
math scores comes from the year effect (changes over time) during 1998-2010.
The proportion of variance among schools: σ2e / (σ2
ε+σ2e+τπ) = 402.68 / (212.34 +
402.68 + 49.12) = 0.6063, which means that 60.63% of total variance in the 5th grade
FCAT math scores exists among schools, within counties.
44
The proportion of variance between counties: τπ / (σ2ε+σ2
e+τπ) = 49.12 / (212.34 +
402.68 + 49.12) = 0.0740, which means that 7.40% of the total variance in the 5th grade
FCAT math scores is found among counties.
Table 4-5 Results from the One-Way ANOVA Models for the FCAT Math Scores
Fixed Effect Coefficient SE t-ratio
G5 Overall mean, β000 320.27 1.14 280.64
G8 Overall mean, β000 309.95 1.25 248.53
G10 Overall mean, β000 308.75 1.28 240.67
Random Effect Variance d.f. χ2 p-value ICC
G5
Year effect, ε 212.34
0.3197
School effect, e0 402.68 2060 36916.84 <0.001 0.6063
County effect, r00 49.12 66 266.22 <0.001 0.0740
G8
Year effect, ε 110.08
0.2450
School effect, e0 302.25 668 19455.05 <0.001 0.6726
County effect, r00 37.05 66 141.81 <0.001 0.0824
G10
Year effect, ε 121.65
0.1385
School effect, e0 738.91 632 25076.19 <0.001 0.8410
County effect, r00 18.00 66 71.35 0.304 0.0205
Reliability of OLS Regression Coefficient estimates Reliability estimate
G5 Year mean, ψ0 0.933
School mean, π00 0.564
G8 Year mean, ψ0 0.959
School mean, π00 0.367
G10 Year mean, ψ0 0.965
School mean, π00 0.163
All other intra-class correlations of the FCAT math and reading scores are shown in the right most
column of the tables. This intra-class correlation analysis shows that most of the variation in the FCAT
math and reading scores exists among schools, but that the county effects are relatively small. One
interesting thing shown in the ICCs is that the school effect increases as the grade increases (say 60.63%
for the 5th math; 76.68% for the 8th math; and 84.10% for the 10th math), while the year effect (31.97%,
17.64%, 13.85%, respectively) and county effect (7.40%; 5.68%; 2.05%, respectively) decrease. The
same is true for reading FCAT scores. This indicates that the school factors play a more important role
as the grades go higher. Therefore I need to focus more on what school characteristics explain the
differences among schools, and then explain what county characteristics have influences on the
45
academic achievement. For these tasks in the next section, I will first model the yearly mean FCAT
scores in terms of to the initial mean scores and the mean yearly change rates of schools by introducing
the year variable in level 1.
The reliability of the OLS estimates is the ratio of the true parameter variance to the total
observed variance. For the 5th grade FCAT math data, i.e., the estimated reliabilities for year means and
the school means were 0.933 and 0.564 respectively indicating that there are significant differences in
both the year means and school means. These reliabilities warrant modeling each parameter as a
function of school-level and county-level variables.
Table 4-6 Results from the One-Way ANOVA Models for the FCAT Reading Scores
Fixed Effect Coefficient SE t-ratio
G5 Overall mean, β000 298.85 1.31 228.71
G8 Overall mean, β000 299.36 1.14 262.10
G10 Overall mean, β000 289.04 1.44 201.05
Random Effect Variance d.f. χ2 p-value ICC
G5
Year effect, ε 169.76
0.2435
School effect, e0 458.01 2065 53787.45 <0.001 0.6570
County effect, r00 69.32 66 364.97 <0.001 0.0994
G8
Year effect, ε 103.28
0.1599
School effect, e0 516.03 844 33768.48 <0.001 0.7990
County effect, r00 26.57 66 114.10 <0.001 0.0411
G10
Year effect, ε 103.20
0.0911
School effect, e0 1010.80 631 41182.70 <0.001 0.8924
County effect, r00 18.73 66 65.78 >.500 0.0165
Reliability of OLS Regression Coefficient estimates Reliability estimate
G5 Year mean, ψ0 0.951
School mean, π00 0.607
G8 Year mean, ψ0 0.964
School mean, π00 0.303
G10 Year mean, ψ0 0.977
School mean, π00 0.134
In order to examine how much change in the FCAT scores public schools make every year, I
built non-linear change models in level 1. If the coefficient for the curvilinear term, or YEARSQ turns
out to be insignificant, I will eliminate it from models in the future analyses:
Level-1 Model
MSSmti = ψ0ti + ψ1ti*(YEARmti) + ψ2ti*(YEARSQmti) + εmti
46
Level-2 Model
ψ0ti = π00i + e0ti
ψ1ti = π10i + e1ti
ψ2ti = π20i + e2ti
Level-3 Model
π00i = β000 + r00i
π10i = β100 + r10i
π20i = β200 + r20i,
where
YEARmti is the year whose value is zero7 when the schools took the FCAT for the first time in
the datasets (It is the year of 1998 for most of the schools);
YEARSQmti is the squared values of YEARmti;
ψ0ti is the mean of the initial FCAT scores of school ti;ψ1ti is the mean change rate of the FCAT
scores of school ti; ψ2ti is the acceleration rate of the FCAT scores of school ti;
π00i represents the mean initial FCAT scores within a county i, while β000 is the overall
mean of the initial FCAT scores for all counties at the first year;
π10i represents the mean yearly change rate in the FCAT scores within a county i, while
β100 is the overall mean yearly change rate in the FCAT scores for all counties;
π20i represents the mean yearly acceleration (or deceleration) rate in the FCAT scores
within a county i, while β200 is the overall mean yearly acceleration (or deceleration)
rate in the FCAT scores for all counties;
εmti is now a level-1 residual variance after controlling the year and the year squared.
(The meanings of other variables and parameters are the same as the previous ANOVA models.)
Table 4-7 presents the results of fixed effects parameters from the non-linear yearly change models for
the FCAT math scores, and Table 4-8 shows results for the FCAT reading scores (See Appendix 3 for
the details). The tables show the initial mean FCAT math and reading scores of all grades, which are
lower than the overall mean FCAT math scores in Table 4-5, but higher than the overall mean FCAT
reading scores in Table 4-6, because these initial mean scores are the mean FCAT scores in the year of
7 I ran models with YEAR and YEARSQ terms centered, which brought some differences on the magnitudes of coefficients,
but they didn’t make any differences on the significance and the directions of coefficients. Therefore, I will use the un-
centered YEAR and YEARSQ terms level 1 in this study.
47
1998 while those in Table 4-5 and Table 4-6 are the mean scores during the period of 1998 through
2010. All the annual change rates for the FCAT math and reading scores show non-linear change
curves except for the 8th grade FCAT math scores. The year square term for the 8th grade FCAT math
scores was insignificant. Therefore, the change model for the 8th grade FCAT math scores will be
modeled as linear hereafter. The coefficients of the year term for all grades in the FCAT math scores
are positive, while the coefficients of the year-squared term are negative. But the yearly change rates
never become negative throughout the period, because the coefficients of the YEAR terms are large
enough to cover the decrease from the YEARSQ terms. For example, the mean FCAT math score of the
5th grade at the first year is 306.32, at the fourth year 318.95 (306.22 + 3.55*4 + (-0.098)*42), at the
eighth year 328.44, and at the last year of the dataset 334.80. However, in the FCAT reading scores, the
coefficients of the YEAR terms are all negative, but the coefficients of the year-squared terms are
positive for all grades. The yearly change rates of the 5th and 8th grade become positive at the fourth or
fifth year, but those for the 10th grade turn out to be positive only at the twelfth (i.e., 0.55 = (-0.72)*11
+ 0.07*112) and the thirteenth year.
Table 4-7 Results from the Yearly Change Models for the FCAT Math Scores
Fixed Effect Coefficient SE t-ratio d.f. p-value
G5 Overall mean, β000 306.32 1.27 241.32 66 <0.001 Overall mean yearly change rate, β100 3.55 0.21 16.60 66 <0.001
Overall acceleration rate, β200 -0.098 0.02 -6.22 66 <0.001
G8 Overall mean, β000 301.99 1.40 216.08 66 <0.001
Overall mean yearly change rate, β100 1.99 0.22 9.09 66 <0.001
Overall acceleration rate, β200 -0.01 0.02 -0.87 66 0.389
G10 Overall mean, β000 298.49 1.26 237.19 66 <0.001
Overall mean yearly change rate, β100 3.68 0.21 17.56 66 <0.001
Overall acceleration rate, β200 -0.15 0.02 -10.20 66 <0.001
Table 4-8 Results from the Yearly Change Models for the FCAT Reading Scores
Fixed Effect Coefficient SE t-ratio d.f. p-value
G5
Overall mean, β000 294.45 1.42 206.94 66 <0.001
Overall mean yearly change rate, β100 -0.57 0.17 -3.27 66 0.002
Overall acceleration rate, β200 0.18 0.01 14.08 66 <0.001
G8
Overall mean, β000 296.92 1.18 251.51 66 <0.001
Overall mean yearly change rate, β100 -0.45 0.20 -2.19 66 0.032
Overall acceleration rate, β200 0.15 0.02 10.26 66 <0.001
G10
Overall mean, β000 289.29 1.10 262.31 66 <0.001
Overall mean yearly change rate, β100 -0.72 0.26 -2.80 66 0.007
Overall acceleration rate, β200 0.07 0.02 3.73 66 <0.001
48
Now, I move on to the consideration of the deviation of the individual school change trajectory
and the county change trajectory from the mean curves. For example, for the 5th grade FCAT math
scores, the estimates for the variance (e0) of individual schools’ initial scores (ψ00) and for the variance
(e1, e2) of the annual change parameters (ψ10, ψ20) are 645.71 and 9.72, 0.05 respectively. In order to
decide whether there are true variation in the individual schools’ initial scores and the annual change
parameters, I use χ2 statistics. A test statistic for the variance of the intercept term of 21218.58 (df =
1906, p < 0.001) leads me to reject the null hypothesis and conclude that schools vary significantly in
their initial FCAT math scores in the first year they took the FCAT math. The corresponding χ2
statistics for the hypothesis that there are no differences among schools’ annual change rates are
4082.01 (df = 1906, p < 0.001) for YEAR term and 3814.81 (df = 1906, p<0.001) for YEARSQ term,
which leads me to conclude that there are significant variation among schools’ annual change rates.
The estimates for the variance of counties’ initial mean scores and their annual change parameters π00,
π10 and π20 are 58.19, 1.58 and 0.008, respectively. The same logic applies to the county initial status
(χ2 = 303.63, df = 66, p < 0.001) and the county change rates (χ2 = 349.46, df = 66, p < 0.001 for YEAR
term and χ2 = 258.28, df = 66, p < 0.001 for YEARSQ term) which means that significant variation exist
among them. The same logic is applicable to the results from the FCAT reading scores. All the random
effects suggest significant variation in the initial status and the annual change rates except the county
parameters for the 10th grade FCAT math scores and the county initial status for the 10th grade FCAT
reading scores (See the tables in Appendix 3). These parameters will be set as non-randomly varying in
the following models in this study.
Table 4-9 Correlations between the initial status and the annual change rates
Initial mean scores School Level County Level
YEAR YEARSQ YEAR YEARSQ
Math
G5 -0.297 0.075 -0.267 0.022
G8 -0.186 -0.155 -0.059 0.281
G10 -0.379 0.163 0.315 -0.584
Reading
G5 -0.117 -0.094 -0.171 -0.148
G8 -0.095 -0.165 -0.205 -0.005
G10 0.074 0.105 0.807 -0.970
In order to check whether the significant variation in the initial status and the annual change
rates among schools and counties come from substantial differences or from model errors, I consider
49
the reliabilities of the initial status and the change rates for schools and counties shown in the Tables in
Appendix 3. The reliability estimates also suggest that sufficient variability exists across schools and
counties as is supported by the χ2 statistics in the homogeneity tests of variance. The results of the
homogeneity tests of variance in the random effect panels and the reliability estimates in the reliability
panels of the Tables in Appendix 3 warrant modeling each parameter as a function of both school- and
county-level variables.
In the last panels of the tables in Appendix 3, we find the decomposition of the correlations
between the initial status and the annual change rates into its school-(level-2) and county-level (level-3)
components. The estimated correlation between the school initial status and the school annual change
rate is, i.e., -0.297, and this relationship at the county level is -0.267 for the 5th grade FCAT math
scores. These negative correlations mean that the higher the initial status of schools and counties are,
the smaller the annual change rates among schools and counties are. On the contrary, as shown in Table
4-9, the correlation between the initial status and the annual change rates are positive in the 10th grade
FCAT math scores at the county level and the 10th grade FCAT reading scores in both school and
county level. This means, for example, that the 10th grade FCAT math and reading scores of counties
grow faster if the county’s 10th grade FCAT scores were higher in the first year (1998).
Table 4-10 Reductions of Variance in year effects by the Yearly Change Models
Random Effect ANOVA Model Yearly Change Model
Variance ICC Variance ICC Var. Explained
Math
G5 Year effect, ε 212.34 0.3197 81.96 0.1174 0.6140
G8 Year effect, ε 110.08 0.2450 42.23 0.0608 0.6164
G10 Year effect, ε 121.65 0.1385 49.40 0.0546 0.5939
Reading
G5 Year effect, ε 169.76 0.2435 93.89 0.1335 0.4469
G8 Year effect, ε 103.28 0.1599 53.99 0.0818 0.4772
G10 Year effect, ε 103.20 0.0911 70.67 0.0697 0.3152
The comparisons of Level 1 variance explained by the models are presented in Table 4-10. The
Yearly Change Models explain almost 60 % of the variance in Level 1, or year effects in the FCAT
math scores by introducing the year terms and year squared terms into the ANOVA models. Though
the year effect variance in the FCAT reading scores are explained less well by the Yearly Change
Models than in the FCAT math scores, the decreases of variance range about from 32 % to 48 %8.
8 The positive yearly change rates for math mean that the Floridian public schools have performed better year by year. The
50
The main interest of this study is what contributes to the differences in the initial mean scores
and the yearly change rates in the FCAT math and reading scores among public schools and between
counties in Florida. Variance are significant except the county variance for the 10th grade FCAT math
scores and for the variance for the overall mean FCAT reading score of the 10th grade (See the random
effects panels in the Appendix 3). Therefore, the following sections will explore where the achievement
variation among schools and counties come from by using three competing theories: the school
effectiveness theory, the market competition theory, and social inequality theory.
In following three sections, I will test whether the theories explaining the academic
achievement of public schools are valid, or which theory would explain the differences in academic
achievements better among public schools and across counties in Florida. The school effectiveness
theory emphasizes the freedom from direct democratic control and bureaucratic red-tape, school
autonomy and accountability, while the market competition theory focuses on the market-like
institutional settings in education. The competition among public schools and various educational
service providers will improve the academic performance of public schools as the free markets are
assumed to do in economics. On the other hand, the social inequality theory argues that it is not the
schools but the families and communities that are more influential on student achievement and the
school performance. These competing theories will be tested by HLM models using the Floridian
public school data.
4.3 Testing the School Effectiveness Theory
In this section, I will examine whether the school effectiveness theory is valid with charter-
school policy in Florida. If the theory works in the public schools of Florida, the achievement levels of
charter schools would be higher than those of traditional public schools, which will be captured by the
higher yearly change rates of charter schools. If charter schools show higher or lower initial mean
scores without the positive annual change rates, then charter schools are thought not to be more
effective than TPSs but to be just ‘cream-skimming’ or ‘drawing low performing students’ from nearby
traditional public schools.
proportion of explained variance by the Yearly Change Models means that about half of the yearly changes in the FCAT
scores are caused just by the year changes! However, what leads to these positive annual change rates in the FCAT math
scores and negative annual change rates in the FCAT reading scores is another issue so that it would not be examined nor
discussed in this study.
51
The charter school advocates contend that charter schools with the new combination of
autonomy and accountability will create better learning programs than their local alternatives. They are
free from the inefficient democratic control by the education committees and from the bureaucratic red-
tape that Chubb and Moe (1990) criticized as the main cause of the failures in public school systems.
When Budde (1988) proposed Education by Charter as a means to renovate failing public schools, he
assumed that education by charter would allow teachers more control over their instruction, which will
make teachers in public schools more responsible for their teachings. On the other hand, charter
schools would encourage the students and the parents to become more responsible for their learning
and behavior, and to get involved more actively. Also one of the main purposes of charter-school
policy introduction in Florida was to improve students’ and schools’ academic performance.
To test whether the assumed improvement in student and school academic performance has
been really achieved by charter schools in Florida, I will examine the public school test scores by
comparing the initial mean status and the annual change rates of charter schools and those of traditional
public schools. If charter schools have outperformed traditional public schools, they will show higher
annual change rates regardless of their initial status. The School Effectiveness Models will be as
follows:
Level-1 Model
MSSmti = ψ0ti + ψ1ti*(YEARmti) + ψ2ti*(YEARSQmti) + εmti
Level-2 Model
ψ0ti = π00i + π01i*(CHARTERti) + e0ti
ψ1ti = π10i + π11i*(CHARTERti) + e1ti
ψ2ti = π20i + π21i*(CHARTERti) + e2ti
Level-3 Model
π00i = β000 + r00i π01i = β010 + r01i π10i = β100 + r10i
π11i = β110 + r11i π20i = β200 + r20i π21i = β210 + r21i,
where
CHARTERti is a dummy variable whose value is one if the school t in county i is a charter
school, and otherwise zero.
Tables 4-11 and Table 4-12 show the fixed effects from the models with charter-school dummy
variables in the school level (level 2). These fixed effects provide information about the charter-school
52
effects on the FCAT scores. If the coefficients of CHARTER variable prove to be significant, the
charter schools differ from traditional public schools in the schools’ average initial status or the annual
mean change rates.
Table 4-11 Results from the School Effectiveness Models for the FCAT Math Scores
Fixed Effect Coefficient SE t-ratio d.f. p-value
G5
For Initial mean score, ψ0
Overall mean score, β000 306.45 1.32 231.81 66 <0.001
CHARTER, β010 -6.33 4.20 -1.51 66 0.137
For YEAR slope, ψ1
Overall mean change rate, β100 3.51 0.22 16.07 66 <0.001
CHARTER, β110 0.97 0.88 1.10 66 0.273
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.10 0.02 -5.99 66 <0.001
CHARTER, β210 -0.006 0.08 -0.08 66 0.940
G8
For Initial mean score, ψ0
Overall mean score, β000 305.90 1.43 213.37 66 <0.001
CHARTER, β010 1.35 2.58 0.52 66 0.603
For YEAR12 slope, ψ1
Overall mean change rate, β100 1.71 0.09 19.49 66 <0.001
CHARTER, β110 1.51 0.27 5.64 66 <0.001
G10
For Initial mean score, ψ0
Overall mean score, β000 300.59 1.48 202.71 66 <0.001
CHARTER, β010 -7.52 5.13 -1.47 66 0.148
For YEAR slope, ψ1
Overall mean change rate, β100 3.84 0.19 19.72 66 <0.001
CHARTER, β110 -1.74 1.15 -1.52 66 0.134
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.17 0.01 -12.35 66 <0.001
CHARTER, β210 0.15 0.11 1.37 66 0.176
Charter schools are similar to TPSs in the initial mean scores of the FCAT math scores in all
grades. As shown in Table 4-11, the coefficients of the CHARTER variables for the 5th and 10th graders
are insignificant for the initial status and the annual change rates, which means the charter schools are
53
not different from traditional public schools in their first year9 FCAT math scores and the annual
change rates throughout the period. However, the coefficient of the CHARTER variable for the 8th
grade FCAT math scores is significant to the annual change rates. This means that the charter-school
students have gained 1.51 scale-score points more on the FCAT math than traditional public school
students every year on average. This could indicate that charter middle schools teach the 8th grade
students to make more progress in the FCAT math scores.
Table 4-12 Results from the School Effectiveness Models for the FCAT Reading Scores
Fixed Effect Coefficient SE t-ratio d.f. p-value
G5
For Initial mean score, ψ0
Overall mean score, β000 295.44 1.40 210.56 66 <0.001
CHARTER, β010 -12.43 3.88 -3.21 66 0.002
For YEAR slope, ψ1
Overall mean change rate, β100 -0.80 0.18 -4.46 66 <0.001
CHARTER, β110 3.79 0.62 6.15 66 <0.001
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.19 0.01 14.40 66 <0.001
CHARTER, β210 -0.20 0.04 -4.47 66 <0.001
G8
For Initial mean score, ψ0
Overall mean score, β000 298.34 1.38 216.79 66 <0.001
CHARTER, β010 -9.89 3.51 -2.82 66 0.006
For YEAR slope, ψ1
Overall mean change rate, β100 -0.99 0.17 -5.85 66 <0.001
CHARTER, β110 4.08 0.62 6.60 66 <0.001
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.19 0.01 13.79 66 <0.001
CHARTER, β210 -0.23 0.05 -4.35 66 <0.001
G10
For Initial mean score, ψ0
Overall mean score, β000 295.28 1.46 202.93 66 <0.001
CHARTER, β010 -21.96 5.93 -3.70 66 <0.001
For YEAR slope, ψ1
Overall mean change rate, β100 -0.86 0.23 -3.75 66 <0.001
CHARTER, β110 0.47 1.61 0.29 66 0.77
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.09 0.02 5.36 66 <0.001
CHARTER, β210 0.00 0.18 -0.02 66 0.985
9 The first year in this study is set by the year that each school took the FCAT and was reported in the FDOE data sets for
the first time.
54
This result is contradictory to the findings of Sass (2006) except the 5th grade FCAT math
scores. His analyses showed that the FCAT math scores of for the 8th and 10th graders were lower at the
first year, but those deficits were eliminated after three to five years of operation (p. 112). Greene et al.
(2003) found greater annual gains in math scores of charter-school students, which is not congruent to
the findings here.
On the other hand, the results from the models for the FCAT reading scores show different
pictures for charter schools. In all grades, the coefficients of the CHARTER variable for the initial
status are negative, and the gap between charter schools and TPSs is greatest among high schools
(21.96 scale-score points) and smallest among middle schools (9.89 scale-score points). However, the
annual change rates in the 5th and 8th grade FCAT reading scores for charters are significantly positive
and large enough to cover the deficits in the initial mean scores in three to five years. These results
could be interpreted as another indicator of charter-school effectiveness. In other words, charter schools
drew low performing students from nearby TPSs, and then they have educated the students with lower
academic achievement to be more proficient in the 5th and 8th grade FCAT reading in three or four
years.
Crew and Anderson (2003) reported similar results that charter schools underperformed
compared to TPSs in the early years after charter schools opened, i.e., 1999 or 2000 in Florida. These
results in reading scores are similar with the findings of Greene et al. (2003), Hoxby (2004), and Sass
(2006). Hoxby found that charter-school students were more likely to be proficient in the 4th grade
FCAT reading in 2002-200310. Sass found that the FCAT reading scores of students in the newly
opened charter schools were below those of students in TPSs, but after five years or longer of operation,
the reading scores of charter-school students were higher than those in TPSs. But, the results for the
reading scores of charter high schools are opposite to Sass’s findings. He found that the students in
charter high schools outperformed their peers in TPSs with the same initial status at the first year, but
had positive annual change rates, but my results show the much lower initial status (21.96 scale-score
points below) of charter high schools than those of TPSs and the same annual change rates.
Overall, charter schools in Florida appear to have recruited low performing or similar students
in math and reading from nearby TPSs or the community, and have operated more effectively than
TPSs did in that they show positive annual change rates in the 8th grade FCAT math and the 5th and 8th
grade FCAT reading scores.
10 I assume that Hoxby’s results reflect this logical inference: The charter schools that opened early could make up the
deficits in the initial scores in 2002-2003.
55
Two points need to be mentioned. Greene et al. (2003), Hoxby (2004), and Sass (2006) did not
control the schools’ or the students’ demographic characteristics11, as I did not in these school
effectiveness models. Logically the next tasks will be the test of robustness of charter-school effects on
schools’ academic achievement by introducing various controls which will be done in the latter part of
this chapter. Second, the reductions in the level 2 variance components are small12, and statistically
significant variation still exists among public schools’ FCAT scores, which warrants more
sophisticated modeling to explain them (See the level-2 random effect panels of the tables in Appendix
4).
Next question is related to the county level effects: Does the introduction of charter-school
policy to promote the effectiveness of public schools by giving more autonomy and requiring stricter
accountability really bring the better academic achievement of public schools within the county? To
explore this county policy effect on public schools, I will formulate the Charter-school Policy Models
by introducing charter-school policy variables in level 3:
Level-1 Model
MSSmti = ψ0ti + ψ1ti*(YEAR12mti) + ψ2ti*(YEARSQmti) + εmti
Level-2 Model
ψ0ti = π00i + e0ti
ψ1ti = π10i + e1ti
ψ2ti = π20i + e2ti
Level-3 Model
π00i = β000 + β001(YEARSADOPTi) + β002(ADOPTIONi) + r00i
π10i = β100 + β101(YEARSADOPTi) + β102(ADOPTIONi) + r10i
π20i = β200 + β201(YEARSADOPTi) + β202(ADOPTIONi) + r20i,
11 Hoxby (2004) picked the nearest regular public schools to be compared with charter schools assuming that those regular
public schools would have similar demographic compositions. But since charter schools usually recruit students from many
neighboring school districts in Florida, this matching method couldn’t replace the controls of demographic characteristics.
Sass (2006) also used non-structural moves as a control variable which can reflect the socio-economic status of student’s
family, but only in indirect way.
12 I calculated the proportions of explained variance in the initial mean scores and the annual change rates by the Charter
School Effects models. Most of them range from 2.97% to 17.79%, but the variance in the 8th reading annual change rates
and that in the 10th reading initial mean scores were 31.17% and 30.77%, respectively.
56
where
YEARSADOPTi means the number of years after the county i adopted the charter-school
policy;
ADOPTIONi is a dummy variable whose value is one if the county i adopted the charter
school policy during the period, otherwise zero.
Table 4-13 and Table 4-14 present the fixed effect results from the Charter-school Policy Models for
the FCAT math and reading scores (See Appendix 4 for the random effect results).
Table 4-13 Results from the Charter Policy Models for the FCAT Math Scores
Fixed Effect Coefficient SE t-ratio d.f. p-value
G5
For Initial mean score, ψ0
Overall mean score, β000 303.09 3.27 92.63 64 <0.001
YEARSADOPT, β001 -0.00 0.42 -0.002 64 0.999
ADOPTION, β002 4.04 5.45 0.74 64 0.461
For YEAR slope, ψ1,ψ1
Overall mean change rate, β100 3.36 0.39 8.70 64 <0.001
YEARSADOPT, β101 0.17 0.08 2.05 64 0.044
ADOPTION, β102 -1.40 0.95 -1.47 64 0.148
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.07 0.03 -2.02 64 0.048
YEARSADOPT, β201 -0.01 0.006 -2.09 64 0.040
ADOPTION, β202 0.08 0.07 1.16 64 0.252
G8
For Initial mean score, ψ0
Overall mean score, β000 297.81 2.91 102.46 64 <0.001
YEARSADOPT, β001 -0.57 0.49 -1.16 64 0.250
ADOPTION, β002 11.22 5.39 2.08 64 0.041
For YEAR slope, ψ1,ψ1
Overall mean change rate, β100 2.05 0.15 13.80 64 <0.001
YEARSADOPT, β101 0.07 0.03 2.23 64 0.029
ADOPTION, β102 -0.90 0.30 -3.00 64 0.004
G10
For Initial mean score, ψ0
Overall mean score, β000 296.68 3.96 74.99 64 <0.001
YEARSADOPT, β001 -0.34 0.28 -1.25 64 0.216
ADOPTION, β002 6.48 4.75 1.36 64 0.177
For YEAR slope, ψ1,ψ1
Overall mean change rate, β100 3.61 0.37 9.79 64 <0.001
YEARSADOPT, β101 -0.11 0.06 -1.95 64 0.055
ADOPTION, β102 1.05 0.58 1.82 64 0.074
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.15 0.02 -6.82 64 <0.001
YEARSADOPT, β201 0.01 0.00 2.35 64 0.022
ADOPTION, β202 -0.09 0.04 -2.32 64 0.024
57
Table 4-14 Results from the Charter Policy Models for the FCAT Reading Scores
Fixed Effect Coefficient SE t-ratio d.f. p-value
G5
Initial mean score, ψ0 Overall mean score, β000 293.27 2.58 113.54 64 <0.001
YEARSADOPT, β001 2.74 5.31 0.52 64 0.608
ADOPTION, β002 -0.08 0.47 -0.16 64 0.871
YEAR slope, ψ1, ψ1 Overall mean change rate, β100 -0.54 0.43 -1.27 64 0.208
YEARSADOPT, β101 -0.63 0.87 -0.73 64 0.471
ADOPTION, β102 0.03 0.07 0.40 64 0.692
YEARSQ slope, ψ2 Overall mean acceleration rate, β200 0.17 0.03 5.71 1597 <0.001
YEARSADOPT, β201 0.04 0.06 0.65 1597 0.519
ADOPTION, β202 0.00 0.01 -0.19 1597 0.852
G8
Initial mean score, ψ0
Overall mean score, β000 294.90 2.26 130.39 64 <0.001
YEARSADOPT, β001 -0.65 0.44 -1.48 64 0.143
ADOPTION, β002 9.24 4.93 1.87 64 0.066
YEAR slope, ψ1,ψ1
Overall mean change rate, β100 -0.94 0.25 -3.68 64 <0.001
YEARSADOPT, β101 0.09 0.08 1.14 64 0.259
ADOPTION, β102 -0.32 0.84 -0.38 64 0.706
YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.20 0.02 10.17 64 <0.001
YEARSADOPT, β201 0.00 0.01 -0.35 64 0.725
ADOPTION, β202 -0.03 0.06 -0.52 64 0.608
G10
Initial mean score, ψ0
Overall mean score, β000 291.22 4.39 66.30 64 <0.001
YEARSADOPT, β001 -0.76 0.27 -2.85 64 0.006
ADOPTION, β002 7.83 5.14 1.52 64 0.133
YEAR slope, ψ1,ψ1
Overall mean change rate, β100 -1.55 0.46 -3.40 64 0.001
YEARSADOPT, β101 -0.12 0.07 -1.56 64 0.124
ADOPTION, β102 1.91 0.72 2.65 64 0.01
YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.12 0.03 3.42 64 0.001
YEARSADOPT, β201 0.01 0.00 2.02 64 0.047
ADOPTION, β202 -0.13 0.05 -2.63 64 0.011
No differences between charter counties and non-charter counties are detected in the counties’
initial mean status in the 5th and 10th grade FCAT math scores and the 5th and 8th grade FCAT reading
scores. Only the FCAT math scores of 8th graders in counties that implemented charter-school policy
58
were higher in the initial mean scores than those in counties that did not, while the initial mean FCAT
reading scores of 10th graders were lower in charter counties. The annual change rates13 of the 8th grade
FCAT math scores in charter counties were negative so that the gaps in the 8th grade FCAT math scores
between TPSs and CSs will get narrower (See the middle panel in Table 4-13). Also the annual change
rates of the 10th grade FCAT math scores in the charter counties were small but negative. However, the
annual change rates of the 5th grade FCAT math scores and the 10th reading scores in charter counties
were positive.
Overall effects of the charter policy adoption in counties were mixed on the initial mean scores
and on the annual change rates of the FCAT math and reading, while the charter-school policy adoption
didn’t affect the 5th and 8th grade FCAT reading scores. When we plug the average years of charter
adoption in counties, the charter-school policy adoption effects on the 5th grade FCAT math and the
10th grade FCAT reading scores were positive, while the effects on the 8th and 10th grade FCAT math
scores were negative.
Even though some county level charter policy predictors are significant, there are still
significant variance among counties except in the results from the models for 10th math and reading
scores. The variance reductions, or the variance explained by the county charter policy adoption
variables are little. The models for the 8th grade FCAT math and reading scores were the exceptions.
Thirty eight percents and 10.34% of the variance in the county initial mean scores for the 8th grade
FCAT math and reading scores14 were reduced by the county charter-school policy variables compared
to the variance in the Yearly Change Model (See the Table A3-2-1 and Table A4-8, and Table A3-5
and Table A4-11 in Appendix).
4.4 Testing the Market Competition Theory at the School level
In this section and the next, I will examine whether the market competition theory is working
with charter-school policy in Florida. The main concern here is whether the introduction and the
increase of charter schools enforce traditional public schools to innovate to survive the competition
from charter schools. I will explore how much variance in the FCAT scores could be explained by the
competition pressure from charter schools on traditional public schools using the presence and the
13 I put the average years of charter policy adoption in counties to calculate the annual change rates, which were 5.94 years
for elementary, 5.49 years for middle school, and 3.97 years for high school.
14 In some models, the level 3 variance was larger than those for the Yearly Change Models, which means that charter
school policy made the county’s initial mean scores and annual change rates more varying.
59
numbers of charter schools within a certain radius and the distances to the nearest charter school at the
school level and the percentage of charter-school students and the percentage of private school and
home education students at the county level as the measures of competition pressure. These analyses
will use datasets containing only traditional public schools that are different from those used in the
previous analyses.
The descriptive characteristics of the competitive environment around TPSs in the datasets are
shown in Table 4-15. Seventy five percent of traditional elementary schools have at least one
elementary charter school within a 5-mile radius, and 69 % and 61% of traditional middle and high
schools do, respectively. Traditional elementary schools have 1.47 elementary charter schools within a
5-mile radius on average, middle schools 1.16, and high schools less than one charter school. The
average distance from an elementary charter school to the nearest elementary charter schools is 6.37
miles, 7.82 miles for middle school, and 13.15 miles for high school.
The analyses of variance among the FCAT test scores of traditional public schools (ANOVA
models) will come first, and then the Yearly Change Models for only TPSs will come next. I will
compare the results from these analyses to the results from the Market Competition Models, but the
result tables from ANOVA Models and the Yearly Change Models for only TPSs are not provided in
this paper15. I build three types of Market Competition Model with charter-school predictors in level 2.
First I put the presence of charter schools within an N-mile radius (ANYCS-N; dummy variable), the
number of charter schools within a certain radius from a TPS (RAD-N), and then the distance to the
nearest charter school (MINDST) as level 2 predictors.
The models with the charter predictors are:
Level-1 Model
MSSmti = ψ0ti + ψ1ti*(YEARmti) + ψ2ti*(YEARSQmti) + εmti
Level-2 Model
ψ0ti = π00i + π01i*(ANYCS-Nti, or RAD-Nti, or MINDSTti) + e0ti
ψ1ti = π10i + π11i*( ANYCS-Nti or RAD-Nti, or MINDSTti) + e1ti
ψ2ti = π20i + π21i*( ANYCS-Nti or RAD-N ti, or MINDSTti) + e2ti
15 They are too many to present all, and they are not much different from the coefficients and variance in the tables in
section 4.2 and in Appendix 3.
60
Level-3 Model
π00i = β000 + r00i π01i = β010 + r01i π10i = β100 + r10i
π11i = β110 + r11i π20i = β200 + r20i π21i = β210 + r21i,
where
ANYCS-Nti is a dummy variable whose value is one if the traditional public school t
in a county i has any charter school within an N-mile radius (N is 25 for 2.5 miles 50 for
5 miles, and 100 for 10 miles), otherwise zero;
RAD-N ti is the number of charter schools within an N-mile radius from a traditional
public school t in a county i;
MINDSTti is the distances to the nearest charter school from a traditional public school t in a
county i.
Table 4-15 Description of Charter Competition Measures
Variable N Minimum Maximum Mean SD
Charter
Presence
Elementary
ANYCS25 1728 0 1 0.5087 0.50
ANYCS50 1728 0 1 0.7483 0.43
ANYCS100 1728 0 1 0.9132 0.28
Middle
ANYCS25 619 0 1 0.4814 0.50
ANYCS50 619 0 1 0.6914 0.46
ANYCS100 619 0 1 0.8578 0.35
High
ANYCS25 438 0 1 0.3744 0.48
ANYCS50 438 0 1 0.6073 0.49
ANYCS100 438 0 1 0.7991 0.40
Number of
Charter
Schools
Elementary
RAD25 1728 .00 5.25 0.48 0.80
RAD50 1728 .00 10.00 1.47 1.77
RAD100 1728 .00 24.50 3.73 3.57
Middle
RAD25 619 .00 4.40 0.40 0.63
RAD50 619 .00 6.50 1.16 1.40
RAD100 619 .00 13.50 2.98 3.07
High
RAD25 438 .00 3.00 0.23 0.41
RAD50 438 .00 5.50 0.65 0.85
RAD100 438 .00 14.67 1.49 1.71
Minimum
Distance
Elementary
MINDST
1728 0.00 137.2816 6.37 6.56
Middle 619 .00 217.57 7.82 11.66
High 438 0.15 239.96 13.15 24.99
16 These large numbers for the minimum distance are shown because some public schools are administered by a different
legal Local Education Agency from their geographical county. Only 12 cases for elementary school, 26 cases for middle
school, and 28 cases for high school were farther than 30 miles from the nearest charter school.
61
The summary of the fixed effects results from these models are presented in Table 4-16 and Table 4-
19 for the FCAT math scores, and in Table 4-17and Table 4-20 for the FCAT reading scores. None of
the fixed effect coefficients for the MINDST variable were statistically significant so that the summary
table is not presented here (See Table 5-12 to Table 5-18 in Appendix 5 for the results with MINDST
variables, the random effects and the details). Since the coefficients for the ANYCS100 and RAD100
variables in most of the models were not significant, I re-run those models without the ANYCS100 and
RAD100 variables. And the level 2 coefficients for the charter-school variables are set as non-
randomly varying, because their random effects were insignificant in most of the models.
The effects of charter-school presence within an N-mile radius on the initial mean scores of
TPSs were negative in the 5th and 8th grade FCAT math scores and the 5th grade FCAT reading scores;
neutral in the 8th and 10th grade FCAT reading scores; and positive in the 10th grade FCAT math
scores. The charter-school presence has negative influences on the annual change rates of the 10th
grade FCAT math and the 8th and 10th grade FCAT reading scores; neutral effects on the other FCAT
scores. One interesting fact is that if the charter-school presence has negative effects on the initial
mean scores, its effects on the annual change rates are neutral, while if its effects on the initial mean
scores are neutral or positive, it affects the annual change rates negatively. One plausible explanation
of the former relationship is that charter schools are more likely to locate in the districts which have
more low performing public schools. Glomm, Harris and Lo (2005) found that charter schools’
locations are negatively related to the test scores in Michigan; even though the relationship
disappeared when controlling other district’ characteristics (p. 454). I found also a significant
negative correlation between the FCAT math and reading scores and the number of charter school
within a certain radius, as shown in Table 4-18. The latter relationship could be a reflection of the
negative correlation between the initial mean scores and the annual change rates as mentioned in
Table 4-9. Another possibility is that charter schools draw more promising students from the nearby
traditional public schools, even though they are performing poorly at the time they move into charter
schools. This will be examined by introducing such variables as demographic characteristics in the
next section.
62
Table 4-16 Fixed Effects Results from the Models with Charter Presence Variable (Math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
G5
For Initial mean score, ψ0
Overall mean score, β000 313.41 1.89 165.83 45 <0.001
ANYCS25, β010 -9.16 2.06 -4.44 1584 <0.001
ANYCS50, β020 -3.37 1.70 -1.98 1584 0.048
For YEAR slope, ψ1
Overall mean change rate, β100 3.67 0.26 14.17 45 <0.001
ANYCS25, β110 0.22 0.31 0.72 1584 0.470
ANYCS50, β120 -0.35 0.28 -1.25 1584 0.212
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.12 0.02 -5.98 45 <0.001
ANYCS25, β210 0.00 0.02 0.01 1584 0.991
ANYCS50, β220 0.03 0.02 1.10 1584 0.271
G8
For Initial mean score, ψ0
Overall mean score, β000 306.74 2.78 110.33 44 <0.001
ANYCS25, β010 -6.41 2.25 -2.85 525 0.004
ANYCS50, β020 0.88 3.51 0.25 525 0.801
For YEAR slope, ψ1
Overall mean change rate, β100 1.73 0.13 13.28 44 <0.001
ANYCS25, β110 -0.16 0.12 -1.39 525 0.166
ANYCS50, β120 0.03 0.12 0.27 525 0.786
G10
For Initial mean score, ψ0
Overall mean score, β000 300.98 2.85 105.72 39 <0.001
ANYCS25, β010 -2.60 3.08 -0.84 309 0.400
ANYCS50, β020 -5.00 3.99 -1.25 309 0.211
ANYCS100, β030 6.84 2.86 2.39 309 0.017
For YEAR slope, ψ1
Overall mean change rate, β100 4.62 0.37 12.54 39 <0.001
ANYCS25, β110 -0.24 0.29 -0.84 309 0.404
ANYCS50, β120 0.26 0.45 0.58 309 0.563
ANYCS100, β130 -1.08 0.45 -2.41 309 0.017
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.23 0.02 -9.93 39 <0.001
ANYCS25, β210 0.03 0.02 1.37 309 0.171
ANYCS50, β220 0.00 0.03 0.04 309 0.971
ANYCS100, β230 0.06 0.03 2.14 309 0.033
63
Table 4-17 Fixed Effects Results from the Models with Charter Presence Variable (Reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
G5
For Initial mean score, ψ0
Overall mean score, β000 301.12 2.01 149.78 45 <0.001
ANYCS25, β010 -7.84 2.11 -3.71 1584 <0.001
ANYCS50, β020 -3.52 1.90 -1.85 1584 0.064
For YEAR slope, ψ1
Overall mean change rate, β100 -0.57 0.22 -2.55 45 0.014
ANYCS25, β110 -0.38 0.32 -1.16 1584 0.245
ANYCS50, β120 -0.13 0.29 -0.45 1584 0.653
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.17 0.02 10.62 45 <0.001
ANYCS25, β210 0.04 0.02 1.82 1584 0.069
ANYCS50, β220 0.01 0.02 0.29 1584 0.773
G8
For Initial mean score, ψ0
Overall mean score, β000 301.41 2.34 128.66 44 <0.001
ANYCS25, β010 -3.65 2.03 -1.79 477 0.074
ANYCS50, β020 0.57 2.54 0.22 477 0.824
For YEAR slope, ψ1
Overall mean change rate, β100 -0.74 0.29 -2.58 44 0.013
ANYCS25, β110 -1.17 0.37 -3.12 477 0.002
ANYCS50, β120 0.33 0.44 0.75 477 0.456
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.17 0.02 8.23 44 <0.001
ANYCS25, β210 0.07 0.03 2.93 477 0.004
ANYCS50, β220 -0.03 0.03 -0.87 477 0.387
G10
For Initial mean score, ψ0
Overall mean score, β000 298.15 2.21 134.81 39 <0.001
ANYCS25, β010 0.05 3.25 0.01 311 0.989
ANYCS50, β020 -2.21 3.34 -0.66 311 0.508
For YEAR slope, ψ1
Overall mean change rate, β100 -0.28 0.36 -0.79 39 0.437
ANYCS25, β110 -0.86 0.29 -2.93 311 0.004
ANYCS50, β120 -0.28 0.40 -0.70 311 0.486
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.05 0.02 2.00 39 0.053
ANYCS25, β210 0.04 0.03 1.68 311 0.095
ANYCS50, β220 0.03 0.03 1.02 311 0.310
64
Table 4-18 Pearson Correlations between the FCAT Scores and Charter Competition Variables
FCAT Scores RAD25 RAD50 RAD100 MINDST
Math G5 -.106** -.076** .022** .058** G8 -.117** -.155** -.096** .048** G10 -.087** -.070** -.010 .011
Reading G5 -.161** -.176** -.116** .120** G8 -.137** -.194** -.153** .059 G10 -.119** -.128** -.103 .023
Note: One asterisk (*) indicates that correlation is significant at the 0.05 level (2-tailed).
Table 4-19 Fixed Effects Results from the Models with Charter Numbers (Math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
G5
For Initial mean score, ψ0 Overall mean score, β000 311.30 1.27 244.43 45 <0.001
RAD25, β010 -4.43 1.09 -4.08 1584 <0.001
RAD50, β020 -2.38 0.61 -3.91 1584 <0.001
For YEAR slope, ψ1
Overall mean change rate, β100 3.49 0.23 14.97 45 <0.001
RAD25, β110 0.31 0.15 2.06 1584 0.039
RAD50, β120 -0.07 0.07 -1.10 1584 0.273
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.10 0.02 -6.02 45 <0.001
RAD25, β210 -0.01 0.01 -0.97 1584 0.334
RAD50, β220 0.00 0.00 0.92 1584 0.359
G8
For Initial mean score, ψ0
Overall mean score, β000 308.19 1.80 171.55 44 <0.001
RAD25, β010 -0.26 2.06 -0.13 525 0.899
RAD50, β020 -4.27 1.03 -4.16 525 <0.001
For YEAR slope, ψ1
Overall mean change rate, β100 1.61 0.09 17.81 44 <0.001
RAD25, β110 -0.30 0.15 -2.02 525 0.044
RAD50, β120 0.20 0.05 3.78 525 <0.001
G10
For Initial mean score, ψ0
Overall mean score, β000 303.06 2.12 143.20 39 <0.001
RAD25, β010 -1.27 3.31 -0.38 312 0.702
RAD50, β020 -0.24 2.15 -0.11 312 0.913
For YEAR slope, ψ1
Overall mean change rate, β100 3.99 0.25 15.86 39 <0.001
RAD25, β110 -0.21 0.41 -0.51 312 0.613
RAD50, β120 -0.13 0.17 -0.77 312 0.442
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.19 0.02 -11.73 39 <0.001
RAD25, β210 0.01 0.04 0.23 312 0.815
RAD50, β220 0.03 0.02 1.60 312 0.112
65
Table 4-20 Fixed Effects Results from the Models with Charter Numbers (Reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
G5
For Initial mean score, ψ0 Overall mean score, β000 299.52 1.36 220.08 45 <0.001
RAD25, β010 -3.74 0.98 -3.80 1584 <0.001
RAD50, β020 -2.74 0.65 -4.19 1584 <0.001
For YEAR slope, ψ1
Overall mean change rate, β100 -0.76 0.20 -3.78 45 <0.001
RAD25, β110 -0.06 0.11 -0.57 1584 0.569
RAD50, β120 -0.03 0.07 -0.42 1584 0.673
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.19 0.02 12.25 45 <0.001
RAD25, β210 0.02 0.01 1.39 1584 0.164
RAD50, β220 0.00 0.00 0.30 1584 0.763
G8
For Initial mean score, ψ0
Overall mean score, β000 303.51 1.44 210.81 44 <0.001
RAD25, β010 0.29 1.93 0.15 477 0.880
RAD50, β020 -4.32 0.92 -4.67 477 <0.001
For YEAR slope, ψ1
Overall mean change rate, β100 -1.03 0.20 -5.17 44 <0.001
RAD25, β110 -0.36 0.31 -1.16 477 0.246
RAD50, β120 0.16 0.16 1.04 477 0.297
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.18 0.02 12.14 44 <0.001
RAD25, β210 0.00 0.02 0.12 477 0.906
RAD50, β220 0.00 0.01 -0.11 477 0.916
G10
For Initial mean score, ψ0
Overall mean score, β000 298.26 1.85 161.16 39 <0.001
RAD25, β010 1.30 2.79 0.47 308 0.641
RAD50, β020 1.06 1.76 0.61 308 0.546
RAD100, β030 -1.88 0.80 -2.36 308 0.019
For YEAR slope, ψ1
Overall mean change rate, β100 -0.71 0.30 -2.38 39 0.022
RAD25, β110 -0.65 0.51 -1.26 308 0.207
RAD50, β120 -0.09 0.38 -0.23 308 0.816
RAD100, β130 0.16 0.11 1.43 308 0.153
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.07 0.02 3.13 39 0.003
RAD25, β210 0.01 0.04 0.31 308 0.755
RAD50, β220 0.00 0.03 0.08 308 0.934
RAD100, β230 0.01 0.01 0.73 308 0.469
66
All the coefficients of the RAD-N variables indicate negative or neutral relations to the initial
mean scores except the 10th grade FCAT math and to the change rates of TPSs. These relations also
may reflect the negative correlation between the initial FCAT scores and charter-school location.
Overall, no evidence is detected in the analysis of this section that charter-school presence, the numbers
of charter schools around TPSs, and the distance to the nearest charter school from a TPS do not create
market competition forcing TPSs to improve their academic effectiveness. The exception was the 5th
grade FCAT math scores, because TPSs that have more charter schools within 2.5-mile radius showed
lower initial status, but higher annual change rate in the FCAT math scores.
These results are different from the findings in Ertas (2007) and quite contradictory to those in
Sass (2006). Ertas found that the charter-school presence within 5-mile radius had no impact on the
writing scores of TPSs in Florida. Sass used the presence and the number of charter schools, and the
market share (a percentage of student enrollments in charter schools within a certain radius) as the
competition measures. His results indicated that all three measures within 2.5-mile radius affected the
math score positively, and that the charter presence within 5-mile radius and the market share of charter
schools within 10-mile radius had positive impacts on the math scores in Florida, while no measure
within any radius harmed the reading scores (p. 117-118). But, my results showed that all measures for
market competition show either negative or neutral effects on initial status except for the 10th initial
math scores. Also effects are negative or neutral on the annual change rates except for the 5th math
scores. For the case of the 5th math scores, the number of charter schools within a 2.5-mile radius
positively affected change rates. For example, if a TPS has 1 charter school within a 2.5 mile radius
(the mean number of elementary charter schools within 2.5-mile radius from an elementary TPS is
0.48), it will not catch up with its peer TPS without a close charter school during the period 1998-2009,
while if a TPS has 2 charter schools within the same radius which is four times larger than the mean
number of charter schools within a 2.5mile radius, it will outperform its peer TPS in 8 years. For the
case of positive impacts of the charter presence within 10-mile radius on the initial mean scores of the
10th grade FCAT math scores will not disappear throughout the period, because the negative YEAR
slope will be decelerated by the YEARSQ slope.
The competition effects of charter schools on TPSs at the county level will be tested in this
section, too. “Do the traditional public schools in counties with more school choice (charter schools,
private schools, and home education) have higher achievement in the initial status and higher mean
change rates of achievement? Does the higher percentage of students choosing alternatives to
traditional public schools create competitive environments in counties? The main contention of charter
school advocates is that destroying the exclusive monopoly by county education committee and
67
creating a market in education would stimulate the public school system to be efficient, innovative, and
better in academic performance.
Table 4-21 Distribution of County Level Competition Variables
N Min Max Mean SD Median*
Elementary
School
PCHARTER 45 0.04 21.72 3.56 4.38 2.47
PCSMED 45 0 1 0.51 0.51
Middle
School
PCHARTER 42 0.37 23.39 4.52 4.50 3.28
PCSMED 42 0 1 0.50 0.51
High
School
PCHARTER 37 0.06 27.15 2.58 4.75 0.86
PCSMED 37 0 1 0.51 0.51
All levels PPVTHE 45 3.38 32.42 12.38 5.80
Note: Twenty three counties have more elementary charter-school students than the median percentage,
21 counties for middle school, and 19 counties for high school.
I formulated the School Choice Models by introducing school choice variables such as the
percentage of charter-school students in a county (PCHARTER), the percentage of private and home
education students in a county (PPVTHE17), a dummy variable for the counties whose PCHARTER
values exceed the median value among charter counties (PCSMED) in level 3. The distributions of
these variables are shown in Table 4-2118:
Level-1 Model
MSSmti = ψ0ti + ψ1ti*(YEAR12mti) + ψ2ti*(YEARSQmti) + εmti
Level-2 Model
ψ0ti = π00i + e0ti
ψ1ti = π10i + e1ti
ψ2ti = π20i + e2ti
17 Since county data do not provide the information for the private and home education students classified by school levels,
the variable for the private and home education students, PPVTHEi, in all models in this section will have the same value
for all three levels of school.
18 The datasets used in the analyses of this section contain only the charter counties that have at least one charter school in
the given grades, because the analyses of the differences in school achievement between charter counties and non-charter
counties were already done in Section 4.3.
68
Level-3 Model
π00i = β000 + β001(PCHARTERi) + β002(PPVTHEi) + β003(PCSMEDi)+ r00i
π10i = β100 + β101(PCHARTERi) + β102(PPVTHEi) + β103(PCSMEDi)+ r10i
π20i = β200 + β201(PCHARTERi) + β202(PPVTHEi) + β203(PCSMEDi)+ r20i,
where
PCHARTERi means the percentage of charter-school students in a given school level in
county i;
PPVTHEi is the percentage of total private and home education students out of the
number of total students in the county i;
PCSMEDi is a dummy variable, which is 1 if the percentage of a county’s charter-school
students exceeds the median value of the percentages of charter-school students among
charter counties, otherwise 0.
The results from the models to test the market competition theory at the county level are
summarized in Table 4-22 for the FCAT math scores and Table 4-23 for the FCAT reading scores. The
percentages of charter-school students in counties (PCHARTER) have no impacts on the FCAT math
and reading scores in all grade levels except on the 5th grade FCAT math and reading scores. The
effects of PCHARTER on the 5th grade FCAT math scores is positive, while the direction of charter-
school competition effects on 5th grade FCAT reading scores is not decisive, because of the negative
YEAR slope (-0.09) and positive YEARSQ slope (0.01). For example, if a county has an average
percentage of charter-school students (3.56%), the negative effect of charter competition on the FCAT
reading scores will turn out to be positive in 10th year: the annual change rate in the 10th year will be
0.356 which comes from (-0.09)*3.56*10 + (0.01)*3.56*102. On the other hand, the dummy variables,
PCSMED, have negative or neutral effects on both the FCAT math and reading scores. The percentages
of private and home education students (PPVTHE) have negative or neutral effects on the schools
FCAT scores except the positive effect on the annual change rates of the 5th grade FCAT math scores.
The county level analyses indicate that, overall, the more charter students a county has, the lower the
FCAT math and reading scores are likely to be.
69
Table 4-22 Fixed effect Results from the Models with School Choice in Level 3 (Math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
G5
For Initial mean score, ψ0
Overall mean score, β000 313.38 4.88 64.24 42 <0.001
PCHARTER, β001 -0.23 0.37 -0.63 42 0.533
PPVTHE, β002 -0.39 0.31 -1.27 42 0.211
PCSMED, β003 0.48 3.48 0.14 42 0.890
For YEAR slope, ψ1
Overall mean change rate, β100 2.00 0.79 2.53 42 0.015
PCHARTER, β101 -0.12 0.07 -1.71 42 0.095
PPVTHE, β102 0.11 0.05 2.28 42 0.028
PCSMED, β103 0.90 0.58 1.56 42 0.126
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.01 0.05 -0.10 42 0.922
PCHARTER, β201 0.01 0.01 2.04 42 0.047
PPVTHE, β202 -0.01 0.00 -2.14 42 0.039
PCSMED, β203 -0.08 0.04 -2.02 42 0.050
G8
For Initial mean score, ψ0
Overall mean score, β000 314.76 4.26 73.90 41 <0.001
PCHARTER, β001 -0.38 0.63 -0.60 41 0.552
PPVTHE, β002 -0.55 0.28 -2.00 41 0.052
PCSMED, β003 -2.23 5.68 -0.39 41 0.696
For YEAR slope, ψ1
Overall mean change rate, β100 1.10 0.25 4.45 41 <0.001
PCHARTER, β101 -0.02 0.05 -0.44 41 0.659
PPVTHE, β102 0.04 0.02 2.08 41 0.043
PCSMED,β103 0.39 0.33 1.18 41 0.246
G10
For Initial mean score, ψ0
Overall mean score, β000 309.72 3.78 81.93 36 <0.001
PCHARTER, β001 0.20 0.30 0.66 36 0.511
PPVTHE, β002 -0.23 0.29 -0.80 36 0.430
PCSMED,β003 -8.27 3.40 -2.43 36 0.020
For YEAR slope, ψ1
Overall mean change rate, β100 3.98 0.68 5.87 36 <0.001
PCHARTER, β101 -0.08 0.06 -1.53 36 0.135
PPVTHE, β102 0.01 0.04 0.37 36 0.716
PCSMED,β103 -0.23 0.40 -0.57 36 0.570
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.21 0.05 -4.42 36 <0.001
PCHARTER, β201 0.01 0.00 1.56 36 0.129
PPVTHE, β202 0.00 0.00 0.01 36 0.990
PCSMED,β203 0.05 0.03 1.96 36 0.057
70
Table 4-23 Fixed effect Results from the Models with School Choice in Level 3 (Reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
G5
For Initial mean score, ψ0
Overall mean score, β000 303.57 5.08 59.74 42 <0.001
PCHARTER, β001 -0.58 0.39 -1.49 42 0.144
PPVTHE, β002 -0.45 0.32 -1.40 42 0.170
PCSMED,β003 0.28 4.13 0.07 42 0.945
For YEAR slope, ψ1
Overall mean change rate, β100 -1.25 0.67 -1.87 42 0.068
PCHARTER, β101 -0.09 0.04 -2.06 42 0.046
PPVTHE, β102 0.04 0.04 0.87 42 0.392
PCSMED,β103 0.46 0.45 1.03 42 0.310
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.21 0.05 4.19 42 <0.001
PCHARTER, β201 0.01 0.00 2.84 42 0.007
PPVTHE, β202 0.00 0.00 -0.57 42 0.571
PCSMED,β203 -0.03 0.03 -0.82 42 0.417
G8
For Initial mean score, ψ0
Overall mean score, β000 309.88 3.20 96.95 41 <0.001
PCHARTER, β001 -0.37 0.46 -0.79 41 0.435
PPVTHE, β002 -0.51 0.20 -2.49 41 0.017
PCSMED,β003 -2.58 4.74 -0.54 41 0.590
For YEAR slope, ψ1
Overall mean change rate, β100 -1.07 0.65 -1.64 41 0.108
PCHARTER, β101 -0.07 0.07 -0.98 41 0.332
PPVTHE, β102 0.01 0.03 0.25 41 0.801
PCSMED,β103 0.49 0.61 0.81 41 0.421
For YEARSQ slope, ψ2 Overall mean acceleration rate, β200 0.14 0.05 2.70 41 0.010
PCHARTER, β201 0.01 0.01 1.10 41 0.278
PPVTHE, β202 0.00 0.00 0.59 41 0.561
PCSMED,β203 -0.02 0.05 -0.35 41 0.731
G10
For Initial mean score, ψ0
Overall mean score, β000 301.91 3.98 75.94 36 <0.001
PCHARTER, β001 0.23 0.32 0.70 36 0.487
PPVTHE, β002 -0.04 0.26 -0.16 36 0.877
PCSMED,β003 -9.53 3.02 -3.16 36 0.003
For YEAR slope, ψ1
Overall mean change rate, β100 -0.91 0.78 -1.17 36 0.248
PCHARTER, β101 -0.06 0.07 -0.84 36 0.406
PPVTHE, β102 0.05 0.05 1.13 36 0.267
PCSMED,β103 -0.80 0.44 -1.83 36 0.075
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.09 0.05 1.76 36 0.087
PCHARTER, β201 0.00 0.00 0.52 36 0.609
PPVTHE, β202 0.00 0.00 -1.38 36 0.176
PCSMED,β203 0.08 0.03 2.93 36 0.006
71
4.5 Testing Social Equality Theory
I built two types of models to test social inequality theory: Charter-school Model and Social
Inequality Model. Charter-school Model is a combined model based on the School Effectiveness Model
and Market Competition Model in both school level and county level. It includes variables used in the
previous sections as CHARTER, ANYCS25, ANYCS50, RAD25, and RAD50 variables at the school
level and ADOPTION, YEARSADOPT, PCSMED, and PPVTHE variables at the county level. Social
Inequality Model will introduce many educational, socio-economic, racial/ethnic factor variables.
School level variables will include educational resources variables such as class size (CLSSZG5,
CLSSZG8L, and CLSSZG8M, etc), the number of students in schools (MEMBER), the percent of the
disabled students (PDABD), the percentage of teachers with advanced degree (PADVDG), the average
years of teacher experience (AVGYREXP), per-pupil-expenditure (PPESCH), the percentage of
instructional staffs (PINSTSTF), socio-economic status variables such as the percentage of students
eligible for free/reduced price lunch program (PFRL), stability rates (STABRATE), school location
(SUBURBAN; dummy variable with 1 for suburban, 0 for others), and racial/ethnic composition such as
the percentage of black students (PBLK), the percentage of Hispanic students (PHSP), and the
percentage of English language learner (PELL). And I will use county characteristics variables:
educational atmosphere variables such as the population per square mile (PPSM), high school
graduation rate (GRADRATE), the percentage of students absent more than 21 days (PABSNT21), the
per-pupil-expenditure for regular public schools (PPEREG), the percentage of classes taught by out-of-
field teachers (PCLSOOFT), the socio-economic status variables such as the median household income
(MINCOME), the percentage of children (age 5~17) in poverty (PPOOR517), the percentage of adults
over 25 with high school diploma or higher (HSOVERCT), and the percentage of adults with bachelor
degree or higher (BAOVERCT), and racial/ethnic composition variables such as the percentage of black
people (CPBLK), the percentage of Hispanics (CPHISP), and the percentage of English language
learner (CPELL) (See Appendix 9 for the definitions and details of variables).
Some school level variables in Social Inequality Models were county-mean-centered: class
sizes, PPE, PINSTSTF, STABRATE, PBLK, and PHSP at the school level. And some county level
variables were state-mean-centered: GRADRATE, PPEREG, MINCOME, HSOVER, BAOVER, CPBLK,
and CPHISP. This is why the overall initial mean scores in the Social Inequality Models for all grades
are much higher than those in the Charter-school Models. Most of level 2 coefficients were specified as
fixed or non-randomly varying in the final model due to the insignificant random effects in the early
72
trials. The results from Charter-school Models and Social Inequality Models are shown in Table 4-24,
Table 4-25, and Table 4-26 for the FCAT math scores and in Table 4-27, Table 4-28, and Table 4-29
for the FCAT reading scores. These tables include only the variables and their statistics whose p-values
are smaller than 0.100 (See Appendix 6 for the details of the results). All the coefficients of charter-
school dummy variables and the distances to the nearest charter schools were insignificant, which
means that charter schools are not different from TPSs in the initial mean scores and the annual change
rates, and that there is no competition pressure from nearby charter schools on student achievement.
For the FCAT math scores, charter schools showed no difference in the 5th and 8th grade
FCAT math scores when other factors are controlled. Especially, the positive change rate in the 8th
grade FCAT math scores disappeared in Social Inequality Model. However, charter schools seem to be
ineffective in that their initial mean scores of the 10th grade FCAT math scores were 13.11 scale-score
points higher than those of TPSs, but their FCAT scores will be below TPSs’ FCAT math scores for
most years during the period because their annual change rates are lower than those of TPSs. The
charter-school competition measures at the school level related to either slightly higher or lower initial
mean status in TPSs with nearby charter schools, but no difference in the annual change rates from
those of TPSs.
On the contrary, the educational resources, socio-economic status, and racial/ethnic
compositions in public schools affect the FCAT math scores significantly. For example, class sizes, the
percentage of disabled students, the percentage of students eligible for free/reduced price lunch, the
percentage of black students, and the percentage of English language learners influences the FCAT
math scores negatively, while teacher quality measures such as the percentage of teachers with
advanced degrees and the average years of experience, and the stability rate of students, have positive
effects on the FCAT math scores.
At the county level, the county's charter-school policy has negative impacts on the FCAT math
scores. Charter-school policy adoption and the years of adoption of a county were related to negative
annual change rates in the 5th and 8th grade. No competition measure at the county level has
significant influences on the FCAT math scores. No evidence supports Effective School Theory or
Market Competition Theory at the county level in Florida. However, the median household income is
positively related to the initial mean scores of the 5th and 8th FCAT math scores, while the county
percentage of black people and the percentage of children in poverty affected the initial mean scores of
the 8th and 10th grade FCAT math scores negatively, but no impact were found on the annual change
rates. At the county level, Social Inequality Theory is more relevant to explaining the variation in the
73
academic performance of counties than the School Effectiveness Theory and the Market Competition
Theory.
Table 4-24 Results from Base Model and Social Inequality Model (5th grade; Math)
Fixed Effect Coefficient d.f. p-value Coefficient d.f. p-value
For Initial mean score, ψ0
INTRCPT, β000 301.55 62 <0.001 364.21 50 <0.001
ADOPTION, β001 6.22 62 0.208 8.00 50 0.010
MINCOME, β0010
0.0007 50 0.029
PPOOR517, β0011
-0.97 50 0.069
CPBLK, β0014
-0.16 50 0.075
CHARTER, β010 3.79 1452 0.591 -3.13 1413 0432
ANYCS25, β020 -3.72 1452 0.010 0.32 1413 0.699
- RAD25, β040 -3.64 1452 <0.001 -1.23 1413 0.029
CLSSZG5, β060
-0.58 1413 <0.001
MEMBER, β070
0.00 1413 0.014
PDABD, β080
-0.37 1413 <0.001
PADVDG, β090
0.07 1413 0.054
AVGYREXP, β0100
0.25 1413 0.032
PPEREG, β0110
0.00 1413 0.029
PFRL, β0130
-0.61 1413 <0.001
PBLK, β0160
-0.20 1413 <0.001
For YEAR slope,ψ1
INTRCPT, β100 2.87 62 <0.001 4.64 50 0.205
ADOPTION, β101 -1.40 62 0.112 -2.42 50 0.011
YEARSADOPT β102 0.16 62 0.076 0.11 50 0.241
GRADRATE, β106
0.10 50 0.019
CHARTER, β110 0.04 1452 0.978 -0.13 1413 0.919
RAD25, β140 0.32 1452 0.086 0.22 1413 0.223
PDABD, β180
-0.16 1413 <0.001
PPEREG, β1110
0.00 1413 0.021
PFRL, β1130
0.03 1413 0.002
STABRATE, β1140
0.23 1413 <0.001
PHSP, β1170
-0.03 1413 0.003
For YEARSQ slope,ψ2
INTRCPT, β200 -0.03 62 0.493 -0.49 50 0.079
ADOPTION, β201 0.08 62 0.219 0.18 50 0.014
YEARSADOPT, β202 -0.01 62 0.046 -0.01 50 0.132
GRADRATE,β206
-0.01 50 0.029
CHARTER β210 0.05 1452 0.618 0.09 1413 0.396
PDABD, β280
0.01 1413 <0.001
PFRL, β2130
0.00 1413 0.027
STABRATE, β2140
-0.02 1413 <0.001
PHSP, β2170
0.00 1413 0.002
74
Table 4-25 Results from Base Model and Social Equality Model (8th grade; Math)
Fixed Effect Coef d.f. p-val Coef d.f. p-val
For Initial mean score, ψ0
INTRCPT, β000 301.14 62 <0.001 351.95 50 <0.001
YEARSADOPT, β002 9.61 62 0.088 -0.74 50 0.806
PCSMED, β003 -2.16 62 0.479 -3.29 50 0.032
MINCOME, β0010
0.0009 50 0.001
PPOOR517, β0011
-1.02 50 0.028
HSOVERCT, β0012
0.48 50 0.002
BAOVERCT, β0013
-0.55 50 0.064
CPBLK, β0014
-0.35 50 <0.001
CPHISP, β0015
-0.24 50 0.068
CPELL, β0016
1.23 50 0.011
CHARTER, β010 -16.54 216 0.205 -7.06 256 0.248
RAD25, β040 1.94 66 0.534 2.74 256 0.009
RAD50, β050 -3.56 66 0.028 0.57 66 0.428
MEMBER, β070
-0.01 256 <0.001
PDABD, β080
-0.73 256 <0.001
PADVDG, β090
0.23 256 <0.001
AVGYREXP, β0100
0.42 256 0.016
PFRL, β0130
-0.52 256 <0.001
STABRATE, β0140
0.66 66 0.012
PBLK, β0160
-0.22 256 <0.001
PELL, β0180
-0.29 256 0.048
For YEAR slope,ψ1
INTRCPT, β100 1.66 62 <0.001 2.65 50 0.046
YEARSADO, β102 -0.62 62 0.048 -0.37 50 0.271
PCSMED, β103 0.33 62 0.038 0.21 50 0.196
PPVTHE, β104 0.04 62 0.029 0.00 50 0.875
CPBLK,β1014
0.03 50 0.011
CHARTER, β110 0.77 216 0.325 0.60 256 0.425
RAD25, β140 -0.45 66 0.018 -0.25 256 0.054
RAD50, ,β150 0.20 216 0.002 0.10 256 0.111
PADVDG, β190
-0.01 256 0.026
AVGYREXP, β1100
-0.04 256 0.059
PPEREG, β1110
0.00 256 0.010
PBLK, β1160
0.01 256 0.051
75
Table 4-26 Results from Base Model and Social Equality Model (10th grade; Math)
Fixed Effect Coefficient d.f. p-value Coefficient d.f. p-value
For Initial mean score, ψ0
INTRCPT, β000 303.77 62 <0.001 321.52 50 <0.001
ADOPTION, β001 10.02 62 0.016 -1.49 50 0.602
GRADRATE,β006
0.39 50 0.008
CPBLK,β0014
-0.24 50 0.012
CHARTER, β010 5.77 164 0.549 13.11 125 0.024
ANYCS25, β020 -7.91 164 0.013 -3.03 125 0.106
ANYCS50, β030 4.62 164 0.097 4.94 125 0.004
RAD25, β040 5.47 164 0.159 5.09 125 0.027
RAD50, β050 -6.88 164 <0.001 -3.66 125 0.002
PADVDG, β090
0.27 125 <0.001
PINSTSTF, β0120
0.30 125 0.038
PFRL, β0130
-0.35 125 <0.001
STABRATE, β0140
1.73 125 <0.001
PBLK, β0160
-0.29 125 <0.001
For YEAR slope,ψ1
INTRCPT, β100 3.62 62 <0.001 8.10 50 0.008
CHARTER, β110 -4.58 164 0.003 -6.03 125 <0.001
MEMBER, β170
0.004 125 0.019
PDABD, β180
-0.23 125 <0.001
PFRL, β1130
0.03 125 0.062
PELL, β1180
-0.11 125 0.031
For YEARSQ slope,ψ2
INTRCPT, β200 -0.17 62 <0.001 -0.57 50 0.008
PCSMED, β203 0.10 62 0.026 0.08 50 0.091
CHARTER, β210 0.38 164 0.002 0.45 125 <0.001
MEMBER, β270
0.00 125 0.068
PDABD, β280
0.02 125 <0.001
PELL, β2180
0.01 125 0.011
For the FCAT reading scores, the results from the models for the FCAT reading scores tell
similar stories about the initial mean scores and the annual change rates in public schools. Charter
schools are not different from TPSs in terms of the initial scores and the annual change rates. The
competition indicators such as the presence and the number of charter schools around TPSs have some
impacts only on the initial mean scores of the 10th grade FCAT reading and the annual change rates of
the 8th grade FCAT reading scores. The TPSs with any charter school within 5 miles radius (ANYCS25)
76
were 3.44 scale-score points higher, and when TPSs have one more charter school within 2.5 miles
radius (RAD25) the initial mean scores increased by 4.97 scale-score points in the initial mean score of
the 10th grade FCAT reading scores. However, they have no impacts on the annual change rates. The
presence of charter schools within 2.5 miles radius affects the annual change rates of the 8th grade
FCAT reading scores negatively. These results indicate that charter schools are drawing low
performing students in reading from nearby TPSs, but that they didn’t force nearby TPSs to be more
effective.
However, educational environment, socio-economic, and racial factors of school level have
significant impacts on the TPS’s academic performance. School size (MEMBER), the percentage of
disabled (PDABD), the percentage of students eligible for free/reduced price lunch program (PFRL),
and the percentage of black students (PBLK) negatively affect the initial mean scores of the FCAT
reading, while the percentage of teachers with advanced degree (PADVDG), the teacher’s average
years of experience (AVGYREXP), and stability rates (STABRATE) have positive effects on the initial
mean scores for all grades. The percentage of the disabled students, the percentage of English language
learner (PELL), the percentage of students free/reduced lunch program, and class size are related to the
negative annual change rates.
At the county level, charter-school policy factors have no impacts on the county public school
performance in the FCAT reading. The effects of charter-school policy adoption on the annual change
rates of the 5th grade FCAT reading scores were mixed. It was negative in the early years and turned to
be positive in the 5th year. The charter-school competition indicator such as the dummy variable
(PCSMED) for the counties with more charter-school students than the state median percentage have
negative effects on the initial mean scores of the 8th grade FCAT reading, and the percentage of private
school and home education students (PPVTHE) have negative influences on the annual change rates of
the 8th grade FCAT reading scores. Similar to the school level variables of educational, socio-economic,
and racial factors, the percentage of the disabled students, the percentage of children in poverty, and the
percentage of black people influenced negatively the public school test scores, but the graduation rates
(GRADRATE), the median household income (MINCOME), and the percentage of adults with high
school diploma or higher (HSOVERCT) affect positively the initial mean scores and the annual change
rates in the FCAT reading.
As compared in Table 4-30 and Table 4-31, Social Inequality Models explained much more
variation among schools and across counties than did Charter-school Models. At the school level, the
variance in the initial school mean scores explained by Charter-school Models less than 18.26%, while
Social Equality Models reduces them more than 73.75%. Thirty six percent of variation in the county
77
initial mean scores of the 10th grade FCAT math were reduced by Charter-school Model, while 77.84%
of the variance was explained by Social Inequality Model. The variation in the annual change rates and
the acceleration rates at the school level and county level are better explained by Social Inequality
Models than by Charter-school Models.
Table 4-27 Results from Base Model and Social Inequality Model (5th grade; Reading)
Fixed Effect Coefficient d.f. p-value Coefficient d.f. p-value
For Initial mean score, ψ0 INTRCPT, β000 293.85 62 <0.001 333.92 50 <0.001 MINCOME,β0010
0.00 50 0.061 CPBLK,β0014
-0.26 50 <0.001 CPELL,β0016
-0.97 50 0.003 CHARTER, β010 -0.40 1386 0.956 -4.34 1347 0.285 ANYCS25, β020 -2.49 1386 0.086 0.78 1347 0.343 RAD25, β040 -3.51 1386 <0.001 -0.87 1347 0.122 MEMBER, β070
-0.01 1347 0.001 PDABD, β080
-0.24 1347 <0.001 PADVDG, β090
0.09 1347 0.009 AVGYREXP, β0100
0.64 1347 <0.001 PPEREG, β0110
0.001 1347 0.044 PFRL, β0130
-0.59 1347 <0.001 PBLK, β0160
-0.21 1347 <0.001
For YEAR slope,ψ1 INTRCPT,π10, β100 -1.27 62 0.033 0.75 50 0.799 ADOPTION, β101 -0.45 62 0.574 -1.56 50 0.045 PPSM,β105
0.00 50 0.069 GRADRATE,β106
0.08 50 0.006 PCLSOOFT,β109
-0.05 50 0.076 PPOOR517,β1011
0.23 50 0.077 CPBLK,β1014
0.04 50 0.066 CHARTER, β110 -0.26 1386 0.843 -0.96 1347 0.415 CLSSZG5, β160
-0.22 1347 <0.001 PDABD, β180
-0.16 1347 <0.001 AVGYREXP, β1100
-0.09 1347 0.007 STABRATE, β1140
0.26 1347 <0.001 PBLK, β1160
0.02 1347 0.018 PHSP, β1170
-0.02 1347 0.032
For YEARSQ slope,ψ2 INTRCPT, β200 0.22 62 <0.001 0.001 50 0.996 ADOPTION, β201 0.03 62 0.613 0.13 50 0.023 PPSM, β205
0.00 50 0.054 GRADRATE,β206
-0.01 50 0.009 CHARTER, β210 0.11 1386 0.285 0.17 1347 0.064 ANYCS25, β220 0.03 1386 0.090 0.03 1347 0.110 CLSSZG5, β260
0.02 1347 <0.001 PDABD, β280
0.01 1347 <0.001 STABRATE, β2140
-0.02 1347 <0.001 PBLK, β2160
0.001 1347 0.082 PHSP, β2170
0.0015 1347 0.027
78
Table 4-28 Results from Base Model and Social Equality Model (8th grade; Reading)
Fixed Effect Coef d.f. p-val Coef d.f. p-val
For Initial mean score, ψ0 INTRCPT, β000 297.25 272 <0.001 333.57 50 <0.001
YEARSADOPT, β002 9.31 272 0.014 0.50 50 0.856
PCSMED, β003 -1.07 272 0.577 -3.58 50 0.004
MINCOME,β0010
0.0009 50 <0.001
PPOOR517,β0011
-1.09 50 0.010
HSOVERCT,β0012
0.35 50 0.008
CPBLK,β0014
-0.35 50 <0.001
CPHSP,β0015
-0.27 50 0.017
CPELL,β0016
1.11 50 0.007
CHARTER, β010 -19.96 272 0.088 -7.00 237 0.242
ANYCS25, β020 1.82 272 0.443 2.16 237 0.074
RAD50, β050 -3.11 66 0.028 -0.61 66 0.512
MEMBER, β070
-0.01 237 <0.001
PDABD, β080
-0.73 237 <0.001
PADVDG, β090
0.23 237 <0.001
AVGYREXP, β0100
0.79 237 <0.001
PPESCH, β0110
0.0029 237 <0.001
PFRL, β0130
-0.31 237 <0.001
STABRATE, β0140
1.04 237 <0.001
PBLK, β0160
-0.19 237 <0.001
PELL, β0180
-0.28 237 0.047
For YEAR slope,ψ1 INTRCPT, β100 -1.32 62 0.015 6.34 50 0.033
PPVTHE, β104 0.00 62 0.967 -0.12 50 0.041
GRADRATE,β106
0.06 50 0.046
BAOVERCT,β1013
0.13 50 0.075
CPBLK,β1014
0.06 50 0.006
CHARTER, β110 0.48 272 0.805 0.48 237 0.773
ANYCS25, β120 -0.84 272 0.033 -0.95 237 0.005
RAD50, β150 0.07 272 0.633 0.31 237 0.029
PDABD, β180
-0.14 237 <0.001
AVGYREXP, β1100
-0.12 237 0.014
PPESCH, β1110
0.0006 237 0.013
PFRL, β1130
-0.04 237 0.006
STABRATE, β1140
0.12 237 0.007
PELL, β1180
-0.18 237 <0.001
For YEARSQ slope,ψ2 INTRCPT, β200 0.21 62 <0.001 -0.26 50 0.239
PPVTHE, β204 0.00 62 0.751 0.01 50 0.043
BAOVERCT, β2013
-0.01 50 0.065
CPBLK, β2014
0.003 50 0.092
CHARTER, β210 0.04 272 0.794 0.02 237 0.866
ANYCS25, β220 0.05 272 0.096 0.06 237 0.025
PDABD, β280
0.01 237 <0.001
PFRL, β2130
0.002 237 0.036
STABRATE, β2140
-0.01 237 0.020
PELL, β2180
0.02 237 <0.001
79
Table 4-29 Results from Base Model and Social Equality Model (10th grade; Reading)
Fixed Effect Coefficient d.f. p-vauel Coefficient d.f. p-vauel
For Initial mean score, ψ0 INTRCPT, β000 302.45 160 <0.001 306.55 109 <0.001
ADOPTION, β001 8.84 160 0.004 -0.81 109 0.714
GRADRATE, β006
0.33 109 0.002
MINCOME, β0010
0.00 109 0.081
CPBLK, β0014
-0.20 109 0.004
CHARTER, β010 -5.62 160 0.503 -1.15 109 0.825
ANYCS25, β020 -5.60 160 0.044 -2.08 109 0.220
ANYCS50, β030 1.92 160 0.442 3.44 109 0.034
RAD25, β040 4.24 160 0.213 4.97 109 0.018
PDABD, β080
-0.35 109 0.019
PADVDG, β090
0.26 109 <0.001
PFRL, β0130
-0.31 109 <0.001
STABRATE, β0140
1.52 109 <0.001
PBLK, β0160
-0.19 109 <0.001
PELL, β0180
-0.33 109 0.080
For YEAR slope,ψ1
INTRCPT, β100 -2.46 62 <0.001 9.02 50 0.004
ADOPTION, β101 1.26 62 0.083 -0.03 50 0.965
PCSMED, β103 -1.52 62 0.032 -0.95 50 0.180
PDABD, β180
-0.29 109 <0.001
CHARTER, β110 -0.86 160 0.641 -1.96 109 0.216
PPESCH, β1110
0.0005 109 0.033
PELL, β1180
-0.23 109 <0.001
For YEARSQ slope,ψ2
INTRCPT, β200 0.20 62 <0.001 -0.56 50 0.018
PCSMED, β203 0.13 62 0.014 0.07 50 0.171
PPVTHE, β204 -0.01 62 0.085 0.00 50 0.449
PPSM, β205
0.00 50 0.074
PPOOR517, β2011
0.02 50 0.023
PDABD, β280
0.02 109 <0.001
CHARTER, β210 0.06 160 0.661 0.11 109 0.397
PPESCH, β2110
-0.00005 109 0.019
PINSTSTF, β2120
-0.01 109 0.080
PELL, β2180
0.02 109 <0.001
4.6 Chapter Conclusion
The descriptive statistics of charter schools and traditional public schools show the main
characteristics of students in public schools. The characteristics of charter schools in the educational
environments, socio-economic status, and racial/ethnic compositions compared to those of TPSs could
80
be understood when they are classified by the school levels. The similarities and differences between
charter schools and TPSs were tested by the mean difference tests in this chapter.
I analyzed where the variance exist among schools and counties, and then check how much the
public schools have changed yearly in the FCAT math and reading scores in this chapter. ANOVA
models show that there are significant variation among public schools and counties in the FCAT math
and reading scores, and that the school characteristics are more influential on the school performance
than county characteristics or the year effects, especially in the higher grades. The reliability analysis
indicated that the significant differences exist in both the year effects and school effects which warrant
modeling each parameter as a function of school-level and county-level variables.
The Yearly Change Models show that the FCAT math and reading scores have changed in non-
linear forms except the 8th math scores, and that the annual change rates in the FCAT math scores
represented by the combination of the YEAR slope and the YEARSQ coefficient have never become
negative, while those of the FCAT reading scores turned to be negative in some years but positive in
most years through the period of 1998 through 2010. The variation in the initial mean scores and the
annual change rates are proved to be significant by the homogeneity tests of variance and the reliability
estimates in these models, too. The negative correlations between the initial mean scores and the annual
change rates were detected in both school level and county level.
This chapter tested three competing theories on school performance. The analyses showed that
school effectiveness theory works in some subjects and grades. Overall, charter schools in Florida
recruited low performing or similar students in math and reading scores from nearby TPSs or the
community, and have operated more effectively than TPSs did in that they show positive annual change
rates in the 8th grade FCAT math and the 5th and 8th grade FCAT reading scores. Market competition
theory does not explain well the variation among public schools and counties in the FCAT scores.
However, when the educational environment, socio-economic, and racial/ethnic factors were
introduced in Social Inequality Models, the significant and positive effects in both School Effectiveness
Models and Market Competition Models disappeared or turned out to be negative. On the other hand,
many educational, socio-economic, and racial/ethnic variables proved to be influential on student
achievement in TPSs. Social Inequality Models also explain better the differences in the FCAT scores
as shown in Table 4-30 and Table 4-31.
The analysis of the FCAT scores of charter schools by comparing those of TPSs showed that
charter schools in Florida attracted more low performing students in the FCAT reading than their
counterparts in the counties. School Effectiveness Models proved to be valid in some cases such as the
8th grade FCAT math scores and the 5th and 8th grade FCAT readings scores, because charter schools
81
achieved higher annual change rates in these areas than their peer TPSs in the counties. However,
charter schools have not made any difference in the other grades or subjects such as the 5th and 10th
grade FCAT math and the 10th grade FCAT reading. At the county level, School Effectiveness Models
were tested by introducing charter-school policy variables. The counties that adopted charter-school
policy have achieved higher annual change rates in the 5th and 10th grade FCAT reading. In other areas
and grades, there were no difference in terms of the FCAT scores between counties that had charter
schools and counties that have not.
Market Competition Theory was tested by the models that used the presence and the numbers of
charter schools within a certain radius and the distances to the nearest charter schools from a TPS as
predictors for the FCAT scores. However, no evidence was found in the school level analyses to
support Market Competition Theory because charter schools had no positive influences on the annual
change rates of TPSs. Instead, TPSs with more charter schools were more likely to be lower in their
initial mean FCAT scores, which may indicate that charter schools are likely to locate around low
performing traditional public schools. The significant negative correlation between the FCAT math and
reading scores and the number of charter school within a certain radius supported the charter-school
location hypothesis.
The county level analyses also proved that market competition theory do not explain the
differences in public school performance among counties because the counties with more charter
schools students and with more private school and home education students achieved lower on the
FCATs than other counties with fewer charter schools except for on the 5th grade FCAT math.
Therefore, I could conclude that the results from the most sophisticated models with various
control variables do not support School Effectiveness Theory or Market Competition Theory. The key
findings of Coleman report (1966) that student socio-economic and racial backgrounds influence
student achievement more in public schools are still true in the public schools in Florida almost five
decades later.
82
Table 4-30 Random Effect Results from Charter-school Models and Social Inequality Models (Math)
Random Effect
Yearly Change Base-Model Social Equality Model
Var Var d.f. χ2 p-value Var. Exp. Var d.f. χ2 p-value Var. Exp.
G5
level-1,ε 76.85 76.85 76.89
School initial mean scores, e0 405.54 356.79 1533 14609.22 <0.001 0.1202 87.09 1520 4712.12 <0.001 0.7852
School mean change rates, e1 7.8 7.71 1575 3446.45 <0.001 0.0115 6.47 1562 3124.1 <0.001 0.1705
School mean acceleration rates, e2 0.05 0.05 1575 3282.83 <0.001 0.0000 0.04 1562 3027.89 <0.001 0.2000
County initial mean scores, r00 63.78 56.72 38 152.83 <0.001 0.1107 15.79 26 187.45 <0.001 0.7524
County mean change rates, r10 1.88 1.54 38 317.64 <0.001 0.1809 1.26 26 257.86 <0.001 0.3298
County mean acceleration rates, r20 0.01 0.01 38 219.24 <0.001 0.0000 0.01 26 218.07 <0.001 0.0000
G8
level-1,ε 39.89 39.89 39.97
School initial mean scores, e0 377.8 308.83 355 10882.22 <0.001 0.1826 56.86 352 2348.838 <0.001 0.8495
School mean change rates, e1 1.03 0.93 385 1964.35 <0.001 0.0971 0.84 422 2012.433 <0.001 0.1845
County initial mean scores, r00 72.6 71.32 26 63.28 <0.001 0.0176 11.23 19 68.93636 <0.001 0.8453
County mean change rates, r10 0.23 0.09 26 49.4 0.004 0.6087 0.05 19 75.06867 <0.001 0.7826
G10
level-1,ε 30.77 30.76 30.8
School initial mean scores, e0 258.91 238.58 308 4932.03 <0.001 0.0785 67.97 295 1682.89 <0.001 0.7375
School mean change rates, e1 3.72 3.52 308 757.71 <0.001 0.0538 2.44 295 645.33 <0.001 0.3441
School mean acceleration rates, e2 0.02 0.02 308 611.71 <0.001 0.0000 0.01 295 535 <0.001 0.5000
County initial mean scores, r00 38.63 24.69 62 99.15 0.002 0.3609 8.56 50 98.55 <0.001 0.7784
County mean change rates, r10 0.9 0.83 62 111.77 <0.001 0.0778 0.51 50 98.68 <0.001 0.4333
County mean acceleration rates, r20 0.0039 0.0027 62 89.78 0.012 0.3077 0.0015 50 79.56 0.005 0.6154
83
Table 4-31 Random Effect Results from Charter-school Models and Social Equality Models (Reading)
Random Effect Yearly Change Base-Model Social Equality Model
Var Var d.f. χ2 p-value Var. Exp. Var d.f. χ2 p-value Var. Exp.
level-1,ε 90.05 90.06 89.99
School initial mean scores, e0 403.51 346.77 1527 12334.12 <0.001 0.1406 75.91 1514 3775.52 <0.001 0.8119
School mean change rates, e1 5.51 5.36 1527 2512.77 <0.001 0.0272 3.18 1514 2093.19 <0.001 0.4229
School mean acceleration rates, e2 0.02 0.02 1569 2157.63 <0.001 0.0000 0.01 1556 1859.27 <0.001 0.5000
County initial mean scores, r00 78.72 58.13 38 137.79 <0.001 0.2616 12.67 26 132.76 <0.001 0.8390
County mean change rates, r10 1.07 1.18 38 163.72 <0.001 -0.1028 0.98 26 139.98 <0.001 0.0841
County mean acceleration rates, r20 0.01 0.01 38 166.75 <0.001 0.0000 0.003 26 110.25 <0.001 0.7000
level-1,ε 43.93 43.92 44.07
School initial mean scores, e0 265.8 242.03 385 4230.08 <0.001 0.0894 43.61 387 1206.18 <0.001 0.8359
School mean change rates, e1 3.75 3.64 416 791.87 <0.001 0.0293 1.78 425 619.73 <0.001 0.5253
School mean acceleration rates, e2 0.02 0.02 416 704.04 <0.001 0.0000 0.01 425 563.37 <0.001 0.5000
County initial mean scores, r00 44.94
10.54 22 73.75 <0.001 0.7655
County mean change rates, r10 0.66 0.63 27 76.25 <0.001 0.0455 0.3 22 57.97 <0.001 0.5455
County mean acceleration rates, r20 0.0043 0.004 27 90.16 <0.001 0.0698 0.0017 22 57.78 <0.001 0.6047
level-1,ε 51.00 51.00 51.01
School initial mean scores, e0 181.59 169.63 275 2223.52 <0.001 0.0659 40.01 262 769.96 <0.001 0.7797
School mean change rates, e1 4.54 4.41 275 545.97 <0.001 0.0286 1.37 262 358.99 <0.001 0.6982
School mean acceleration rates, e2 0.02 0.02 275 427.17 <0.001 0.0000 0.01 262 346.37 <0.001 0.5000
County initial mean scores, r00 23.9 12.17 35 59.78 0.006 0.4908 13.34 35 100.96 <0.001 0.4418
County mean change rates, r10 1.08 0.59 31 59.76 0.002 0.4537 0.4 19 65.47 <0.001 0.6296
County mean acceleration rates, r20 0.0072 0.0032 31 58.35 0.002 0.5556 0.0012 19 45.09 <0.001 0.8333
84
CHAPTER FIVE
SOCIAL IMPACTS OF CHARTER SCHOOLS
I tested three theories on charter-school movement using Florida public school data.
School effectiveness theory and Market competition theory have no or very weak explanatory
power to explain where the variance among schools and across counties comes from and what
factors affect public school performance in terms of the FCAT math and reading scores. Since
“Florida’s charter law currently boasts an “A” grade and ranks as the 6th strongest charter school
law out of 41 in the nation.” (p. 22) according to The Accountability Report by the Center for
Education Reform, the findings in the chapter 4 are embarrassing. Then, one of the logically
following questions is: Does charter schools in Florida have any negative effect socially?
The opponents against school choice, especially against charter-school policy, have
argued that it would exacerbate the racial and residential segregation (Clotfelter, 2001; C.
Lubienski, 2001, 2005b; Renzulli, 2006; Renzulli & Evans, 2005). Recent studies have reported
that the desegregation trends are losing the momentum, and its negative effects may influence
black student academic achievement and widen the gap between racial groups (Hanushek, et al.,
2009; Hanushek & Rivkin, 2006). In this chapter, the main issue under investigation will be the
charter-school effects on racial segregation and socio-economic stratification in Floridian public
schools.
5.1 Preliminary Analyses of the Distribution of Demographic Compositions
In this section, I will examine how much charter schools and traditional public schools
differ from each other, and how much variation exists among public schools and across counties.
Table 5-1 shows the distributions of the mean absolute dissimilarity indexes (absolute DIs) and
the dissimilarity indexes (DIs), and the mean differences of them between TPSs and charter
schools. All mean absolute DIs for all racial/ethnic and socio-economic groups in TPSs and
Charter Schools (CSs) are significantly different each other. Charter schools deviate further from
the mean demographic composition of the counties in which they are located than their
85
counterparts in the counties during the period of 1998 through 2009 on average, as shown in the
first panels of each school level. The second panels indicate that elementary charter schools have
drawn much fewer black students, but that middle and high charter schools have recruited more
of them than TPSs have. The DIs of white students, or the mean differences of the percentages of
white students from the county means, looks small in both TPSs and CSs, but the absolute DIs
are relatively large in all school levels, suggesting that the proportion of white students in TPSs
and charter schools look like mirroring the county means in sector level, but that, at the school
level, there are many variation between schools. On the other hand, TPSs in a county have
served more students eligible for free/reduced price lunch (FRL) program than CSs have in all
grades.
Figure 5-1 shows the changes of absolute DIs and the DIs in demographic compositions
during the period for elementary schools. Middle schools and high schools have similar patterns
in absolute DIs and DIs, even though the slopes of all absolute DIs and DIs are less steep in both
of them. Figure 5-1 makes it clear that the differences of black students and the FRL recipient
percentages from the county means have increased, while a lower percentage of white students
and Hispanic students than the county mean have enrolled in elementary TPSs.
For the counties, I calculated the exposure rates and segregation index of all 67 counties
to check the differences at the county level19. The distributions of these indexes and racial/ethnic
compositions are presented in Table 5-2. The exposure rates of white students to non-white
students, black students and Hispanic students decrease due to the increase in the percentage of
white students as the school levels go higher. However, the segregation indexes decrease because
the possible exposure rates of white students to other racial/ethnic students decrease as the
percentages of non-white students in regular public schools go down20.
19 However, the datasets used in the later analyses of this chapter contains only those counties that have charter
schools, because the main purpose of this chapter is explore the charter school effects on the demographic
compositions in TPSs.
20 The segregation of non-white students from regular public schools could happen if more black students enroll in
vocational schools or other types of alternative schools. But this is not a research focus in this study. Therefore, at
the county level, the segregation indexes and the integration indexes could be misleading if they are not calculated
by using the data including the whole schools in a given jurisdiction.
86
Table 5-1 Mean Percentage Comparisons of Demographic Characteristics (1998-2009)
Indexes TPSs CSs Mean
Diff.
SE
Diff. Sig.
N Mean N Mean
Elem
entary
Sch
ool
Absolute DI for black student 19498 17.39 980 20.18 -2.80 0.54 .000
Absolute DI for white student 19498 16.07 980 18.59 -2.52 0.42 .000
Absolute DI for Hispanic student 19498 10.95 980 13.02 -2.07 0.39 .000
Absolute DI for F/RP Lunch Recipient 19498 18.72 980 24.32 -5.60 0.42 .000
DI for black student (DIBLK) 19498 2.78 980 -12.86 15.63 0.74 .000
DI for white student (DIWHT) 19498 2.51 980 1.94 0.57 0.78 .465
DI for Hispanic student (DIHSP) 19498 -1.51 980 2.09 -3.60 0.68 .000
DI for F/RP Lunch Recipient (DIFRL) 19498 -.86 980 -3.56 2.70 0.54 .000
Mid
dle S
cho
ol
Absolute DI for black student 6688 13.21 680 19.19 -5.97 0.56 .000
Absolute DI for white student 6688 12.37 680 17.05 -4.67 0.45 .000
Absolute DI for Hispanic student 6688 8.20 680 11.71 -3.51 0.43 .000
Absolute DI for F/RP Lunch Recipient 6688 14.03 680 23.59 -9.55 0.45 .000
DI for black student 6688 1.75 680 3.61 -1.85 0.79 .019
DI for white student 6688 -1.25 680 -0.31 -0.93 0.69 .175
DI for Hispanic student 6688 -0.43 680 -2.66 2.23 0.55 .000
DI for F/RP Lunch Recipient 6688 2.05 680 -6.87 8.92 0.75 .000
Hig
h S
choo
l Absolute DI for black student 4853 11.66 319 18.58 -6.91 0.75 .000
Absolute DI for white student 4853 11.22 319 15.81 -4.59 0.61 .000
Absolute DI for Hispanic student 4853 6.64 319 10.25 -3.61 0.54 .000
Absolute DI for F/RP Lunch Recipient 4853 10.11 319 17.32 -7.21 0.55 .000
DI for black student 4853 1.72 319 4.33 -2.62 1.02 .010
DI for white student 4853 -1.00 319 -4.64 3.64 0.90 .000
DI for Hispanic student 4853 -0.60 319 1.31 -1.91 0.67 .005
DI for F/RP Lunch Recipient 4853 1.70 319 -1.13 2.83 0.82 .001
87
Table 5-2 County Descriptive Statistics in Demographic Compositions (1998-2009)
N Min Max Mean SD
Elem
entary
Sch
ool
Percentage of black students 67 2.63 80.77 19.09 15.03
Percentage of white student 67 4.94 94.83 65.56 20.63
Percentage of Hispanic student 67 .68 61.45 13.54 14.41
ER of white students to non-white students 67 0.051 0.907 0.301 0.180
ER of white students to black students 67 0.026 0.864 0.191 0.143
ER of white students to Hispanic students 67 0.008 0.702 0.158 0.164
Segregation Index 67 0.000 0.328 0.106 0.093
Integration Index 67 0.672 1.000 0.894 0.093
Mid
dle S
cho
ol
Percentage of black students 67 1.80 79.69 18.51 15.42
Percentage of white student 67 5.95 96.51 67.58 20.31
Percentage of Hispanic student 67 .68 63.21 12.27 13.31
ER of white students to non-white students 67 0.034 0.885 0.298 0.186
ER of white students to black students 67 0.018 0.850 0.196 0.158
ER of white students to Hispanic students 67 0.008 0.725 0.149 0.159
Segregation Index 67 0.000 0.263 0.070 0.073
Integration Index 67 0.737 1.000 0.930 0.073
Hig
h S
choo
l Percentage of black students 67 1.79 79.17 18.78 14.33
Percentage of white student 67 6.63 96.55 68.47 19.26
Percentage of Hispanic student 67 .79 60.60 10.97 12.22
ER of white students to non-white students 67 0.034 0.883 0.296 0.176
ER of white students to black students 67 0.018 0.847 0.201 0.150
ER of white students to Hispanic students 67 0.008 0.718 0.138 0.155
Segregation Index 67 0.000 0.236 0.049 0.058
Integration Index 67 0.764 1.000 0.951 0.058
Note: The student demographic characteristics in counties are calculated only by using the regular public schools which excluded vocational schools, special educations, and alternative schools.
88
Changes in DIs Changes in Absolute DIs
Figure 5-1 Changes in Absolute DIs and the MDs in elementary TPSs by Demographic Groups
89
Table 5-3 Paired Mean Comparison of the Percentages of Demographic Groups between in a TPS and in its nearest CS (2009)
Level Pair Mean N SD SE Mean Corr. Sig. Mean SD SE Mean t-ratio d.f. Sig.
Elem
entary
Sch
ool
black in TPSs 28.94 1522 28.04 0.72 .613 .000 -0.38 26.81 0.69 -0.55 1521 .582
black in CSs 29.32 1522 32.29 0.83
white in TPSs 39.27 1522 28.47 0.73 .678 .000 -3.51 24.46 0.63 -5.59 1521 .000
white in CSs 42.78 1522 31.94 0.82
Hispanic in TPSs 28.79 1522 24.99 0.64 .763 .000 3.55 17.48 0.45 7.93 1521 .000
Hispanic in CSs 25.24 1522 25.72 0.66
FRL recipient in TPSs 61.58 1522 25.17 0.65 .397 .000 18.02 28.82 0.74 24.39 1521 .000
FRL recipient in CSs 43.56 1522 27.25 0.70
Mid
dle S
chool
black in TPSs 27.29 534 25.17 1.09 .545 .000 -1.36 26.43 1.14 -1.19 533 .235
black in CSs 28.65 534 29.65 1.28
white in TPSs 40.85 534 27.69 1.20 .495 .000 0.49 29.08 1.26 0.39 533 .695
white in CSs 40.36 534 30.06 1.30
Hispanic in TPSs 28.97 534 24.98 1.08 .859 .000 1.57 13.71 0.59 2.65 533 .008
Hispanic in CSs 27.40 534 26.44 1.14
FRL recipient in TPSs 56.12 534 23.55 1.02 .497 .000 12.79 25.44 1.10 11.62 533 .000
FRL recipient in CSs 43.33 534 26.87 1.16
Hig
h S
choo
l
black in TPSs 28.17 275 24.45 1.47 .330 .000 -8.90 31.39 1.89 -4.70 274 .000
black in CSs 37.07 275 29.34 1.77
white in TPSs 38.98 275 26.23 1.58 .342 .000 7.18 28.84 1.74 4.13 274 .000
white in CSs 31.79 275 23.94 1.44
Hispanic in TPSs 29.75 275 24.74 1.49 .823 .000 0.98 14.85 0.90 1.09 274 .277
Hispanic in CSs 28.77 275 25.22 1.52
FRL recipient in TPSs 46.51 275 19.20 1.16 .298 .000 11.91 24.55 1.48 8.05 274 .000
FRL recipient in CSs 34.60 275 22.06 1.33
90
5.2 Analyses of the DIs of Charter Schools
Do charter schools serve more students from a certain racial/ethnic group or a certain
socio-economic stratum? In other words, are they used as pockets for self-isolation, white flight,
or as socialization venues for the students from the more affluent families? To answer this
research question, first, I compare the mean percentages of each demographic group in TPSs
with those of the nearest charter schools. The results from the paired mean comparison are
presented in Table 5-3. Elementary charter schools have more white students but fewer Hispanic
students, middle charter schools have fewer Hispanic students, and high charter schools have
more black students but fewer white students than their nearest TPSs. One consistent and
significant characteristic in the comparisons is the percentage differences of the free/reduced
price lunch program students between TPSs and CSs. TPSs have a much higher proportion of
FRL students compared with that of the nearest charter schools in all school levels, indicating the
possibilities of charter schools cream-skimming students of higher socio-economic status from
nearby TPSs.
Now, I will build a HLM model to investigate the demographic compositions and their
changes in charter schools. The age of charter schools (SCHAGE) will replace the YEAR variable,
because the YEAR variable has zero value at the year of 1998. However, being different from
TPSs, most of charter schools opened later than 1998. As presented in Table 4-2, the average
ages of charter schools are 3.15 years, 2.98 years, and 2.77 years for elementary, middle, and
high charter schools, respectively. I will use the charter-school variables in the school level to
predict the demographic composition changes in charter schools such as the number of charter
schools within 10-mile radius (RAD100), the maximum percentage of a certain demographic
group in the nearest two charter schools if it has one or more CSs within a 10-mile radius
(MAXBLK for black students, MAXWHT for white students, and MAXHSP for Hispanic students),
other school variables like the location (METRO for large city location, SUBURABAN for
suburban location, and others are reference groups), and the school size (MEMBER). One thing
needs to be mentioned is that the demographic characteristics of charter schools will be
controlled by the DIs. For DIs of racial/ethnic groups, the DIFRL will be used as a control
variable, while the DIBLK, DIWHT, and DIHSP will be employed as control variables for the
DIFRL.
91
Table 5-4 Descriptive Statistics of Charter-school Variables
N Minimum Maximum Mean SD
RAD100 1640 0.00 17.14 3.52 3.52
MEMBER 1640 36.50 1953.33 436.11 372.54
MAXBLK (%) 1640 0.00 98.43 30.52 31.93
MAXWHT (%) 1640 0.00 95.88 34.87 32.84
MAXHSP (%) 1640 0.00 97.66 29.35 30.44
At the county level, I will use the years of charter-school policy adoption (YEARADOPT),
the per-pupil expenditure of regular public schools (PPEREG; state-mean-centered), the
population density (PPSM; state-mean-centered), the household median income (MINCOME;
state-mean-centered), the percentage of adults over 25 with high school diploma or higher
(HSOVER; state-mean-centered), and drop-out rates (DROPOUT). Since the number of charter
schools is much smaller than that of TPSs, I will not use separate datasets for each school level.
Instead, I will introduce dummy variable such as ELT for elementary schools and MID for
middle schools (high schools will be the reference group) in level 2. These dummy variables will
inform whether charter schools of different levels would show different patterns in the initial
status and the annual change rates or not.
This time, the Yearly Change Models will be the base models to check how the school
level and county level variables affect the DIs of charter schools. The analytic model is similar to
the Yearly Change Model in Section 4-4 except there is no quadratic term in the models of this
section. The linear change trajectories are assumed because all the coefficients of YEARSQ
terms were insignificant in the results from preliminary analyses. All the change parameters, or
the coefficient of SCHAGE term, are specified as non-randomly varying, and level 2 slopes for
school level predictors are fixed due to the insignificant variance. The results from the models
are shown in Table 5-5 for fixed effect estimates and Table 5-6 for random effects.
92
Table 5-5 Fixed Effect Results from Yearly Change Models for Charter School DIs
Fixed Effect Coefficient. SE t-ratio d.f. p-value
DIBLK
For initial mean DI, π0
Overall mean DI, γ000 -2.50 3.48 -0.72 38 0.477
ELEMENTARY, π01 3.68 2.54 1.45 182 0.149
MIDDLE, π02 0.75 3.23 0.23 182 0.817
For SCHAGE slope,ψ1
Overall mean change rate, π10 0.49 0.27 1.81 182 0.072
ELEMENTARY, π01 -0.73 0.27 -2.70 182 0.008
MIDDLE, π02 0.03 0.30 0.09 182 0.925
DIWHT
For initial mean DI, π0
Overall mean DI, γ000 2.18 2.00 1.09 38 0.282
ELEMENTARY, π01 -1.73 2.47 -0.70 182 0.486
MIDDLE, π02 3.50 2.57 1.36 182 0.175
For SCHAGE slope,ψ1
Overall mean change rate, π10 -0.39 0.27 -1.47 182 0.144
ELEMENTARY, π01 0.69 0.32 2.14 182 0.034
MIDDLE, π02 -0.07 0.28 -0.26 182 0.793
DIHSP
For initial mean DI, π0
Overall mean DI, γ000 1.65 2.09 0.79 38 0.435
ELEMENTARY, π01 -3.86 2.02 -1.91 182 0.058
MIDDLE, π02 -5.02 1.80 -2.78 182 0.006
For SCHAGE slope,ψ1
Overall mean change rate, π10 -0.26 0.23 -1.14 182 0.256
ELEMENTARY, π01 0.24 0.27 0.89 182 0.374
MIDDLE, π02 0.17 0.21 0.81 182 0.419
DIFRL
For initial mean DI, π0
Overall mean DI, γ000 -6.29 2.97 -2.12 38 0.041
ELEMENTARY, π01 -8.75 3.16 -2.77 182 0.006
MIDDLE, π02 -8.00 3.14 -2.55 182 0.012
For SCHAGE slope,ψ1
Overall mean change rate, π10 -0.76 0.19 -4.02 182 <0.001
ELEMENTARY, π01 1.07 0.38 2.83 182 0.005
MIDDLE, π02 1.28 0.38 3.35 182 <0.001
93
The results indicate that the initial mean percentages of FRL students in CSs are quite
lower than the county mean. Charter high schools have a 6.29 % lower proportion of FRL
students, charter elementary and middle schools have a 15.04% and 14.29% lower proportion in
their starting year, respectively. The percentages of FRL recipients in high charter schools
decrease annually by 0.76 % a year, while those in elementary and middle schools increase by
0.31 and 0.52 % per year. However, even in those CSs which are older than 10years, the
percentages of FRL students in elementary and middle CSs did not get close to the county mean.
The percentages of black students in elementary charter schools decreased by 0.73% per year,
while middle and high charter schools show no change by year. But the percentages of white
students in elementary charter schools increase by 0.69% per year. Charter schools have slightly
lower proportions of Hispanic student than the county mean. Over all, charter schools have lower
proportions of black students, Hispanic students and FRL students, while they have similar or
higher proportion of white students than the county mean on average.
Table 5-6 Random Effect Results from Yearly Change Models for Charter School DIs
Random Effect Variance d.f. χ2 p-value
DIBLK
level-1,e 7.61
School initial mean, r0 591.40 181 36471.72 <0.001
School mean change rate, r1 1.06 219 1203.89 <0.001
County initial mean, u00 47.63 38 49.86 0.094
County mean change rate, u10
DIWHITE
level-1,e 11.55
School initial mean, r0 444.55 181 18474.50 <0.001
School mean change rate, r1 1.37 219 1247.45 <0.001
County initial mean, u00 43.65 38 58.18 0.019
County mean change rate, u10
DIHSP
level-1,e 8.06
School initial mean, r0 234.31 181 14879.33 <0.001
School mean change rate, r1 0.94 219 1207.99 <0.001
County initial mean, u00 23.45 38 61.32 0.01
County mean change rate, u10
DIFRL
level-1,e 95.79
School initial mean, r0 434.43 181 2206.05 <0.001
School mean change rate, r1 2.41 219 438.59 <0.001
County initial mean, u00 69.16 38 65.43 0.004
County mean change rate, u10
94
The random effect results show that most of the variation in the proportion of each
demographic group exists among schools, and less than 12 % of variation in all DIs come from
the differences across counties. Therefore, the focus of analyses in this section will be on the
school level variables.
Table 5-7 presents the fixed effect results from the models with school-level and county-
level predictors with the yearly change model in level 1. I do not present those variables that
have no significant effects on any DI (See Appendix 7 for the full tables). The proportions of
black students at the starting points are much higher in urban charter schools, especially in urban
elementary charter schools, while the proportions of Hispanic students in charter schools in
similar areas are much lower. Furthermore, the percentages of black students will increase year
by year in elementary charter schools. But, the large city location or school level will not affect
the proportions of white students in charter schools. The percentages of FRL students have the
opposite effects on the proportions of black students and white students in charter schools. They
increase the black student percentages, but decrease the white student percentages in charter
schools. The years of charter-school adoption in a county have similar effects on both groups.
These segregation effects between black and white students in charter schools will be worse in
elementary schools, because they have negative yearly change rates. The percentage change
patterns of Hispanic students are similar to those of black students at large. The percentages of
Hispanic students will be higher in the charter schools that have more FRL students and are
located in large cities.
The percentages of FRL students in charter schools show a similar picture, as shown in
the last two columns. They have positive relations to the percentages of black and Hispanic
students, and are smaller proportions in elementary charter schools at the initial points and
changed little during the period, while the proportions of FRL students increased in middle
charter schools along the years.
95
Table 5-7 Fixed Effect Results from Models for Charter School DIs
Fixed Effect DIBLK DIWHT DIHSP DIFRL
Coef. t-ratio Coef. t-ratio Coef. t-ratio Coef. t-ratio
For initial mean DI, ψ0 INTRCPT3, β000 14.76 1.75 -20.94 -2.71 2.48 0.40 -19.55 -2.23
YEARSADOPT, β001 -1.58 -2.22 1.78 2.69 -0.41 -0.77 1.44 1.85
PPEREG, β002 -0.01 -1.87 0.00 1.36 0.00 1.47 0.00 0.71
PPSM, β003 0.00 0.08 0.00 -0.79 0.00 0.80 -0.01 -2.31
MINCOME, β004 0.00 1.66 0.00 -1.38 0.00 -1.82 0.00 -1.12
HSOVER, β005 -0.23 -0.43 0.73 1.52 1.01 2.36 0.56 0.81
DROPOUT, β006 -1.28 -1.16 1.29 1.28 0.06 0.08 -0.01 -0.01
RAD100, π01 -0.07 -0.16 -0.71 -2.02 -0.58 -1.85 0.40 0.98
MAX(D/G),π02; (DIBLK) 0.13 2.81 -0.01 -0.22 0.32 6.98 1.05 3.86
DIFRL; (DIWHT) 0.46 9.00 -0.49 -10.52 0.09 2.33 0.42 1.52
(DIHSP)
0.88 3.18
MEMBER, π03 0.00 -0.12 0.00 -1.04 0.00 0.81 -0.01 -2.31
METRO, π04 13.78 3.83 -5.87 -1.80 -6.36 -2.39 2.10 0.62
SUBURBAN, π05 -1.04 -0.33 2.75 0.94 -2.77 -1.18 5.01 1.71
ELT, π06 7.99 2.27 -4.33 -1.34 -3.01 -1.15 -9.81 -2.99
MID, π07 3.83 1.11 -0.71 -0.23 -2.43 -0.95 -4.56 -1.47
For SCHAGE slope, ψ1
INTRCPT3, β100 0.27 0.43 0.35 0.47 -0.58 -0.95 -0.61 -0.53
YEARSADOPT, β101 0.01 0.12 -0.07 -1.11 0.04 0.80 0.07 0.68
PPEREG, β102 0.00 1.10 0.00 0.06 0.00 -0.90 0.00 -0.68
PPSM, β103 0.00 -0.96 0.00 0.35 0.00 0.42 0.00 0.96
MINCOME, β104 0.00 0.64 0.00 -0.59 0.00 -0.09 0.00 -0.67
HSOVER, β105 0.02 0.63 0.02 0.36 -0.02 -0.55 -0.06 -0.97
DROPOUT, β106 0.12 1.57 0.03 0.33 -0.14 -1.80 -0.10 -0.69
RAD100, π11 0.08 2.07 -0.04 -1.01 -0.07 -2.07 0.04 0.69
MAX(D/G), π12 0.00 0.11 0.00 0.10 0.01 1.46 0.08 0.85
DIFRL 0.00 -0.71 0.00 1.10 0.00 -0.26 0.05 0.60
0.09 0.97
MEMBER,π13 0.00 -1.15 0.00 -0.11 0.00 1.35 0.00 -0.21
METRO,π14 -0.43 -1.65 0.28 0.92 0.05 0.21 -0.63 -1.27
SUBURBAN,π15 -0.10 -0.44 0.09 0.33 -0.14 -0.63 -0.67 -1.58
ELT,π16 -1.03 -3.86 0.78 2.46 0.47 1.80 0.65 1.27
MID,π17 -0.18 -0.70 -0.06 -0.20 0.37 1.47 1.24 2.55
96
Neighboring charter schools influence positively the percentages of black students and
Hispanic students, but negatively on the percentages of white students represented by the
coefficients of RAD100 and MAX (D/G) variables. This means that charter schools have
different relationships each other concerning black students and white students. These
phenomena could be called “demand-creating relationship” vs. “competition-creating
relationship”. Charter schools that have higher proportion of black students are likely to locate
more in large cities, while charter schools that have higher percentage of white students locate in
suburban area as shown by the correlations in Table 5-8. However, the distribution of charter
schools is skewed toward the suburban locations. Therefore, charter schools in large cities that
increase the availability of charter schools to black students are shown to have a “trickle-down
effect” which provides opportunities to the poor by lowering the cost of certain product
consumption or services. More charter schools in large cities would lower the cost of attending
charter schools, i.e., by shortening the distance to commute because charter schools usually do
not provide busing services. On the other hand, charter schools with higher proportion of white
student in suburban areas face a certain degree of competition with each other and TPSs over
white students.
Table 5-8 Correlations among Variables and Distributions of Charter Schools
Pearson Correlations Number of CSs
DIBLK DIWHT DIHSP N %
METRO Correlation .275* -.161* -.179*
446 28.41 N 1640 1640 1640
SUBURBAN Correlation -.082* .059** .044
744 45.37 N 1640 1640 1640
Note: One asterisk (*) or two indicate that correlation is significant at the 0.01 or 0.05 level,
respectively (2-tailed).
97
Table 5-9 Comparisons of the Variance Explained by Models
Random Effect
Base Model21
NO DIs Model22
With DIs Model
Variance Variance Var. Exp. Variance Var. Exp.
DIBLK
level-1,e 7.61 7.65
7.64
School initial mean, r0 591.4
(p.<0.001) 489.1
(p.<0.001) 0.1730
354.16 (p.<0.001)
0.4011
School mean change, r1 1.06
(p.<0.001) 0.92
(p.<0.001) 0.1321
0.91 (p.<0.001)
0.1415
County initial mean, u00 47.63
(p.= 0.094) 0.16
(p.>0.500) 0.19
(p.>0.500)
DIWHT
level-1,e 11.55 11.56
11.55
School initial mean, r0 444.55
(p.<0.001) 418.59
(p.<0.001) 0.0584
289.3 (p.<0.001)
0.3492
School mean change, r1 1.37
(p.<0.001) 1.31
(p.<0.001) 0.0438
1.3 (p.<0.001)
0.0511
County initial mean, u00 43.65
(p.=0.001) 0.83
(p.=0.26) 0.9810
0.11 (p.=0.422)
DIHSP
level-1,e 8.06 8.06793
8.07
School initial mean, r0 234.31
(p.<0.001) 202.2
(p.<0.001) 0.1370
188.84 (p.<0.001)
0.1941
School mean change, r1 0.94
(p.<0.001) 0.83
(p.<0.001) 0.1170
0.83 (p.<0.001)
0.1170
County initial mean, u00 23.45
(p.=0.01) 0.07
(p.=0.447) 0.9970
0.12 (p.=0.369)
DIFRL
level-1,e 95.79 95.85
96.56
School initial mean, r0 434.43
(p.<0.001) 366.24
(p.<0.001) 0.1570
221.42 (p.<0.001)
0.4903
School mean change, r1 2.41
(p.<0.001) 2.14
(p.<0.001) 0.1120
1.6 (p.<0.001)
0.3361
County initial mean, u00 69.16
(p.=0.004) 40.16
(p.=0.016) 0.4193
54 (p.<0.001)
Over all, if other things are equal, charter schools in large cities have a higher proportion
of black students and lower percentage of Hispanic students; the percentage of black students
will decrease and the proportion of white students will increase at a higher velocity in elementary
charter schools than in middle and high school charter schools as the years of operation increase. 21 The random effects come from the Yearly Change Models in Table 6-6.
22 I ran the models in which the DIs were dropped from each model, but all other variables included as the same as
in the models in Table 5-7. The random effects of those models are presented in this column.
98
The FRL student proportion in charter schools is much lower in elementary charter schools. Only
middle charter schools will accommodate more FRL students as they get older. The smaller
charter schools in lower population density counties have higher percentage of FRL students; the
longer it is since a county introduced charter school policy, the fewer black students and the
more white students will enroll in charter schools.
How much variance among schools and counties are explained by these Models is
important to check the validity of the inferences in this section. Table 5-9 shows the comparisons
of the variance from the three models and the variance explained by the models in the next to the
variance columns. The explained variance proportions of deviations from the county means in
the percentages of black, white, Hispanic and FRL students were 40.11 %, 34.92%, 19.41%, and
49.03%, respectively. The gap of explained variance between No-DIs Models and With-DIs
Models are quite large except for the model for DIs of Hispanic students. The gap is largest
between models for DIs of white students, almost six times more. This means that the racial
compositions of charter schools are closely correlated to the socio-economic status, especially in
the case of the proportions of white students, in Floridian public charter schools. Most of the
county level variation in the initial county mean DIs turned out to be insignificant in the models
except for the models for DIs of FRL students.
The analysis of the explained proportions of variance by the models suggests that more
than half of the school variation is left unexplained, and that further research is required with
more relevant variables introduced into the models to explain the demographic differences in
charter schools.
5.3 Analysis of Variance in the DIs of Traditional Public Schools
In this section, the DI distributions of traditional public schools will be examined, which
will give the bases for the following analyses. The analysis of variance will show how the
variance of DIs is distributed among different levels. For this purpose, I formulated One-Way
ANOVA HLM Models, or fully unconditional HLM models for the DIs of elementary, middle,
and high TPSs. The analytic model is:
99
Level-1 Model
DImti = ψ0ti + εmti
Level-2 Model
ψ0ti = π00i + e0ti
Level-3 Model
π00i = β000 + r00i
where
DImti is the dissimilarity index of traditional public schools as the deviations of the
demographic composition from the county mean composition at year m for school t in
county i;
ψ0ti is the initial mean DI of school ti in 1998 (coded as zero);
π00i represents the mean DI score within a county i, while β000 is the overall mean DI for
all counties through the years;
εmti is a level1 random effect, or “year effect” that represents the deviation of school ti’s
DI in YEAR m from the overall mean DI. These residual year effects are assumed
normally distributed with mean of 0 and variance σ2ε;
e0ti is a random “school effect”, that is, the deviation of school ti’s mean DI from the
county mean. These effects are assumed normally distributed with mean of 0 and
variance σ2e;
r00i is a random “county effect”, that is, the deviation of county i’s mean DI from the
overall county mean. These effects are assumed normally distributed with a mean of
0 and variance τπ.
I ran One-Way ANOVA models for the DIs of each group: Black students (DIBLK),
white students (DIWHT), Hispanic students (DIHSP), and FRL recipients (DIFRL). The results
from ANOVA models for each DI are shown in Table 5-10 for three school levels with intra-
class correlations (ICC) in the random effect table. The overall means for DIs ensure that the
mean of DIs are quite different from zero except those of DIs for Hispanic students, indicating
that demographic groups are distributed unequally when they are contrasted to the average
100
compositions of a county’s regular public schools. TPSs have higher proportion of black students
and FRL students and lower percentage of white students than the county average percentages in
all school levels. This fixed effects coefficient table shows a more precise picture than the overall
means of DIs in Table 5-1, because these fixed effects are calculated by taking into account
school and county variation in level 2 and level 3. However, the overall means are misleading
because the positive DIs off-set the negative DIs. The means of absolute DIs in Table 5-1 show a
more precise picture regarding the dispersion of DIs in TPSs.
One of the merits using HLM is that it shows how much variation comes from which
levels. Most of the variance in DIs exist among schools ranging from 87.4 % for DIs of FRL
students in high schools to 97.21% for DIs of elementary black students. There are small
portions of variation across the years, and little variance at the county level. This means that the
mean DIs of TPSs in a county do not vary significantly across counties while traditional public
schools are quite different one another in the demographic compositions within counties, which
are also supported by the reliabilities of OLS regression coefficient estimates in Table 5-10c.
Therefore the level 2 coefficients that predicted by county level variables will be set as fixed or
non-randomly varying in most of the models in this section.
Table 5-10 Results from One-Way ANOVA Models by School Level
5-10a Fixed Effects
Fixed Effect Coefficient SE t-ratio d.f. p-value
Elementary
School
DIBLK Overall mean, β000 3.12 0.57 5.50 36 <0.001
DIWHT Overall mean, β000 -2.09 0.56 -3.72 36 <0.001
DIHSP Overall mean, β000 -0.61 0.57 -1.09 36 0.285
DIFRL Overall mean, β000 2.47 0.36 6.76 36 <0.001
Middle
School
DIBLK Overall mean, β000 2.23 0.33 6.75 29 <0.001
DIWHT Overall mean, β000 -1.84 0.41 -4.49 29 <0.001
DIHSP Overall mean, β000 -0.33 0.29 -1.12 29 0.270
DIFRL Overall mean, β000 2.18 0.45 4.79 29 <0.001
High
School
DIBLK Overall mean, β000 2.59 0.53 4.87 23 <0.001
DIWHT Overall mean, β000 -1.89 0.72 -2.61 23 0.016
DIHSP Overall mean, β000 -0.74 0.58 -1.27 23 0.218
DIFRL Overall mean, β000 0.84 0.38 2.22 23 0.037
101
Table 5-10 Continued
5-10b. Random Effects
Random Effect Variance d.f. χ2 p-value ICC
Elementary
School
DIBLK Year effect, ε 17.71 0.0279
School effect, e0 616.99 1282 516692.50 <0.001 0.9721
County effect, r00 0.06 36 15.89 >.500
DIWHT Year effect, ε 19.96
0.0461
School effect, e0 413.46 1282 302219.84 <0.001 0.9539
County effect, r00 0.00 36 31.58 >.500
DIHSP Year effect, ε 12.41
0.0399
School effect, e0 298.79 1282 358885.72 <0.001 0.9601
County effect, r00 1.48 36 41.81 0.233
DIFRL Year effect, ε 33.43
0.0598
School effect, e0 525.78 1282 229389.04 <0.001 0.9402
County effect, r00 0.11 36 19.93 >.500
Middle
School
DIBLK Year effect, ε 18.75
0.0416
School effect, e0 431.67 361 96939.17 <0.001 0.9584
County effect, r00 0.11 29 3.62 >.500
DIWHT Year effect, ε 16.58
0.0552
School effect, e0 283.70 361 69733.35 <0.001 0.9448
County effect, r00 0.06 29 16.21 >.500
DIHSP Year effect, ε 9.75
0.0413
School effect, e0 226.34 361 95154.72 <0.001 0.9587
County effect, r00 0.06 29 11.04 >.500
DIFRL Year effect, ε 31.66
0.0833
School effect, e0 348.35 361 44556.22 <0.001 0.9167
County effect, r00 0.11 29 12.10 >.500
High
School
DIBLK Year effect, ε 13.34
0.0312
School effect, e0 414.55 200 75250.30 <0.001 0.9688
County effect, r00 0.13 23 4.10 >.500
DIWHT Year effect, ε 13.89
0.0509
School effect, e0 259.26 200 43840.70 <0.001 0.9491
County effect, r00 0.09 23 7.54 >.500
DIHSP Year effect, ε 7.44
0.0368
School effect, e0 194.61 200 63939.19 <0.001 0.9632
County effect, r00 0.08 23 4.13 >.500
DIFRL Year effect, ε 23.33
0.1260
School effect, e0 161.79 200 16376.32 <0.001 0.8740
County effect, r00 0.06 23 3.77 >.500
102
Table 5-10 Continued
5-10c. Reliabilities of Coefficient Estimates
Reliability of OLS Regression Coefficient Estimates Reliability estimate
Elementary
School
DIBLK Year mean, ψ0 0.997
School mean, π00 0.003
DIWHT Year mean, ψ0 0.996
School mean, π00 0.000
DIHSP Year mean, ψ0 0.996
School mean, π00 0.124
DIFRL Year mean, ψ0 0.994
School mean, π00 0.007
Middle
School
DIBLK Year mean, ψ0 0.995
School mean, π00 0.003
DIWHT Year mean, ψ0 0.994
School mean, π00 0.003
DIHSP Year mean, ψ0 0.995
School mean, π00 0.003
DIFRL Year mean, ψ0 0.990
School mean, π00 0.004
High
School
DIBLK Year mean, ψ0 0.996
School mean, π00 0.003
DIWHT Year mean, ψ0 0.994
School mean, π00 0.003
DIHSP Year mean, ψ0 0.996
School mean, π00 0.004
DIFRL Year mean, ψ0 0.985
School mean, π00 0.003
I now formulate Yearly Change Models for all DIs of all school levels with a year term in
level 1 in the same way as done in Section 4-2, and ran them23. But I would not paste all the
results here. Table 5-11 shows only the summary of the annual change rates and their
significance for all DIs. These results suggest that the increasing proportion of black students and
FRL recipients have enrolled in TPSs for all school levels along the years during the period of
1998-2009, but that the percentages of white students in TPSs have decreased year by year even
23 I checked the possibility of quadratic changes in the DIs, but all quadratic terms proved to be insignificant, which
means that linear modeling is appropriate for the analyses of the DIs.
103
though the rates are small. However, the enrollments of Hispanic students in all levels of TPSs
have stayed around the county means during the period.
Table 5-11 Annual change rates from Yearly Change Models for the DIs
Fixed Effect Coefficient SE t-ratio d.f. p-value
Elementary
School
DIBLK 0.18 0.04 4.47 36 <0.001
DIWHT -0.12 0.03 -3.67 36 <0.001
DIHSP -0.03 0.04 -0.69 36 0.494
DIFRL 0.40 0.05 8.40 36 <0.001
Middle
School
DIBLK 0.32 0.08 4.15 29 <0.001
DIWHT -0.23 0.06 -3.86 29 <0.001
DIHSP -0.11 0.05 -2.11 29 0.044
DIFRL 0.40 0.08 5.04 29 <0.001
High
School
DIBLK 0.29 0.07 4.35 23 <0.001
DIWHT -0.21 0.06 -3.78 23 <0.001
DIHSP -0.04 0.06 -0.67 23 0.509
DIFRL 0.19 0.06 3.38 23 0.003
Therefore, the next logical task will be to investigate the sources of school variation in
the demographic compositions of TPSs, and what leads to the differences in the annual change
rates of individual demographic groups in TPSs.
5.4 Analyses of Charter-school Effect on the DIs of Traditional Public Schools
In this section, the charter-school effects on the DIs of TPSs will be examined by
Charter-school Effect Models which have charter school related variables such as the presence
and the number of charter schools within a 5-mile radius, the distances to the nearest charter
school, the demographic compositions of the nearest charter schools (NRST(D/G), and the
maximum percentage of a certain racial/ethnic or socio-economic group among charter schools
within a 10-mile radius (MAXCS(D/G) 24. I will build Charter-school Effect Models which have
24 All school characteristics used in this study were calculated using the CCD 1998-2009 and the FSIR 1998-2006
datasets, but the demographic variables of the nearby charter schools, i.e., the percentage of black students in the
104
only charter-school-related variables in level 2 and level 3, because the analyses in this section
will focus on charter-school effects on the nearby TPSs: What influence have charter schools had
on the demographic changes in TPSs when charter schools entered the established public
educational jurisdictions in Florida? Therefore, the other social conditions around TPSs in a
county are considered as given by the previous paths the schools and the counties have walked
along. Another reason is that the DIs of demographic compositions in a county, a kind of county-
mean-centered indexes, show little variation across counties as shown by county-level random
effects, or county effects in Table 5-10b. Charter-school Effect Models with the DIs as
dependent variables and with charter-school factors as predictors in level 2 and level 3 are:
Level-1 Model
DImti = ψ0ti + ����������� + εmti
Level-2 Model
ψ0ti = π00i + ��������+e0ti
ψ1ti = π10i + ��������+e1ti
Level-3 Model
πpqi = βpq0 + ∑ ������� ������ + rpqi,
where
DImti is the DI value of Florida traditional public schools at year m for school t in county i;
ψ0ti is the initial status of school ti, that is, the expected DI values for school ti in 1998
(coded as zero);
ψ1ti is the annual mean change rate for school ti over the time period from 1998 to 2009;
εmti is now the residual assumed to be independently distributed. These residuals are
assumed independently distributed with a mean of 0 and variance σ2e. Correspondingly,
the variance σ2e is a residual or conditional variance, the school level variance in π00i
after controlling for YEAR;
Xqti is a charter-school factors used as a predictor or a control of the school effect ψpti ;
nearest charter school from a TPS introduced in this chapter came from only CCD 2009 datasets.
105
π00i represents the mean initial DI of schools within county i when Xqti = 0 or the mean
value of centered variables;
π10i represents the mean yearly change rates of school DIs within county i when Xqti = 0
or the mean value of centered variables;
epti represents now residual dispersion in ψpti and after controlling for school level
variables Xqti. It is multivariate normally distributed with mean of zero and variance-
covariance matrix;
Wsi is a county level variables adopted as predictors or controls for school effect, πpqi;
β0q0 is the overall mean DIs and β1q0 is the overall mean yearly change rate of DIs for all
counties;
βpqs is the level 3 coefficient corresponding to the relationship between county level
variables Wsi and the school effect, πpqi;
rpqi is the residual dispersion in πpqi after controlling for county level variables Wsi. It is
multivariate normally distributed with mean of zero and variance- covariance matrix;
Table 5-12, Table 5-13, and Table 5-14 provide the coefficient estimates of fixed effects from
the models for elementary, middle, and high TPSs, respectively.
The presence and the number of charter schools have significant impacts on the
percentages of every demographic group in TPSs. The number of charter schools within a 5-mile
radius increases the percentage of black students in all levels of TPSs and FRL students in
elementary and middle TPSs. However, the percentage of white students in elementary and
middle schools decreased when they have more charter schools within a 5-mile radius. The
existence of charter schools within a 5-mile radius increases the percentage of FRL and Hispanic
students, while it influences negatively the percentage of white students in high school TPSs.
The presence of charter schools within a 5 mile radius will decrease the proportion of white
students in elementary TPSs and that of Hispanic students in middle TPSs as time goes on, while
the number of charter schools around middle and high TPSs leads to increases in the percentage
of black students in those TPSs. The mean distances to the nearest charter schools have no
effects in all models. The traditional elementary schools in large cities would have a much higher
proportion of black students and FRL students, while the percentage of white students in TPSs in
106
large cities will be much lower in all levels of schools. But the suburban location of TPSs has no
influence on the demographic compositions.
The percentages of the same demographic groups in nearby charter schools affect
positively, or neutrally. No negative effects from the demographic compositions of nearby
charter schools may be caused by the charter-school location issue. In other words, charter
schools are likely to locate around TPSs that have a similar or higher proportion of a certain
demographic group. Therefore, the relationship might be reversed in these cases: the higher
proportion of a certain demographic groups in a certain area would induce charter schools to
target these groups.
At the county level, the percentages of private school and home education students are
related to the lower percentage of black student and the higher percentage of white students in
elementary TPSs. Considered the correlations between the proportion of private school and home
education students and the racial/ethnic composition in TPSs, this relationship might be
interpreted as the issue of private school location and targeting. Private schools might be seeking
to locate in and target the markets that have with more potential consumers. For example, the
counties with lower percentage of black students have lesser private schools because many of the
black students do not afford private schooling financially, while counties with higher percentage
of white students have more private schools targeting white students. The percentage of charter-
school students in a county has a negative relation with the percentage of FRL students in middle
TPSs. This means that more affluent counties are more likely to introduce and promote charter-
school policy. But, the relationship is not decisive in high TPSs because of positive annual
change rate.
107
Table 5-12 Fixed Effect Results from Charter-school Effect Models (Elementary School)
Fixed Effect DIBLK DIWHT DIHSP DIFRL
For initial mean DI, π0
Overall mean DI, γ000 5.81
(0.76) -19.10 (-1.70)
-3.15 (-0.19)
-14.93 (-2.17)
YEARSADOPT, γ001 -0.42
(-0.68) 0.37
(0.60) -0.17
(-0.30) -0.22
(-0.49)
PCHARTER, γ002 0.09
(0.21) 0.12
(0.22) -0.68
(-1.31) -0.24
(-0.76)
PPVTHE, γ003 -1.30
(-3.66) 0.87
(2.31) -0.23
(-0.23) -0.25
(-1.01)
ANYCS50, β01 3.76
(1.81) -3.83
(-1.45) 2.43
(1.46) 3.95
(1.23)
RAD50, β02 1.89
(3.82) -3.18
(-6.34) 0.12
(0.24) 2.89
(4.79)
MINDTCS, β03 -0.06
(-0.22) 0.06
(0.08) 0.21
(0.73) 0.06
(0.09)
NRST(D/G), β04 0.35
(15.48) 0.23
(5.31) 0.53
(10.38)
MAXCS(D/G), β05 0.05
(1.68) -0.02
(-0.33) -0.14
(-0.59) 0.26
(4.87)
METRO,β06 7.97
(3.25) -8.73
(-3.85) 0.02
(0.01) 6.59
(2.14)
SUBURBAN, β07 2.85
(1.30) -3.37
(-1.92) 2.14
(3.17) 2.37
(1.47)
For YEAR slope, π1
Overall mean change rate, γ100 -0.26
(-0.93) 0.41
(1.00) 0.83
(2.88)
YEARSADOPT, γ101 0.00
(-0.00) -0.02
(-0.72) -0.04
(-1.52)
PCHARTER, γ102 0.02
(1.57) 0.02
(1.09) 0.01
(0.71)
PPVTHE, γ103 0.01
(0.97) -0.01
(-0.49) 0.00
(-0.17)
ANYCS50, β11 0.13
(1.43) -0.24
(-2.81) 0.19
(1.92)
RAD50, β12 0.00
(0.15) 0.04
(0.84) -0.04
(-0.97)
MINDTCS, β13 0.01
(0.58) 0.00
(-0.28) -0.03
(-1.97)
NRSTBLK, β14 0.00
(3.38) 0.00
(-0.20)
MAXCSBLK, β15 0.00
(1.22) 0.00
(-0.66) 0.00
(-1.93)
METRO, β16 -0.13
(-1.13) 0.17
(1.19) 0.02
(0.10)
SUBURBAN, β17 -0.09
(-0.86) 0.01
(0.10) 0.22
(1.97)
108
Table 5-13 Fixed Effect Results from Charter-school Effect Models (Middle School)
Fixed Effect DIBLK DIWHT DIHSP DIFRL
For initial mean DI, π0
Overall mean DI, γ000 -8.93
(-0.75) -6.93
(-0.91) -4.34
(-0.64) 5.20
(0.64)
YEARSADOPT, γ001 -0.14
(-0.20) 0.32
(0.61) 0.14
(0.22) -0.47
(-0.88)
PCHARTER, γ002 0.04
(0.07) 0.39
(1.79) -0.94
(-1.55) -0.89
(-2.96)
PPVTHE, γ003 -0.56
(-0.96) 0.56
(1.76) -0.28
(-0.74) -0.63
(-1.59)
ANYCS50, β01 0.52
(0.27) -1.97
(-0.61) 1.03
(0.54) -0.39
(-0.13)
RAD50, β02 4.91
(10.21) -3.34
(-3.75) -1.30
(-0.99) 4.67
(8.94)
MINDTCS, β03 0.28
(1.56) -0.01
(-0.07) -0.03
(-0.14) -0.01
(-0.06)
NRST(D/G), β04 0.27
(2.96) 0.05
(1.11) 0.49
(3.22) 0.17
(3.75)
MAXCS(D/G), β05 0.07
(1.49) 0.00
(-0.05) 0.05
(0.58)
METRO,β06 -0.88
(-0.16) -7.69
(-2.38) 3.35
(0.77) 2.35
(0.59)
SUBURBAN, β07 0.58
(0.34) -1.43
(-0.64) 2.15
(1.05) -0.15
(-0.06)
For YEAR slope, π1
Overall mean change rate, γ100 -0.11
(-0.23) -0.10
(-0.20) -0.11
(-0.31) 0.01
(0.02)
YEARSADOPT, γ101 0.01
(0.39) -0.04
(-1.58) 0.02
(0.73) -0.03
(-0.81)
PCHARTER, γ102 -0.01
(-0.69) 0.01
(0.33) -0.02
(-0.71) 0.03
(1.44)
PPVTHE, γ103 0.02
(1.19) 0.00
(-0.14) -0.02
(-0.97) 0.03
(1.18)
ANYCS50, β11 -0.04
(-0.27) -0.06
(-0.36) 0.07
(0.37) 0.06
(0.35)
RAD50, β12 0.08
(2.61) 0.07
(1.23) -0.13
(-5.07) -0.02
(-0.37)
MINDTCS, β13 0.00
(0.14) 0.00
(0.11) 0.00
(-0.63) -0.01
(-0.84)
NRSTBLK, β14 0.00
(1.26) 0.00
(1.75) 0.01
(5.15) 0.00
(-0.40)
MAXCSBLK, β15 0.00
(-1.09) 0.00
(-0.07) 0.00
(1.70)
METRO, β16 -0.01
(-0.12) 0.06
(0.25) -0.01
(-0.03) 0.07
(0.24)
SUBURBAN, β17 -0.17
(-1.38) 0.17
(0.81) 0.08
(0.33) 0.24
(0.79)
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Table 5-14 Fixed Effect Results from Charter-school Effect Models (High School)
Fixed Effect DIBLK DIWHT DIHSP DIFRL
For initial mean DI, π0
Overall mean DI, γ000 -9.51
(-0.55) 1.89
(0.21) -4.35
(-0.21) -3.64
(-1.08)
YEARSADOPT, γ001 -0.18
(-0.21) 0.00
(-0.01) -1.15
(-1.01) 0.21
(0.86)
PCHARTER, γ002 -0.02
(-0.03) 0.18
(0.51) 0.42
(0.77) -0.38
(-2.80)
PPVTHE, γ003 -0.67
(-0.59) 0.10
(0.40) 0.05
(0.04) -0.30
(-1.56)
ANYCS50, β01 1.19
(0.49) -7.39
(-3.93) 5.36
(2.96) 4.51
(3.32)
RAD50, β02 3.16
(2.07) -1.15
(-0.98) -2.14
(-1.58) 0.88
(0.46)
MINDTCS, β03 -0.18
(-0.52) 0.06
(0.27) -0.02
(-0.06) 0.13
(0.56)
NRST(D/G), β04 0.23
(2.74) 0.13
(1.59) 0.16
(3.44) 0.04
(0.64)
MAXCS(D/G), β05 0.25
(1.48) -0.07
(-1.38) 0.43
(7.14)
METRO, β06 7.12
(1.57) -2.90
(-0.70) -6.92
(-3.00) 3.19
(0.79)
SUBURBAN, β07 -0.27
(-0.11) 2.76
(1.19) -3.20
(-1.89) -0.84
(-0.36)
For YEAR slope, π1
Overall mean change rate, γ100 -0.01
(-0.01) -0.31
(-0.43) -0.02
(-0.09)
YEARSADOPT, γ101 -0.03
(-1.42) 0.02
(0.55) -0.03
(-1.45)
PCHARTER, γ102 0.03
(1.90) -0.01
(-0.30) 0.05
(2.74)
PPVTHE, γ103 0.01
(0.51) 0.00
(-0.04) 0.00
(0.17)
ANYCS50, β11 0.18
(0.84) -0.36
(-1.41) 0.45
(1.96)
RAD50, β12 0.16
(2.04) 0.06
(0.36) -0.08
(-0.69)
MINDTCS, β13 -0.01
(-0.88) 0.00
(0.04) -0.02
(-1.66)
NRST(D/G), β14 0.00
(-0.71) 0.00
(0.26) 0.01
(1.84)
MAXC(D/G), β15 0.00
(4.08) 0.00
(0.28)
METRO, β16 0.06
(0.32) 0.17
(0.64) -0.05
(-0.23)
SUBURBAN, β17 0.05
(0.27) 0.08
(0.32) 0.07
(0.29)
110
The findings in this section need to be combined with the results from the mean
difference tests in Table 5-1 to explain the results logically. In elementary schools, the
withdrawal of more white students than black students by charter schools from TPSs leads to the
positive coefficient of RAD50 on DIs of black students, while it leads to the negative coefficients
of RAD50 on DIs of white students. However, in middle and high schools, the effects from
charter-school locations are large enough to cover the withdrawal effects, because charter
schools have slightly higher proportion on black students and lower proportion of white students
in Table 5-1, but charter-school presence and numbers have positive effects on the percentages
of black students and negative effects on the percentage of white students in the tables in this
section. Therefore, I can say that the location effects represented by NRST(D/G) and
MAXCS(D/G) are off-set by the withdrawal effects in elementary schools, while the location
effects are more influential in middle and high schools. All these results suggest that charter
schools have drawn white students or black students from TPSs disproportionally, and much
fewer FRL students at all school levels from TPSs, but the direction of effects on Hispanic
student enrollment in TPSs is not decisive.
Now, how much did these Charter-school Effect Models explain the variance in the DIs among
traditional public schools? In the ANOVA analysis in Section 5.2, the variance in the DIs exist
mainly at the school levels, meaning that the deviations of demographic compositions in
traditional public schools from the county mean composition are varying significantly across
schools. Therefore, the exploratory power of the models can be tested by the explained variance
in school effects. Table 5-15 presents the variance from the ANOVA models and Charter-school
Effect Models with the proportions of variance explained by the later models in the last column.
Charter-school-related predictors at the school level explained the variance in the DIs of black
students and of Hispanic students better (ranging from 28.01% to 43.86%) than those of white
students (ranging from 8.53% to 15.50%) in TPSs. The proportions of explained variance in DIs
of FRL students are between ranging from 14.20% to 24.33%. These Charter-school Effects
models do not control the racial/ethnic factors of TPSs for DIs of FRL students and the socio-
economic factors of TPSs for DIs of racial/ethnic groups, which are closely correlated as
discussed in Section 5.2 and presented in Table 5-9. The use of these factors for controls would
have increased the exploratory power of the models in this section, but this was not tried because
the main purpose of this section is to examine the charter-school effects on the established TPSs
111
when they entered the given educational arenas. However, the other school factors to explain the
remaining school variation in demographic compositions will be introduced to the models in next
section. Future research would examine whether traditional public schools react differently to
charter-school entry into their territory according to their demographic compositions.
Table 5-15 Comparison of the variance Explained by Models in Level 2
ANOVA Model Charter-school Effect Model Variance
Explained Variance d.f. Variance d.f. χ2 p-value
Elementary School
DIBLK 616.99 1282 443.87 1278 300833.7 <0.001 0.2806
DIWHT 413.46 1282 349.38 1278 223752.1 <0.001 0.1550
DIHSP 298.79 1282 215.11 1278 262368.3 <0.001 0.2801
DIFRL 525.78 1282 451.1 1279 88622.42 <0.001 0.1420
Middle School
DIBLK 431.67 361 281.89 352 57531.46 <0.001 0.3470
DIWHT 283.70 361 259.49 352 45776.07 <0.001 0.0853
DIHSP 226.34 361 127.06 352 41015.11 <0.001 0.4386
DIFRL 348.35 361 272.09 353 15573.72 <0.001 0.2189
High School
DIBLK 414.55 200 260.27 191 50280.86 <0.001 0.3722
DIWHT 259.26 200 229.11 191 36953.27 <0.001 0.1163
DIHSP 194.61 200 135.39 193 41612.54 <0.001 0.3043
DIFRL 161.79 200 122.42 192 6462.51 <0.001 0.2433
5.5 Multivariate Analyses of the DIs among Traditional Public Schools
The separate models examining the charter-school effects on the proportion changes of
demographic groups in TPSs raise an important research question: Then, do charter schools
affect the demographic groups in TPSs equally, or differently? The separate models indicated
that charter schools influenced the percentage increases of black students and free/reduced price
lunch recipients and the percentage decrease of white students in TPSs, but the influence on the
proportion of Hispanic students was not decisive. It was between the influences on black
students and on white students. However, each separate model does not provide a solid answer to
this research question, because the separate models do not take into account the influences from
the proportional changes of other demographic groups at the same time. Therefore, I built
112
hierarchical multivariate linear models (HMLM) which take into consideration the correlation
among the multiple dissimilarity indexes of TPSs simultaneously.
The DIs of FRL students will be used as control variables to check how much the socio-
economic conditions of school students affect the racial/ethnic compositions in traditional public
schools. The county-mean-centered FCAT math and reading scores (MG(N)CTR for math, and
RG(N)CTR for reading) of TPSs are also employed as control variable to examine the
relationship of school academic performance to the racial/ethnic groups. The models in the
HMLM analyses have no yearly change models in level 1, because most of the variation among
DIs of racial/ethnic groups existed between schools (more than 94% of the total variance in
every DIs of racial/ethnic group), while small portion of variance were between the years. The
year effects were the highest in the DIs of white students in high schools as of 5.09% (See Table
5-10b in Section 5.3). Hence, the HMLM model will be:
Level 1Model
DImtik = ∑ δ�(���� + ∑ ������������ + ����� )
Level-2 Model
π00i = β000 + ∑ ������� ����
To specify a multivariate multilevel model, let DImtik be an outcome variable for an
individual school t in county i at time m on outcome variable k (1 for DIs for black students, 2
for DIs of white students, and 3 for DIs for Hispanic students). Then the model defines dummy
variables, δk which would be 1 for the given measure on DIk, and δk = 0 otherwise. The level 2 is
the same as the county level model in the previous section. But this time, the county level model
is defined only to predict the intercept, or the initial county mean, because previous analyses
showed that most of the impacts from the county variables were on the initial status. And the
level 1 intercept, or the initial mean status of a county will be specified as non-randomly varying,
because the variance at the county level were all insignificant as presented in Table 5-10b.
Another thing different from the previous settings is the datasets: I use the datasets of the school
year 2009-2010 from the CCD and the FSA for the county percentages of private school and
113
home education students, because the HMLM analyses in this section is cross-sectional, and it
contains more charter schools and their information than any other year’s dataset.
First, I ran One-Way ANOVA Models to explore the overall mean of three kinds of DIs
and the distributions of variance. I compared the overall means of the three DIs. The results from
One-Way ANOVA models are presented in Appendix 8. The DIs of all racial/ethnic groups in all
school levels were significantly different from the county means except the DIs of Hispanic
students in elementary TPSs. The mean differences between the DIs of black students and of
white students, and between the DIs of black students and of Hispanic students in every school
level were significantly different each other, while the mean differences between those of white
students and of Hispanic student were statistically identical in all school level. The variation of
DIs between TPSs was largest in the DIs of black students and smallest in the DIs of Hispanic
students in every school level.
The results from the Two-Level HMLM models with school and county level predictors
are presented in Table 5-17, Table 5-18, and Table 5-19 for each school level. First, elementary
TPSs have fewer black students if they have more charter schools within a 10-mile radius, or if
they are closer to charter schools, they have fewer white students. This puzzle is a little bit
confusing, because since the DIs are relative indexes, each racial/ethnic group’s move should
affect the other group’s DIs in the opposite direction. However, if the results for elementary
TPSs are combined with the mean comparison of TPSs with CSs in Table 5-1 and the paired
mean comparisons of TPSs with the nearest CSs in Table 5-3, I can conclude that charter
elementary schools have been serving much lower percentages of black students than the TPSs
have. In Table 5-1, the mean DI of black students in CSs was -12.86 indicating that elementary
charter schools have 12.86% lower proportion of black students than the county average public
schools, while elementary TPSs have 2.78% higher percentage of black students. Also the mean
absolute deviations of CSs in Table 5-1 were larger than those of nearby TPSs, which means that
charter schools are more segregated than their nearby TPSs.
In conclusion, Floridian elementary charter schools have targeted white students on
average. Therefore, elementary charter schools have been likely to locate near those public
schools that have more white students and they draw white students from TPSs. This has two
effects: locating around more white TPSs and fewer black students represented by the coefficient
of RAD100 for DI of black students (-0.48, t = -4.08), and lowering the proportion of white
114
students in nearby TPSs represented by the MINDTCS coefficient (0.31, t = 2.00). Location
issues are verified by the coefficients of the maximum percentage of a certain racial/ethnic
groups in nearby TPSs within a 10-mile radius. The coefficients, MAXCS(D/G), were all
positive for three groups: 0.09 (t = 5.12) for DIBLK, 0.04 (t = 2.39) for DIWHT, and 0.18 (t =
7.35) for DIHSP. This means that the percentages of a certain group in elementary charter
schools are positively correlated to those of nearby TPSs. These relationships are supported by
the high correlations between them as shown by the paired mean comparisons in Table 5-3. The
DIs of Hispanic students move toward the opposite direction of the moves of DIs of black
students as shown by the coefficients of those variables and the high negative correlation
(Corr.(3.1) = -0.81, p<0.000) in Table 5-18. The location and targeting issues are supported also
by the correlations between the differences of demographic proportions in TPSs and those in the
nearby CSs. If a TPS has higher proportion of black students than that of white students, it is
more likely to have a CS with higher proportion of black students and lower percentage of white
students. These relationships are significant in all school level. Similar patterns exist among
other demographic groups.
Almost the same patterns are found in the relationships among traditional public middle
schools and nearby charter schools. One thing that is different in the case of middle schools is
that middle CSs are likely to locate around the TPSs with more white students and less Hispanic
students, while elementary CSs open more around the TPSs with fewer black students. The
location and targeting issues affect also the racial/ethnic distributions in high schools, even
though the relationship gets weaker. Since high school charters have a higher proportion of black
students, the numbers of charter schools within a 10-mile radius are related to the higher
percentage of black students in TPSs, at the same time they are related to the lower proportion of
Hispanic students in TPSs as shown in Table 5-19. However, the relationship of the proportion
of white students in high TPSs and in high CSs is mixed, because the distances to the nearest
charter schools from a TPS have positive effects on the proportion of white students in TPSs.
This suggest that closer high CSs decrease the DIWHT in TPSs, while the numbers of charter
schools within a 10-mile radius are related to the higher proportion of white students in TPSs.
115
Table 5-16 Correlations between the differences in DIs of TPSs and the demographic compositions in nearby CSs.
NRSTBLK NRSTWHT NRSTHSP MAXBLK MAXWHT MAXHSP
Elem
entary
(N=
15
22)
B-W .441* -.312 -.153 .230* -.124* -.015
B-H .451* -.194* -.309* .227* -.103* -.035
W-H -.033 .182* -.183* -.027 .040 -.024
Mid
dle
(N=
53
4)
B-W .468* -.235* -.128* .345* -.147* -.031
B-H .473* -.082 -.335* .378* -.037 -.136*
W-H -.037 .218* -.254* .011 .155* -.133*
Hig
h
(N=
27
5)
B-W .340* -.216* -.189* .302* -.015 -.146*
B-H .344* -.073 -.319* .378* .139* -.255*
W-H -.015 .211* -.169* .089 .215* -.144*
Note: * means the statistical significance at 0.05 level. B, W, and H stand for the DIs of black students, white
students, and Hispanic students, respectively. B-W, i.e., means the difference in DIs of black students and white
students.
My findings show a little different but more precise picture about how the charter schools
act and the nearby TPSs’ demographic compositions change by the entry of charter schools than
the previous studies did. For example, Ertas (2007) found that the percentage of white students
decreased in Floridian traditional public schools when they have charter school within 5-mile
radius. However, my analyses show that the percentage differences of racial/ethnic groups in
TPSs from the county means are still significantly large even though TPSs lost students of a
certain racial/ethnic group to the nearby charter schools because of charter school’s location
decision and targeting strategies. Also he did not consider the percentage changes of the minority
groups in TPSs.
The academic performance of TPSs is highly and negatively related to the proportion of
black students, while the relationship becomes much weaker to the percentage of white students
and neutral to that of Hispanic students. The proportions of FRL students in TPSs have
consistently and significantly negative influence on the proportion of white students and positive
influence on those of black and Hispanic students in TPSs. This indicates that the socio-
economic status of traditional public schools affect their racial/ethnic compositions more
116
consistently. Also the metropolitan location of charter schools is connected to the higher
proportion of black and Hispanic students in high TPSs and the lower percentage of white
students in elementary TPSs. This relationship of metropolitan location is also positive in the
move of DIs of FRL students.
County level variation was small, but the percentages of black and white students in TPSs
are positively related to higher percentages of charter-school students in elementary level, even
though the effect sizes were very small. This could be understood as another sign of charter-
school location and targeting strategies, or the results of the decrease in DIs of Hispanic students
in TPSs which could lead to higher proportions of black and white students. I calculated the
county percentage of Hispanic students in charter schools and got the correlation with the
percentages of charter-school students in counties which resulted in insignificant correlation.
Therefore, I could say that location and targeting explain the coefficient of PCHARTER in
elementary level better. In other words, more elementary charter schools have opened in those
counties that TPSs have higher percentages of black and white students, but lower percentages of
Hispanic students. The years of charter-school policy adoption have negative impact on the
percentage of white students in middle TPSs. This suggests that middle school charters located
near TPSs with a higher proportion of a certain racial/ethnic group and that had targeted those
students, and this will decrease the proportion of that group in the middle TPSs in the long run.
117
Table 5-17 Results from Two-Level HMLM models (Elementary School)
Fixed Effect DIBLK DIWHT DIHSP
Coef. (t-ratio) Coef. (t-ratio) Coef. (t-ratio)
Intercept, π00 10.20 (1.95) -5.02 (-1.56) -5.17 (-1.09)
YEARSADOPT, β 001 -3.35 (-0.91) -0.90 (-0.40) 4.25 (1.27)
PCHARTER, β 002 0.01 (10.31) 0.00 (5.42) -0.02 (-14.93)
PPVTHE, β 003 -0.29 (-1.98) 0.13 (1.40) 0.17 (1.26)
RAD50, π01 -0.48 (-4.08) 0.09 (1.19) 0.41 (3.80)
MINDTCS, π 02 -0.40 (-1.62) 0.31 (2.00) 0.12 (0.54)
MAXBLK, π 03 0.09 (5.12) -0.01 (-0.51) -0.08 (-5.26)
MAXWHT, π 04 -0.04 (-1.39) 0.04 (2.39) 0.00 (-0.16)
MAXHSP, π 05 -0.16 (-6.02) -0.02 (-1.29) 0.18 (7.35)
DIFRL, π06 0.40 (9.64) -0.66 (-25.69) 0.30 (7.81)
METRO, π 07 3.36 (1.82) -2.79 (-2.46) -0.44 (-0.27)
SUBURBAN, π 08 -1.23 (-0.75) -0.05 (-0.05) 1.09 (0.73)
MG5CTR, π 09 -0.14 (-2.05) 0.03 (0.76) 0.09 (1.54)
RG5CTR, π 10 -0.16 (-2.18) 0.05 (1.08) 0.10 (1.54)
Covariance Parameter Coefficient SE Wald Z Sig.
DIBLK Var(1) 345.79 13.18 26.24 .000
DIWHT Var(2) 130.70 4.98 26.24 .000
DIHSP Var(3) 285.56 10.88 26.24 .000
Corr(2,1) -0.42 0.02 -19.23 .000
Corr(3,1) -0.80 0.01 -82.79 .000
Corr(3,2) -0.19 0.03 -7.21 .000
118
Table 5-18 Results from Two-Level HMLM models (Middle School)
Fixed Effect DIBLK DIWHT DIHSP
Coef. t-ratio Coef. t-ratio Coef. t-ratio
Intercept, π00 1.01 (0.14) -5.10 (-1.14) 4.42 (0.67)
YEARSADOPT, β 001 0.15 (0.38) -0.52 (-2.10) 0.34 (0.94)
PCHARTER, β 002 0.01 (0.11) 0.15 (1.85) -0.16 (-1.39)
PPVTHE, β 003 -0.04 (-0.15) 0.18 (1.21) -0.12 (-0.54)
RAD100, π01 0.15 (0.56) 0.46 (2.86) -0.58 (-2.43)
MINDTCS, π 02 -0.31 (-0.77) 0.31 (1.25) 0.01 (0.03)
MAXBLK, π 03 0.14 (4.40) -0.01 (-0.30) -0.14 (-4.78)
MAXWHT, π 04 -0.03 (-0.72) 0.06 (2.13) -0.03 (-0.73)
MAXHSP, π 05 -0.09 (-1.95) -0.01 (-0.41) 0.10 (2.23)
DIFRL, π06 0.30 (3.52) -0.73 (-13.79) 0.44 (5.55)
METRO, π 07 1.00 (0.36) -1.53 (-0.90) 0.43 (0.17)
SUBURBAN, π 08 -0.54 (-0.22) 1.12 (0.74) -0.34 (-0.15)
MG5CTR, π 09 -0.63 (-3.00) 0.24 (1.84) 0.34 (1.77)
RG5CTR, π 10 0.22 (1.10) -0.29 (-2.31) 0.06 (0.32)
Covariance Parameter Coefficient SE Wald Z Sig.
DIBLK Var(1) 273.71 18.93 14.46 .000
DIWHT Var(2) 103.83 7.18 14.46 .000
DIHSP Var(3) 228.62 15.81 14.46 .000
Corr(2,1) -0.42 0.04 -10.50 .000
Corr(3,1) -0.81 0.02 -48.01 .000
Corr(3,2) -0.18 0.05 -3.76 .000
119
Table 5-19 Results from Two-Level HMLM models (High School)
Fixed Effect DIBLK DIWHT DIHSP
Coef. t-ratio Coef. t-ratio Coef. t-ratio
Intercept, π00 2.62 (0.30) -6.90 (-1.34) 5.04 (0.65)
YEARSADOPT, β001 -0.57 (-1.29) 0.09 (0.35) 0.52 (1.32)
PCHARTER, β002 0.32 (1.21) 0.13 (0.81) -0.42 (-1.76)
PPVTHE, β003 -0.54 (-1.87) -0.02 (-0.14) 0.58 (2.27)
RAD100, π01 1.32 (2.55) 0.70 (2.29) -1.91 (-4.14)
MINDTCS, π02 -0.32 (-0.76) 0.52 (2.09) -0.18 (-0.48)
MAXBLK, π 03 0.18 (3.94) 0.01 (0.37) -0.19 (-4.84)
MAXWHT, π 04 0.07 (0.99) 0.00 (0.02) -0.09 (-1.36)
MAXHSP, π 05 -0.07 (-0.81) -0.05 (-0.89) 0.09 (1.23)
DIFRL, π06 0.46 (4.25) -0.87 (-13.63) 0.39 (4.05)
METRO, π 07 6.68 (1.98) 0.60 (0.30) -7.39 (-2.46)
SUBURBAN, π 08 -1.86 (-0.59) 2.86 (1.56) -1.60 (-0.57)
MG5CTR, π 09 -0.28 (-0.83) 0.31 (1.56) -0.06 (-0.18)
RG5CTR, π 10 -0.10 (-0.45) -0.20 (-1.50) 0.25 (1.25)
Covariance Parameter Coefficient SE Wald Z Sig.
DIBLK Var(1) 220.60 20.48 10.77 .000
DIWHT Var(2) 76.21 7.08 10.77 .000
DIHSP Var(3) 174.99 16.25 10.77 .000
Corr(2,1) -0.46 0.05 -8.83 .000
Corr(3,1) -0.82 0.02 -37.84 .000
Corr(3,2) -0.12 0.06 -1.88 .061
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Overall, the charter schools decide their location under the consideration of their target
groups. Therefore, the relationships between the racial/ethnic compositions in TPSs to those in
CSs need to be understood in a reverse way: Charter school do not cause lower or higher
proportion of a certain racial/ethnic group in TPSs, instead, they decide to locate around the
TPSs that have a higher proportion of a certain racial/ethnic group which they target. This
tendency was examined in the paired-mean comparisons of the DIs of TPSs with the DIs of
nearby CSs in Table 5-3. The absolute deviations of charter school DIs are significantly higher
than those of nearby TPSs. Combined and considered together, charter schools locate near those
TPSs that have a higher proportion of a certain group, and recruit students from a certain
racial/ethnic group more. In the long run, the proportions of the targeted demographic groups by
charter schools will decrease in TPSs, as is the case of middle TPSs at the county level. Then
they create more racially segregated educational institutes in public education. All these things
being considered, the racial/ethnic compositions in TPSs are closely interrelated to the issues of
the socio-economic stratification, residential division, and academic achievement.
Now, let the proportion of explained variance be checked to examine the explanatory
power of the Two-Level HMLM models and compare it with those of Charter-school Effect
models that have no socio-economic, residential, or academic performance controls in Section
5.4. The proportions of explained variance in the Two-Level HMLM models are quite high,
especially for the DIs of white students. The variance in the DIs of black students explained by
the models was 46.65%, 43.15%, and 40.08% for each level of schools. The models in this
section increase the proportion of explained variance in the DIs of white students a lot. In the last
column of Table 5-20, I copied the explained proportion of variance in Charter-school Effect
models in section 5.4. Even though they are not comparable directly with the results in this
section because they used longitudinal data from 1998 to 2009 while the models in this section
used cross-sectional data of the school year 2009, the important implications could be found in
the comparisons: The percentage of white students is much more sensitive to the socio-economic
and residential factors than the proportion of black students, while the proportion of Hispanic
students is much more sensitive to the charter-school factors which is revealed by the
comparison of the Two-Level HMLM models (in the fifth column) with Charter-school Effect
models (in the last column). All racial/ethnic groups are not sensitive to the TPSs’ academic
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performance except the high school Hispanic students as we can see in the differences between
the fifth column and the seventh column25.
Table 5-20 Comparisons of the Explained Proportions in School Variance
ANOVA
Model
Two-Level
HMLM
Model
Two-Level
HMLM model
(No FCAT scores)
Charter
School
Effect
Model
Variance Variance Variance
Explained Variance
Variance
Explained
Variance
Explained
ELEMEN-
TARY
DIBLK 648.17 345.79 0.4665 355.20 0.4520 0.2806
DIWHT 416.01 130.7 0.6858 131.37 0.6842 0.1550
DIHSP 356.33 285.56 0.1986 289.65 0.1871 0.2801
MIDDLE
DIBLK 481.48 273.71 0.4315 286.65 0.4046 0.3470
DIWHT 296.76 103.83 0.6501 105.20 0.6455 0.0853
DIFRL 272.9 228.62 0.1623 239.14 0.1237 0.4386
HIGH
DIBLK 368.16 220.6 0.4008 240.56 0.3466 0.3722
DIWHT 228.57 76.21 0.6666 77.73 0.6599 0.1163
DIHSP 202.65 174.99 0.1365 194.19 0.0417 0.3043
5.6 Chapter Conclusion
This chapter investigated whether charter-school policy would exacerbate the racial and
socio-economic segregation in traditional public schools and in charter schools themselves
(Clotfelter, 2001; C. Lubienski, 2001, 2005b; Renzulli, 2006; Renzulli & Evans, 2005). The
analyses of the DI distribution among charter schools and TPSs revealed that the demographic
compositions in charter schools deviate more from the county means than do those of TPSs
during the period of 1998 through 2009. The DI distribution showed that the percentages of free
25 I ran all the Two-Level HMLM models after eliminating the FCAT scores whose variance components are
presented in the sixth column in Table 6-19.
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and reduced priced lunch program students in charter schools were much lower than the county
means at all school levels when they are compared to that of TPSs. The paired-mean
comparisons indicated that elementary charter schools have more white students but fewer
Hispanic students, middle charter schools have fewer Hispanic students, and high school charters
have more black students but fewer white students. TPSs have much higher proportion of FRL
students compared with that of the nearest charter schools in all school levels, indicating the
possibilities of cream-skimming higher socio-economic students from nearby TPSs.
The ANOVA analysis of the charter school DIs also indicated that the initial mean
percentages of FRL students in CSs were quite a bit lower than the county mean. Charter high
schools have 6.29 % lower proportions of FRL students, charter elementary and middle schools
have 15.04% and 14.29% lower proportions in their starting years, respectively. According to the
results of yearly change models, the percentages of black students in elementary charter schools
decrease by 7.3% per year, but the percentages of white students in elementary charter schools
increase by 0.69% per year.
The models for charter school DIs using DIs of FRL students, charter-school location,
and some county level variables as control variables suggested that the percentage of FRL
students have opposite effects on the proportions of black students and on the percentages of
white students in charter schools. DIFRL increases the black student percentages, but decrease
the white student percentages in charter schools. The years of charter-school adoption in a
county have similar effects on both groups: The longer it is since a county introduced charter-
school policy, the fewer black students and the more white students will enroll in charter schools.
These segregation effects between black and white students in charter schools will be worse in
elementary schools, because they have negative yearly change rates. Neighboring charter schools
influence positively on the percentage of black students and Hispanic students, but negatively on
the percentage of white students represented by the coefficients of the number of charter schools
within a 10-mile radius (RAD100) and the demographic compositions in the nearest charter
school (MAXCS(D/G) variables on the school age (SCHAGE) slopes. Charter schools in large
cities have higher percentages of black students, and they are likely to increase the availability of
charter schools to black students which is known as the “trickle-down effect” which provides
opportunities to the poor by lowering the cost of certain product consumption or services. The
dissimilarity index (DI) analyses of charter school suggested that, over all, charter schools have
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lower proportions of black students, Hispanic students and FRL students, while they have similar
or higher proportion of white students than the county mean on average. And the racial
compositions of charter schools are closely correlated to the socio-economic status in Floridian
public charter schools.
The results from the yearly change models for the demographic composition changes in
traditional public schools indicated that the increasing proportion of black students and FRL
recipients have enrolled in TPSs for all school levels along the years during the period of 1998-
2009, but that the percentages of white students in TPSs have decreased year by year even
though the rates are small. The models using charter-school variables at the school level and
county level (Charter-school Effect Model) ensured the finding in the analyses of charter school
DIs. The percentages of the same demographic groups in nearby charter schools affect positively,
or neutrally. No negative effects from the demographic compositions of nearby charter schools
may be caused by the charter-school location decisions. In other words, charter schools are likely
to locate around TPSs that have a higher proportion of a certain demographic group. Therefore,
the relationship might be reversed: the higher proportion of a certain demographic groups in a
certain area would induce charter schools to target these groups. Also the results suggested that
charter schools have drawn more white students than black students or FRL students from TPSs,
but the direction of effects on Hispanic student enrollment in TPSs is not decisive. Charter-
school-related predictors at the school level explained the variance in the DIs of black students
and of Hispanic students better (ranging from 28.01% to 43.86%) than those of white students
(ranging from 8.53% to 15.50%) in TPSs. The proportions of explained variance in DIs of FRL
students are between ranging from 14.20% to 24.33%.
The separate models examined the influence of charter schools on the each demographic
group independently. However, the changes in demographic compositions of TPSs are
interrelated closely each other, because the proportions of a certain group will be dependent on
the other groups movements. To investigate the relative changes of DIs in TPSs, I introduced
hierarchical multivariate linear models (HMLM) in this chapter. The ANOVA HMLM models
showed that the mean differences between the DIs of black students and of white students, and
between the DIs of black students and of Hispanic students at every school level were
significantly different each other, while the mean differences between those of white students
and of Hispanic student were statistically identical at all school level.
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In conclusion, Floridian elementary charter schools have targeted white students at large.
Therefore, elementary charter schools have been likely to locate near those public schools that
have more white students and they draw more white students from TPSs. The DIs of Hispanic
students move in the opposite directions of the moves of DIs of black students as shown by the
coefficients of those variables and the high negative correlation. One thing different in the case
of middle schools is that middle CSs are likely to locate around the TPSs with more white
students and fewer Hispanic students, while elementary CSs open more around the TPSs with
fewer black students. The location decision and targeting strategies of charter schools affect also
the racial/ethnic distributions in high schools, even though the relationship gets weaker. The
academic performance of TPSs is highly and negatively related to the proportion of black
students, while the relationship becomes much weaker to the percentage of white students and
neutral to that of Hispanic students. The proportions of FRL students in TPSs have a consistently
and significantly negative influence on the proportion of white students and a positive influence
on those of black and Hispanic students in TPSs.
Combined and considered together, charter schools locate near those TPSs that have a
higher proportion of a certain group, and recruit students from a certain racial/ethnic group more.
Then they create more racially segregated educational institutes in public education. The
racial/ethnic compositions in TPSs are closely interrelated to the issues of the socio-economic
stratification and residential division.
The HLML models in the last section greatly increased the proportion of explained
variance in the DIs of white students. Comparisons of the proportions of variance explained by
HMLM models and those of other models in this chapter revealed that the percentage of white
students is much more sensitive to the socio-economic and residential factors than the proportion
of black students, while the proportion of Hispanic students is much more sensitive to the
charter-school factors. All proportions of racial/ethnic groups are not sensitive to the TPSs’
academic performance except the high school Hispanic students. The HMLM models provide a
more precise and dynamic picture about how the demographic groups in TPSs and CSs behave
by considering the relative relationships among multiple demographic groups when a public
policy is introduced.
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CHAPTER SIX
CONCLUSION AND DISCUSSION
6.1 Research Design and Framework
Charter-school policy has multiple goals: to enhance the quality of public schooling, to
satisfy the expectations of parents, and to improve the efficiency of public school administration.
Developing effective schools and promoting market for education are two of the main goals of
the charter-school movement, while the racial and residential segregation (Clotfelter, 2001; C.
Lubienski, 2001, 2005a; Renzulli, 2006; Renzulli & Evans, 2005), cream-skimming and
cropping (Henig, 1996; Lacireno-Paquet, et al., 2002), and withdrawal of financial and human
resources from traditional public schools have been frequently mentioned as reasons to oppose
the charter-school policy. To evaluate the contradictory argument on the same policy issue, “the
evaluator should actively search for and construct a theoretically justified model” (Chen & Rossi,
1980, p. 111) Also public policy analysis should apply multiple perspectives. “Policy analysis
without broad, philosophical frames of reference is blind to the most important policy impacts
(deHaven-Smith, 1988, p. 1).
The previous studies on charter-school effects focused on one or two issues. Most
previous studies tested hypotheses from one perspective and tried to find evidence to falsify or
verify it. However, as deHaven-Smith (1988) emphasized, in a perspectival analysis, “the
possibility that conflicting perspectives might conceptualize the subject matter of policy analysis
in entirely different ways was overlooked” (p. 120). I investigated the charter-school effects on
student achievement in TPSs as well as in charter schools, and competition effects on student
achievement in TPSs from the market approach and from the socio-cultural approach as well. I
also explored the unintended consequences of charter-school policy regarding racial/ethnic
segregation and socio-economic stratification effects.
This study carved out from the school achievement literature three theories or rationales
for and against charter-school policy to analyze the charter-school impacts in Florida: 1) school
effectiveness theory, 2) market competition theory in education, and 3) social inequality theory.
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School effectiveness theory assumes that those schools with more autonomy, less political
control, and more sensitivity to parental preferences would create more effective instructional
programs, administrate schools more efficiently, and be more accountable for improving student
achievement. As a result, those schools would outperform the other schools (Budde, 1988;
Bulkley & Fisler, 2003; Chubb & Moe, 1990; Friedman, 1997). Market Competition theory
assumes that public choice would produce the Pareto optimum in the educational policy area,
which will lead to an efficient public school system (Chubb, 2006; Friedman, 1955; Tiebout,
1956). On the other hand, Social Inequality theory emphasizes the equality of educational
opportunity, and argues that such a quasi-market approach would produce unintended and
pernicious consequences such as racial segregation and socio-economic stratification, cream-
skimming of high performing students, and further weakening of public schools financially and
academically.
6.2 Primary Findings and Conclusions
6.2.1 Public School Characteristics
The descriptive statistics of charter schools and traditional public schools show that the
characteristics of charter schools in the educational environments, socio-economic status, and
racial/ethnic compositions compared to those of TPSs could be understood better when they are
classified by school level. Floridian charter schools and traditional public schools were
significantly different from each other in many educational, socio-economic and racial/ethnic
compositions. ANOVA models showed significant variation among public schools and counties
in FCAT math and reading scores, and showed that the school characteristics were more
influential on school performance than county characteristics or year effects, especially in the
higher grades.
6.2.2 Tests of competing theories on student achievement
The three competing theories on school performance were tested and the results showed
that school effectiveness theory works in some subjects and grades. Overall, charter schools in
Florida recruited low performing students or similarly performing student in math and reading
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scores from nearby TPSs or the community, and have operated more effectively than TPSs did in
that they show positive annual change rates in the 8th grade FCAT math and the 5th and 8th grade
FCAT reading scores. Market competition theory does not explain well the variation among
public schools and counties in the FCAT scores.
However, when the educational environment, socio-economic, and racial/ethnic factors
were introduced in the Social Inequality Models, the significant and positive effects in both
School Effectiveness models and Charter-school Effect Models disappeared or turned out to be
negative. Therefore, the Social Inequality Models explain better the differences in the FCAT
scores. The results from the most sophisticated models with various control variables did not
support the School Effectiveness Theory or the Market Competition Theory in charter-school
movement. The findings of the Coleman report (1966) are still true in the public schools in
Florida almost five decades later. Also the results are quite different from the findings of Forster,
and Winters (2003), Hoxby (2004), and Sass (2006), but in accord with the findings of Borman
et al. (2004), Hanushek and Rivkin (2006), Roy and Mishel (2005), and Rumberger and Palardy
(2005). The most significant difference between these two groups is that the former didn’t
control the demographic characteristics, while the latter and I did. The meta-analysis of studies
on student achievement of Floridian charter schools by Chung et al. (2009) reported results
similar to mine.
6.2.3 Distributions of Dissimilarity Indexes in Public Schools
This study explored the question of whether charter-school policy would exacerbate the
racial and socio-economic segregation in traditional public schools and in charter schools
themselves (Clotfelter, 2001; C. Lubienski, 2001, 2005b; Renzulli, 2006; Renzulli & Evans,
2005). The analyses of the Dissimilarity Index distributions among charter schools and TPSs
revealed that the demographic compositions in charter schools deviate more from the county
means than do those of TPSs during the period of 1998 through 2009. The DI distribution
showed that the percentages of free/reduced price lunch program students in charter schools were
much lower than the county mean in all school levels when they are compared to those of TPSs.
The paired-mean comparisons indicated that elementary charter schools have more white
students but fewer Hispanic students, middle charter schools have fewer Hispanic students, and
high charter schools have more black students but fewer white students. TPSs have much higher
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proportions of FRL students compared with those of the nearest charter schools in all school
levels, indicating the possibilities of cream-skimming higher socio-economic students from
nearby TPSs. Charter schools are more segregated racially, ethnically, and socio-economically
than traditional public schools.
6.2.4 Demographic composition and its changes in charter schools
The ANOVA analysis of the charter school DIs also indicated that the initial mean
percentages of FRL students in CSs are considerably lower than the county mean. The models
for charter school DIs using DIs of FRL students, charter-school location, and some county level
variables as control variables suggested that the percentage of FRL students have the opposite
effects on the proportions of black students and white students in charter schools. They increase
the black student percentages, but decrease the white student percentages in charter schools. The
years of charter-school adoption in a county have similar effects on both groups: The longer it
was since a county introduced charter-school policy, the fewer black students and the more white
students would enroll in charter schools. These segregation effects between black and white
students in charter schools were worse in elementary schools. Neighboring charter schools
influence positively on the percentage of black students and Hispanic students (demand-creating
relationship among blacker charter schools), but negatively on the percentage of white students
(competition-creating relationship among whiter charter schools). Charter schools in large cities
have a higher percentage of black students, and they are likely to increase the availability of
charter schools to black students that is known as “trickle-down effect” which provides
opportunities to the poor by lowering the cost of certain product consumption or services.
The dissimilarity index (DI) analyses of charter school suggested that, overall, charter
schools have lower proportions of black students, Hispanic students and FRL students, while
they have similar or higher proportions of white students than the county mean. And the racial
compositions of charter schools are closely correlated to socio-economic status in Floridian
public charter schools. Therefore, charter schools are likely used as pockets for white flight and
exacerbate socio-economic stratification in public schools. The analyses of charter school DIs
supported the warnings of white flight, self-isolation, and socio-economic stratification (Carnoy,
2000; Frankenberg, et al., 2003; Rivkin, 1994).
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6.2.5 Demographic composition and its changes in traditional public schools
The results from the yearly change models for the demographic composition changes in
traditional public schools indicated that the increasing proportion of black students and FRL
recipients have enrolled in TPSs for all school levels along the years during the period of 1998-
2009, but that the percentages of white students in TPSs have decreased year by year even
though the rates are small. The models using charter-school variables at the school level and
county level (Charter-school Effect Model) ensured the findings in the analyses of charter school
DI distributions. The percentages of the same demographic groups in nearby charter schools
affect positively, or neutrally. No negative effects from the demographic compositions of nearby
charter schools may be caused by the charter school location and targeting strategies. In other
words, charter schools are likely to locate around TPSs that have a higher proportion of a certain
demographic group. The relationship might be reversed: the higher proportion of certain
demographic groups in the area could induce charter schools to target these groups. Also the
results suggested that charter schools have drawn more white students than black students or
FRL students from TPSs, but the direction of effects on Hispanic student enrollment in TPSs is
not decisive.
Charter-school related predictors at the school level explained the variance in the DIs of
black students and of Hispanic students better (ranging from 28.01% to 43.86%) than those of
white students (ranging from 8.53% to 15.50%) in TPSs. The proportions of explained variance
in DIs of FRL students are between ranging from 14.20% to 24.33%.
6.2.6 Multivariate analyses of demographic compositions in TPSs
Since the changes in demographic compositions of TPSs are interrelated closely with
each other, investigation of the relative changes of DIs in TPSs requires multivariate analysis.
Therefore, hierarchical multivariate linear models (HMLM) were introduced. The ANOVA
HMLM modes showed that the mean differences between the DIs of black students and of white
students, and between the DIs of black students and of Hispanic students in TPSs of every school
level were significantly different from each other, while the mean differences between those of
white students and of Hispanic student were statistically identical in all school level. The results
from HMLM analyses suggested that Floridian elementary charter schools have targeted white
students at large. Therefore, elementary charter schools have been likely to locate near those
130
public schools that have more white students and they drew white students from TPSs more. The
DIs of Hispanic students moved to the opposite directions of the movements of DIs of black
students. In other words, they are negatively correlated in traditional public schools. One thing
different in the case of middle schools was that middle CSs are likely to locate around the TPSs
with more white students and fewer Hispanic students, while elementary CSs opened more
around the TPSs with fewer black students. The location and targeting strategies of charter
schools affected also the racial/ethnic distributions in high TPSs, even though the relationship
got weaker.
The academic performance of TPSs was highly and negatively related to the proportion
of black students, while the relationship becomes much weaker to the percentage of white
students and neutral to that of Hispanic students. The proportions of FRL students in TPSs have
a consistently and significantly negative influence on the proportions of white students and
positive influences on the percentages of black and Hispanic students in TPSs. Combined and
considered together, charter schools located near those TPSs that had a higher proportion of a
certain group, and recruited students from a certain racial/ethnic group more. Then they created
more racially segregated educational institutes in the public school system in Florida. The
racial/ethnic compositions in TPSs were closely interrelated to the issues of the socio-economic
stratification and residential division (Carnoy, 2000; Frankenberg, et al., 2003; Rivkin, 1994).
The HMLM models in the last chapter increased the proportion of explained variance in
the DIs of white students a lot. The comparisons of the explained variance proportions by
HMLM models and those of other models revealed that the percentages of white students were
much more sensitive to the socio-economic and residential factors than the proportions of black
students were, while the proportions of Hispanic students were much more sensitive to the
charter-school factors. All racial/ethnic groups were not sensitive to the TPSs’ academic
performance except the high school Hispanic students.
6.3 Contributions of This Study
This study put a focus on the impacts of institutional change by charter-school
introduction on student achievement and demographic compositions vis-à-vis the established
public educational system. “Institutions define and limit the set of choices of individuals” (North,
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1990, p. 4), and “the persistence of inefficient institutions” induces poor performance (North,
1990, p. 7). When institutions are changed by the introduction of a new public policy, the actors
in society should adapt their actions and strategies to get the most benefit from the new settings.
This study provided information on the way the public schools, both charter schools and
traditional public schools, behave when they faced institutional changes. They had their own
strategies regardless of the official purposes of a public policy. Charter schools strategically
decided their location and their targets. Traditional public schools reacted to the entry of charter
schools into their jurisdictions in the various ways regardless of the expectations of public policy
or of the contention of the policy advocate groups. This study is one example of institutional
change and the people’s reactions.
This study employed multiple perspectives. Most previous studies on charter-school
effects tested hypotheses from one perspective and tried to find evidence to falsify or verify it.
However, as deHaven-Smith (1988) emphasized, in a perspectival analysis, “the possibility that
conflicting perspectives might conceptualize the subject matter of policy analysis in entirely
different ways was overlooked” (p. 120). I investigated the charter-school effects on student
achievement in TPSs as well as in charter schools, and competition effects on student
achievement in TPSs from the market approach and from the socio-cultural approach as well. I
also explored the unintended consequences of charter-school policy regarding racial/ethnic
segregation and socio-economic stratification effects.
This study is the first research using Hierarchical Linear Modeling and Multivariate
Hierarchical Linear Modeling to investigate charter-school effects on student achievement from
competition impacts and on student racial/socio-economic compositions in traditional public
schools. Most of the previous studies used traditional regression analyses and put different levels
of information into the same level ignoring the nested nature of educational data. HLM enables
researchers to disaggregate the effects from different levels into separate levels, to examine from
what level the variance in the interested dependent variables mainly come, and to explain those
variation with appropriate level predictors. I examined the school differences in student
achievement and racial/socio-economic compositions by partitioning the effects into 3 levels
such as year effects, school effects and county effects.
This study will give policy makers and public administrators useful guidelines regarding
what they should focus on and where they put more emphasis to enhance public education
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system. This study could advise policy makers about how to prioritize among the policy
instruments. For instance, in order to improve public school effectiveness, policy makers can
promote more competition among schools, or introduce some compensatory courses for the
disadvantaged or poor students, or adopt mandatory balancing policy of racial composition in
accordance with that of county. This study will give some practical advice regarding these issues
to the policy makers and educational administrators.
6.4 Limitations of This Study
This study investigated some sources of school variance and county variance in student
achievement and demographic compositions. However, still, there are significant variation left
among schools and across counties, which requires more in-depth and sophisticated research
designs and projects. First of all, this project did not study where the year effects come from.
This is an important educational policy issue because the FCAT math scores have increased
yearly and steadily while the FCAT reading scores have decreased in the first couple of years but
turned to increase in the remaining years during the period, which is supposed to be equalized
based on the Sunshine State Standards by the educational authority. Then the issue in question is:
have Floridian elementary and secondary schools really improved their academic performance in
math and in reading after the FCAT introduction? Or are the increasing reading scores the results
of teaching for test, of adaptation to test, or of something else? What leads to the differences in
the change rates between of math and of reading?
This study used school performance data from FCAT math and reading scores to test
charter-school effects on student achievement and on demographic compositions. However, if
available, student level longitudinal data could have showed the more precise and detailed
picture about charter-school effects in Florida. Charter schools were not classified by their
educational and managerial characteristics. Charter schools serve a more diverse although
usually focused group of students than TPSs, because some are targeting at-risk students while
others focus academic excellence, and because some charter schools are established and
managed by public organizations or groups of teachers and parents while some are by
Educational Management Organizations for profits. Therefore, more in-depth research needs to
classify charter schools by the management body, their instructional strategies, target students,
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and so on. The school outcome in not only academic achievements, but many kinds of outcomes
such as student experiences, parent involvement and satisfaction, and managerial efficiency are
also important measures for school performance. Therefore, research on these outcomes is
required in the future studies in Florida.
In the analyses of segregation effects of charter-school policy introduction on charter
schools and traditional public schools as well, I suggested the possibility of the location and
targeting strategies of charter schools. This argument requires more sophisticated and in-depth
research and case studies for the details and the effects of their strategies on nearby TPSs.
Regarding segregation and stratification issues, they exist not just in regular public schools but
also between different types of schools, i.e., among vocational schools, alternative schools and
regular schools. This is another important issue in educational equality and the rights to learn,
which is not addressed in this study and warrants promising research.
6.5 Concluding Remark
Friedman (1955) argued:
The widening of the range of choice under a private system would operate to reduce both
kinds of stratification (General Education for Citizenship, para. 12) … Privately
conducted schools can resolve the dilemma. They make unnecessary either choice. Under
such a system, there can develop exclusively white schools, exclusively colored schools,
and mixed schools. Parents can choose which to send their children to. The appropriate
activity for those who oppose segregation and racial prejudice is to try to persuade others
of their views; if and as they succeed, the mixed schools will grow at the expense of the
non-mixed, and a gradual transition will take place. (Note 2, para. 2)
This is his belief on choice, community, and public policy. Mine is quite different from
his: Life is not started by choice. Choices could be chosen only on the basis of numerous non-
choices. Zhuangzi said that we could not walk if there are only the spots on earth for our feet.
Therefore, the trodden spots are useful only based on no use of the non-trodden spots. The
mission of public policy, public administrators, public offices regarding choice, I believe, is to
make it sure that all people could have choices by their own will regardless of their non-choices,
134
so to speak, such as the color of skin, their wealth from parents, their origin and gender, and so
on in lives. I believe also that Friedman’s choice will ruin the common ground for all including
the choosers.
The rich, the wealthy, and the powerful have many choices and they could wield them in
the way as they want to, while the poor, the have-nots, and the weak have few choices in every
arena of lives. Their habits, attitude, knowledge, experiences, mind-sets and so on are influenced
strongly by the poor and dire environment, which will be likely to lead them to the every adverse
of life. Therefore, public policies must lessen the influences of non-choices and strengthen the
role of choices in everyone’s life. However, according to my study and findings, charter school
as a kind of school choice is not the case to lessen the influence of non-choices on students in
public schools or to strengthen the role of choices for choosers in the path of their lives in charter
schools.
135
APPENDIX 1
CHARTER SCHOOL GROWTH IN FLORIDA
A1-1. Charter school growth in numbers of schools and students
School
Year
Number of charter schools Number of
CS students
Percentage of
CS students (%) Operated Increase Change (%)
1996-97 5
1997-98 30 25 500.0
1998-99 74 44 146.7
1999-00 118 44 59.5
2000-01 182 64 54.2
2001-02 201 19 10.4 40,465 1.62
2002-03 223 22 10.9 53,016 2.09
2003-04 257 34 15.2 67,512 2.60
2004-05 301 44 17.1 82,531 3.13
2005-06 334 33 11.0 92,214 3.45
2006-07 356 22 6.6 98,755 3.72
2007-08 358 2 0.6 105,239 3.97
2008-09 389 31 8.7 117,602 4.47
2009-10 410 21 5.4 137,196 5.21
2010-11 459 49 12.0 154,780 5.86
136
APPENDIX 2
DESCRIPTIVE STATISTICS OF FLORIDIAN PUBLIC SCHOOLS
A2-1. Public Elementary School
Traditional Public Schools Charter Schools t-test for Equality of
Means (Sig.)
Data
Source N Mean SD N Mean SD
Number of Students 19,519 711.15 250.10 988 389.39 329.24 .000 CCD
Free Lunch (%) 19,519 47.11 23.71 988 33.97 24.55 .000 CCD
Reduced Price Lunch (%) 19,519 10.06 4.20 988 8.63 6.02 .000 CCD
Free/Reduced Price Lunch (%) 19,519 57.17 24.68 988 42.60 27.43 .000 CCD
Stability Rate (%) 9,596 93.43 3.01 425 92.95 5.84 .097 FSIR
black Student (%) 19,519 26.95 26.82 988 26.35 30.98 .551 CCD
Hispanic Student (%) 19,519 21.29 23.38 988 22.65 25.36 .101 CCD
white Student (%) 19,519 49.50 30.28 988 48.89 32.80 .566 CCD
Disabled Student (%) 12,644 15.93 6.05 434 14.44 16.03 .053 FSIR
Gifted Student (%) 12,928 12.34 22.21 379 22.03 29.47 .000 FSIR
English Language Learner (%) 13,894 20.90 36.87 476 17.23 31.76 .014 FSIR
Students Absent more than 21 days (%) 14,315 6.86 3.94 555 6.72 5.29 .521 FSIR
Pupul-Teacher Ratio 19,508 15.93 2.59 708 19.34 24.48 .000 CCD
Class Size 7,833 20.95 6.31 110 25.09 46.39 .351 FSIR
Teacher with Advanced Degree (%) 14,314 31.24 11.38 555 12.25 19.46 .000 FSIR
Teachers' Experience (Years) 12,619 12.59 3.57 41 10.30 5.94 .018 FSIR
Classes Taught by Out-of-Field Teachers (%) 8,155 19.10 26.68 473 23.51 32.02 .003 FSIR
Per Pupil Expenditure (Regular) 12,651 4865.17 1391.32 0
FSIR
Instructional Staff (%) 12,641 64.58 7.48 439 37.18 36.90 .000 FSIR
Administrative Staff (%) 12,641 2.68 .87 439 3.11 6.62 .179 FSIR
137
A2-2. Public Middle School
Traditional Public Schools Charter Schools t-test for Equality of
Means (Sig.)
Data
Source N Mean SD N Mean SD
Number of Students 6,689 1040.18 405.17 682 389.92 367.42 .000 CCD
Free Lunch (%) 6,689 39.75 19.60 682 33.77 25.04 .000 CCD
Reduced Price Lunch (%) 6,689 9.80 3.68 682 8.55 6.05 .000 CCD
Free/Reduced Price Lunch (%) 6,689 49.55 21.14 682 42.32 27.94 .000 CCD
Stability Rate (%) 3,812 93.15 4.65 360 91.14 9.87 .000 FSIR
black Student (%) 6,689 24.30 22.78 682 27.81 31.39 .005 CCD
Hispanic Student (%) 6,689 19.00 21.51 682 23.01 26.57 .000 CCD
white Student (%) 6,689 54.48 28.37 682 47.38 33.64 .000 CCD
Disabled Student (%) 4,843 15.76 5.82 379 14.86 15.64 .267 FSIR
Gifted Student (%) 4,553 6.99 6.19 242 8.27 7.46 .009 FSIR
English Language Learner (%) 4,602 4.69 5.99 278 3.48 5.39 .000 FSIR
Students Absent more than 21 days (%) 4,862 11.52 6.53 388 9.78 9.04 .000 FSIR
Pupul-Teacher Ratio 6,676 17.96 3.03 475 20.23 24.47 .044 CCD
Class Size (Language Art) 2,032 24.39 4.13 80 25.77 14.08 .384 FSIR
Class Size (Math) 2,032 25.12 4.59 80 24.34 13.94 .621 FSIR
Teacher with Advanced Degree (%) 4,862 32.22 10.59 388 13.77 19.71 .000 FSIR
Teachers' Experience (Years) 4,836 12.10 3.05 42 10.56 8.07 .224 FSIR
Classes Taught by Out-of-Field Teachers (%) 2,830 7.95 9.20 307 11.95 20.91 .001 FSIR
Per Pupil Expenditure (Regular) 4,863 4824.67 1823.30 1 4799.00 - - FSIR
Instructional Staff (%) 4,862 66.86 6.54 388 39.58 38.00 .000 FSIR
Administrative Staff (%) 4,862 3.59 1.11 388 2.97 5.09 .017 FSIR
138
A2-3. Public High School
Traditional Public Schools Charter Schools t-test for
Equality of
Means (Sig.)
Data
Source N Mean SD N Mean SD
Number of Students 4,867 1721.63 927.08 326 462.30 461.71 .000 CCD
Free Lunch (%) 4,867 27.78 15.79 326 27.23 19.55 .619 CCD
Reduced Price Lunch (%) 4,867 6.89 3.59 326 6.83 5.72 .853 CCD
Free/Reduced Price Lunch (%) 4,867 34.67 17.89 326 34.06 21.94 .624 CCD
Stability Rate (%) 2,721 91.71 4.37 164 84.78 14.28 .000 FSIR
black Student (%) 4,867 23.71 21.44 326 28.01 28.64 .008 CCD
Hispanic Student (%) 4,867 16.46 19.15 326 23.26 26.82 .000 CCD
white Student (%) 4,867 57.50 27.15 326 47.10 31.06 .000 CCD
Disabled Student (%) 3,404 13.12 5.25 167 14.08 14.46 .396 FSIR
Gifted Student (%) 2,556 4.39 4.88 102 3.88 3.57 .295 FSIR
English Language Learner (%) 3,256 4.02 4.67 138 4.72 7.74 .288 FSIR
Students Absent more than 21 days (%) 3,427 15.28 8.41 168 17.29 16.11 .109 FSIR
Pupil-Teacher Ratio 4,825 18.75 3.79 225 26.87 37.41 .001 CCD
Class Size (Language Art) 1,426 24.65 4.31 24 26.28 22.27 .723 FSIR
Class Size (Math) 1,426 25.02 4.48 24 24.62 14.48 .895 FSIR
Teacher with Advanced Degree (%) 3,427 37.48 10.71 168 17.25 26.19 .000 FSIR
Teachers' Experience (Years) 3,405 13.51 2.90 26 6.96 5.02 .000 FSIR
Classes Taught by Out-of-Field Teachers (%) 1,995 6.83 8.76 144 14.69 25.18 .000 FSIR
Per Pupil Expenditure (Regular) 3,428 5191.60 2043.95 1 9691.00 . - FSIR
Instructional Staff (%) 3,427 68.52 7.31 168 42.33 38.60 .000 FSIR
Administrative Staff (%) 3,427 3.33 1.27 168 4.88 9.26 .031 FSIR
Note: The shaded cells are significantly different in the means between traditional public schools and charter schools. The data sets from CCD contain public school information from 1998 to 2009, and those from FSIR from 1998 to 2006.
139
A2-4. Characteristics of counties by School Level
N Min Max Mean SD
Elem
entary
Sch
ools
Number of Charter Students 807 0 16773 604.86 1590.82
Number of Regular Public Schools 804 500 180265 18966.31 30702.93
Percent of Free/Reduced Lunch Student 597 22.1 89.7 55.36 12.68
Stability Rate 469 86.1 98.0 94.15 1.42
Percent of Disabled Student 603 9.5 32.3 17.52 3.60
Percent of Gifted Student 575 .1 12.1 2.59 1.88
Percent of English Language Learners 592 .0 26.6 4.67 5.43
Graduation Rate 507 .0 94.3 66.02 22.38
Percent of Student Absent more than 21 Days 603 .7 23.8 7.58 3.22
Dropout Rate 353 .0 8.5 2.51 2.00
Percent of Suspensions (In School) 603 .0 25.8 3.33 4.05
Percent of Suspensions (Out of School) 603 .1 16.6 3.12 2.46
Average Class Size 268 16.4 31.3 22.09 2.11
Percent of Administrative Staffs 603 .0 5.6 2.53 .59
Percent of Instructional Staffs 603 42.9 78.6 61.86 5.63
Charter-school Presence 807 0 1 .49 .50
Mid
dle S
cho
ols
Number of Charter Students 807 0 14525 495.57 1349.88
Number of Regular Public Schools 804 232 161525 12256.14 20942.75
Percent of Free/Reduced Lunch Student 564 12.5 85.2 46.96 12.92
Stability Rate 466 87.3 97.6 93.73 1.53
Percent of Disabled Student 603 5.1 30.5 16.72 3.54
Percent of Gifted Student 577 .1 19.2 5.26 3.13
Percent of English Language Learners 574 .0 15.9 2.62 2.92
Graduation Rate 566 .0 94.3 69.06 15.78
Percent of Student Absent more than 21 Days 603 .9 29.6 12.28 4.52
Dropout Rate 394 .0 10.9 3.06 2.00
Percent of Suspensions (In School) 603 .0 55.6 19.28 11.85
Percent of Suspensions (Out of School) 603 .0 44.2 15.39 6.99
Average Class Size (Language Arts) 268 15.1 29.5 22.90 3.14
Average Class Size (Language Arts) 268 11.0 32.0 23.48 3.60
Percent of Administrative Staffs 603 .0 6.4 3.36 .85
Percent of Instructional Staffs 603 36.0 81.1 64.95 5.70
Charter-school Presence 807 0 1 .46 .50
140
N Min Max Mean SD
Hig
h S
choo
ls
Number of Charter Students 806 0 7256 240.44 767.23
Number of Regular Public Schools 804 284 117694 11463.20 18479.38
Percent of Free/Reduced Lunch Student 330 .0 74.3 8.70 18.97
Stability Rate 469 84.5 98.6 92.15 1.69
Percent of Disabled Student 603 7.0 26.8 14.40 3.38
Percent of Gifted Student 531 .0 12.4 3.42 2.69
Percent of English Language Learners 569 .0 14.5 2.39 2.75
Graduation Rate 603 43.1 94.3 71.00 9.20
Percent of Student Absent more than 21 Days 603 1.0 38.3 15.76 6.22
Dropout Rate 603 .0 13.3 3.54 1.87
Percent of Suspensions (In School) 603 .0 57.1 17.91 12.34
Percent of Suspensions (Out of School) 603 .0 43.3 13.33 5.94
Average Class Size (Language Arts) 268 12.7 32.3 22.77 3.48
Average Class Size (Mathematics) 268 12.8 32.5 23.16 3.66
Percent of Administrative Staffs 603 1.1 5.9 3.27 .79
Percent of Instructional Staffs 603 36.3 80.3 66.81 5.45
Charter-school Presence 806 0 1 .33 .471
All S
cho
ols
Per Pupil Expenditures (Regular) 603 3514 9287 4825.94 837.82
Percent of Teachers with Advanced Degrees 603 .0 54.6 30.16 8.05
Teachers Average Years of Experience 600 3.2 25.6 13.22 1.94
Percent of Classes Taught by Out-of-Field
Teachers 335 .0 43.6 8.33 7.16
A2-5. Demographic Characteristics of Counties
N Min Max Mean SD
Median household Income (USD) 536 23852 67238 37510.59 7945.86
Percent of People in Poverty 536 6.7 29.3 14.59 4.58
Percent of Children in Poverty (5-17) 536 7.7 37.0 19.66 5.92
Population 804 6961 2477289 256722.52 413943.93
Population Per Square Mile 804 8.4 3384.1 308.61 499.27
Percent of white 804 3.2 95.4 64.61 19.39
Percent of black 804 2.5 85.5 19.90 14.60
Percent of Hispanic 804 .2959 64.3 11.85 13.06
Number of Private School Students 804 0 73733 5052.74 10614.68
Number of Home Education Students 804 5 4443 730.51 886.07
Percent of Adult with High School Diploma 807 59.5 91.7 81.57 7.21
Percent of Adult with BA degrees (over 25) 807 5.8 41.0 18.98 8.62
141
APPENDIX 3
RESULTS FROM THE YEARLY CHANGE MODELS
A3-1. Results from the models for the 5th grade FCAT math scores
Fixed Effect Coefficient SE t-ratio d.f p-value
Overall mean, β000 306.32 1.27 241.32 66 <0.001
Overall mean yearly change rate, β100 3.55 0.21 16.60 66 <0.001
Overall acceleration rate, β200 -0.098 0.02 -6.22 66 <0.001
Random Effect Variance d.f. χ2 p-value
level-1, ε 81.96
School initial mean scores, e0 546.71 1906 21218.58 <0.001
School mean change rates, e1 9.72 1906 4082.01 <0.001
School mean acceleration rates, e2 0.05 1906 3814.81 <0.001
County initial mean scores, r00 58.19 66 303.63 <0.001
County mean change rates, r10 1.58 66 349.46 <0.001
County mean acceleration rates, r20 0.008 66 258.28 <0.001
Random level-1 and level-2 coefficient Reliability estimate
School initial status, ψ0 0.919
Yearly change rate, ψ1 0.504
acceleration rate, ψ2 0.450
County initial status, π00 0.538
County yearly change rate, π10 0.507
County acceleration rate, π20 0.464
Variance-Covariance Components and Correlations (italics)
Among the Level-2 and Level-3 Random Effects
Level 2, σ2e
ψ0 546.71 -21.67 0.41
ψ1 -0.297 9.72 -0.68
ψ2 0.075 -0.928 0.05
Level 3, τπ
π00 58.19 -2.56 0.01
π10 -0.267 1.58 -0.10
π20 0.022 -0.927 0.01
142
A3-2. Results from the models for the 8th grade FCAT math scores
Fixed Effect Coefficient SE t-ratio d.f p-value
Overall mean, β000 301.99 1.40 216.08 66 <0.001
Overall mean yearly change rate, β100 1.99 0.22 9.09 66 <0.001
Overall acceleration rate, β200 -0.01 0.02 -0.87 66 0.389
Random Effect Variance d.f. χ2 p-value
level-1, ε 44.34
School initial mean scores, e0 625.75 729 15933.49 <0.001
School mean change rates, e1 7.74 729 2030.79 <0.001
School mean acceleration rates, e2 0.03 729 1665.09 <0.001
County initial mean scores, r00 50.30 66 127.55 <0.001
County mean change rates, r10 1.42 66 138.39 <0.001
County mean acceleration rates, r20 0.01 66 160.60 <0.001
Random level-1 coefficient Reliability estimate
School initial status, ψ0 0.957
Yearly change rate, ψ1 0.524
acceleration rate, ψ2 0.413
County initial status, π00 0.382
County yearly change rate, π10 0.432
County acceleration rate, π20 0.439
Variance-Covariance Components and Correlations (italics)
Among the Level-2 and Level-3 Random Effects
Level 2, σ2e
ψ0 625.75 -12.92 -0.72
ψ1 -0.186 7.74 -0.46
ψ2 -0.155 -0.903 0.03
Level 3, τπ
π00 50.30 -4.37 0.18
π10 -0.518 1.42 -0.10
π20 0.281 -0.928 0.01
143
A3-2-1. Results from the models for the 8th grade FCAT math scores (Linear Model)
Fixed Effect Coefficient SE t-ratio d.f p-value
Overall mean, β000 306.49 1.32 232.61 66 <0.001 Overall mean yearly change rate, β100 1.79 0.09 20.06 66 <0.001
Random Effect Variance d.f. χ2 p-value
level-1, ε 42.23
School initial mean scores, e0 446.07 666 21206.29 <0.001
School mean change rates, e1 1.32 666 3182.10 <0.001
County initial mean scores, r00 44.28 66 137.41 <0.001
County mean change rates, r10 0.23 66 160.66 <0.001
Random level-1 coefficient Reliability estimate
School initial status, ψ0 0.965
Yearly change rate, ψ1 0.677
County initial status, π00 0.372
County yearly change rate, π10 0.426
Variance-Covariance Components and Correlations (italics)
Level 2, σ2e
ψ0 446.07 -0.545
ψ1 -0.545 1.32
Level 3, τπ π00 44.28 -0.689
π10 -0.689 0.29
Note: Since the quadratic term in Table A3-2 was insignificant, I eliminated it and re-run the model. The results from a linear model are presented in this table.
144
A3-3. Results from the models for the 10th grade FCAT math scores
Fixed Effect Coefficient SE t-ratio d.f. p-value
Overall mean, β000 298.49 1.26 237.19 66 <0.001
Overall mean yearly change rate, β100 3.68 0.21 17.56 66 <0.001
Overall acceleration rate, β200 -0.15 0.02 -10.20 66 <0.001
Random Effect Variance d.f. χ2 p-value
level-1, ε 49.40
School initial mean scores, e0 833.21 515 12242.83 <0.001
School mean change rates, e1 10.63 515 1517.62 <0.001
School mean acceleration rates, e2 0.05 515 1181.56 <0.001
County initial mean scores, r00 11.56 66 63.65 >.500
County mean change rates, r10 0.68 66 75.59 0.196
County mean acceleration rates, r20 0.00 66 74.79 0.214
Random level-1 coefficient Reliability estimate
School initial status, ψ0 0.964
Yearly change rate, ψ1 0.570
acceleration rate, ψ2 0.456
County initial status, π00 0.107
County yearly change rate, π10 0.223
County acceleration rate, π20 0.209
Variance-Covariance Components and Correlations (italics)
Among the Level-2 and Level-3 Random Effects
Level 2, σ2e
ψ0 833.21 -35.63 1.01
ψ1 -0.379 10.63 -0.67
ψ2 0.163 -0.957 0.05
Level 3, τπ
π00 11.56 0.88 -0.11
π10 0.315 0.68 -0.04
π20 -0.584 -0.897 0.00
145
A3-4. Results from the models for the 5th grade FCAT reading scores
Fixed Effect Coefficient SE t-ratio d.f. p-value
Overall mean, β000 294.45 1.42 206.94 66 <0.001
Overall mean yearly change rate, β100 -0.57 0.17 -3.27 66 0.002
Overall acceleration rate, β200 0.18 0.01 14.08 66 <0.001
Random Effect Variance d.f. χ2 p-value
level-1, ε 93.89
School initial mean scores, e0 519.57 1883 17282.87 <0.001
School mean change rates, e1 7.16 1883 3185.51 <0.001
School mean acceleration rates, e2 0.03 1883 2690.84 <0.001
County initial mean scores, r00 81.95 66 474.79 <0.001
County mean change rates, r10 0.84 66 171.13 <0.001
County mean acceleration rates, r20 0.004 66 156.44 <0.001
Random level-1 coefficient Reliability estimate
School initial status, ψ0 0.886
Yearly change rate, ψ1 0.410
acceleration rate, ψ2 0.313
County initial status, π00 0.603
County yearly change rate, π10 0.409
County acceleration rate, π20 0.397
Variance-Covariance Components and Correlations (italics)
Among the Level-2 and Level-3 Random Effects
Level 2, σ2e
ψ0 519.57 -7.12 -0.37
ψ1 -0.117 7.16 -0.44
ψ2 -0.094 -0.929 0.03
Level 3, τπ
π00 81.95 -1.42 -0.09
π10 -0.171 0.84 -0.05
π20 -0.148 -0.842 0.00
146
A3-5. Results from the models for the 8th grade FCAT reading scores
Fixed Effect Coefficient SE t-ratio d.f. p-value
Overall mean, β000 296.92 1.18 251.51 66 <0.001
Overall mean yearly change rate, β100 -0.45 0.20 -2.19 66 0.032
Overall acceleration rate, β200 0.15 0.02 10.26 66 <0.001
Random Effect Variance d.f. χ2 p-value
level-1, ε 53.99
School initial mean scores, e0 567.86 729 11809.95 <0.001
School mean change rates, e1 10.44 729 1927.28 <0.001
School mean acceleration rates, e2 0.04 729 1531.89 <0.001
County initial mean scores, r00 26.55 66 109.79 <0.001
County mean change rates, r10 0.79 66 101.55 0.003
County mean acceleration rates, r20 0.004 66 110.94 <0.001
Random level-1 coefficient Reliability estimate
School initial status, ψ0 0.944
Yearly change rate, ψ1 0.543
acceleration rate, ψ2 0.425
County initial status, π00 0.284
County yearly change rate, π10 0.280
County acceleration rate, π20 0.291
Variance-Covariance Components and Correlations (italics)
Among the Level-2 and Level-3 Random Effects
Level 2, σ2e
ψ0 567.87 -7.32 -0.83
ψ1 -0.095 10.44 -0.64
ψ2 -0.165 -0.940 0.04
Level 3, τπ
π00 26.55 -0.94 -0.002
π10 -0.205 0.79 -0.05
π20 -0.005 -0.912 0.004
147
A3-6. Results from the models for the 10th grade FCAT reading scores
Fixed Effect Coefficient SE t-ratio d.f. p-value
Overall mean, β000 289.29 1.10 262.31 66 <0.001
Overall mean yearly change rate, β100 -0.72 0.26 -2.80 66 0.007
Overall acceleration rate, β200 0.07 0.02 3.73 66 <0.001
Random Effect Variance d.f. χ2 p-value
level-1, ε 70.67
School initial mean scores, e0 923.90 505 8398.41 <0.001
School mean change rates, e1 10.31 505 1123.03 <0.001
School mean acceleration rates, e2 0.04 505 986.47 <0.001
County initial mean scores, r00 7.93 66 55.89 >.500
County mean change rates, r10 1.45 66 107.21 0.001
County mean acceleration rates, r20 0.01 66 95.28 0.011
Random level-1 coefficient Reliability estimate
School initial status, ψ0 0.955
Yearly change rate, ψ1 0.502
acceleration rate, ψ2 0.392
County initial status, π00 0.071
County yearly change rate, π10 0.323
County acceleration rate, π20 0.286
Variance-Covariance Components and Correlations (italics)
Among the Level-2 and Level-3 Random Effects
Level 2, σ2e
ψ0 923.90167 7.26913 0.67819
ψ1 0.074 10.31259 -0.62049
ψ2 0.105 -0.912 0.04490
Level 3, τπ
π00 7.93410 2.74035 -0.22050
π10 0.807 1.45270 -0.08997
π20 -0.970 -0.925 0.00651
148
APPENDIX 4
RESULTS FROM THE CHARTER-SCHOOL EFFECT MODELS
A4-1. Results from the Model with Charter Dummy in Level 2 (5th grade; math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 306.45 1.32 231.81 66 <0.001
CHARTER, β010 -6.33 4.20 -1.51 66 0.137
For YEAR slope, ψ1
Overall mean change rate, β100 3.51 0.22 16.07 66 <0.001
CHARTER, β110 0.97 0.88 1.10 66 0.273
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.10 0.02 -5.99 66 <0.001
CHARTER, β210 -0.006 0.08 -0.08 66 0.940
Random Effect Variance d.f. χ2 p-value
level-1, ε 81.08
School initial mean scores, e0 483.27 1693 19214.62 <0.001
School mean change rate, e1 9.17 1693 3679.26 <0.001
School mean acceleration rate, e2 0.05 1693 3429.91 <0.001
County initial mean, r00 67.05 34 289.22 <0.001
CHARTER effects on School initial mean, r01 445.50 34 158.49 <0.001
County mean change rates, r10 1.67 34 313.44 <0.001
CHARTER effects on School mean change rate, r11 18.31 34 82.07 <0.001
County mean acceleration rate, r20 0.008 34 211.12 <0.001
CHARTER effects on School mean acceleration rate, r21 0.14 34 72.20 <0.001
149
A4-2. Results from the Model with Charter Dummy in Level 2 (8th grade; math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For INTRCPT1, ψ0
Overall mean score, β000 305.90 1.43 213.37 66 <0.001
CHARTER, β010 1.35 2.58 0.52 66 0.603
For YEAR12 slope, ψ1
Overall mean change rate, β100 1.71 0.09 19.49 66 <0.001
CHARTER, β110 1.51 0.27 5.64 66 <0.001
Random Effect Variance d.f. χ2 p-value
level-1, ε 42.15
School initial mean scores, e0 432.78 527 18644.60 <0.001
School mean change rate, e1 1.10 527 2460.55 <0.001
County initial mean, r00 57.29 30 102.73 <0.001
CHARTER effects on School initial mean, r01 52.19 30 41.13 0.085
County mean change rates, r10 0.23 30 122.27 <0.001
CHARTER effects on School mean change rate, r11 0.87 30 55.93 0.003
150
A4-3. Results from the Model with Charter Dummy in Level 2 (10th grade; math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 300.59 1.48 202.71 66 <0.001
CHARTER, β010 -7.52 5.13 -1.47 66 0.148
For YEAR slope, ψ1
Overall mean change rate, β100 3.84 0.19 19.72 66 <0.001
CHARTER, β110 -1.74 1.15 -1.52 66 0.134
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.17 0.01 -12.35 66 <0.001
CHARTER, β210 0.15 0.11 1.37 66 0.176
Random Effect Variance d.f. χ2 p-value
level-1, ε 46.91
School initial mean scores, e0 703.76 371 8593.00 <0.001
School mean change rate, e1 9.46 371 923.18 <0.001
School mean acceleration rate, e2 0.04 371 720.90 <0.001
County initial mean, r00 43.01 27 50.77 0.004
CHARTER effects on School initial mean, r01 513.62 27 61.81 <0.001
County mean change rates, r10 0.42 27 39.40 0.058
CHARTER effects on School mean change rate, r11 25.56 27 69.89 <0.001
County mean acceleration rate, r20 0.002 27 43.77 0.022
CHARTER effects on School mean acceleration rate, r21 0.22 27 79.56 <0.001
151
A4-4. Results from the Model with Charter Dummy in Level 2 (5th grade; reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 295.44 1.40 210.56 66 <0.001
CHARTER, β010 -12.43 3.88 -3.21 66 0.002
For YEAR slope, ψ1
Overall mean change rate, β100 -0.80 0.18 -4.46 66 <0.001
CHARTER, β110 3.79 0.62 6.15 66 <0.001
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.19 0.01 14.40 66 <0.001
CHARTER, β210 -0.20 0.04 -4.47 66 <0.001
Random Effect Variance d.f. χ2 p-value
level-1, ε 93.46
School initial mean scores, e0 464.02 1668 15679.28 <0.001
School mean change rate, e1 6.20 1668 2774.02 <0.001
School mean acceleration rate, e2 0.03 1668 2379.10 <0.001
County initial mean, r00 79.61 34 436.57 <0.001
CHARTER effects on School initial mean, r01 350.91 34 118.67 <0.001
County mean change rates, r10 0.95 34 130.42 <0.001
CHARTER effects on School mean change rate, r11 5.94 34 77.99 <0.001
County mean acceleration rate, r20 0.01 34 125.34 <0.001
CHARTER effects on School mean acceleration rate, r21 0.02 34 65.66 0.001
152
A4-5. Results from the Model with Charter Dummy in Level 2 (8th grade; reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 298.34 1.38 216.79 66 <0.001
CHARTER, β010 -9.89 3.51 -2.82 66 0.006
For YEAR slope, ψ1
Overall mean change rate, β100 -0.99 0.17 -5.85 66 <0.001
CHARTER, β110 4.08 0.62 6.60 66 <0.001
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.19 0.01 13.79 66 <0.001
CHARTER, β210 -0.23 0.05 -4.35 66 <0.001
Random Effect Variance d.f. χ2 p-value
level-1, ε 53.41
School initial mean scores, e0 466.81 596 9727.75 <0.001
School mean change rate, e1 7.29 596 1419.52 <0.001
School mean acceleration rate, e2 0.03 596 1161.80 <0.001
County initial mean, r00 52.34 32 92.84 <0.001
CHARTER effects on School initial mean, r01 256.38 32 84.64 <0.001
County mean change rates, r10 0.43 32 51.60 0.015
CHARTER effects on School mean change rate, r11 6.60 32 55.91 0.006
County mean acceleration rate, r20 0.00 32 64.04 <0.001
CHARTER effects on School mean acceleration rate, r21 0.04 32 60.11 0.002
153
A4-6. Results from the Model with Charter Dummy in Level 2 (10th grade; reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 295.28 1.46 202.93 66 <0.001
CHARTER, β010 -21.96 5.93 -3.70 66 <0.001
For YEAR slope, ψ1
Overall mean change rate, β100 -0.86 0.23 -3.75 66 <0.001
CHARTER, β110 0.47 1.61 0.29 66 0.77
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.09 0.02 5.36 66 <0.001
CHARTER, β210 0.00 0.18 -0.02 66 0.985
Random Effect Variance d.f. χ2 p-value
level-1, ε 67.77
School initial mean scores, e0 639.54 369 4951.39 <0.001
School mean change rate, e1 9.07 369 708.35 <0.001
School mean acceleration rate, e2 0.04 369 596.54 <0.001
County initial mean, r00 46.46 27 42.91 0.027
CHARTER effects on School initial mean, r01 880.16 27 83.37 <0.001
County mean change rates, r10 0.87 27 50.16 0.005
CHARTER effects on School mean change rate, r11 58.11 27 69.08 <0.001
County mean acceleration rate, r20 0.00 27 52.11 0.003
CHARTER effects on School mean acceleration rate, r21 0.73 27 104.86 <0.001
154
A4-7. Results from the Model with Charter Policy Variables in Level 3 (5th grade; math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 303.09 3.27 92.63 64 <0.001
YEARSADOPT, β001 -0.00 0.42 -0.002 64 0.999
ADOPTION, β002 4.04 5.45 0.74 64 0.461
For YEAR slope, ψ1, ψ1
Overall mean change rate, β100 3.36 0.39 8.70 64 <0.001
YEARSADO, β101 0.17 0.08 2.05 64 0.044
ADOPTION, β102 -1.40 0.95 -1.47 64 0.148
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.07 0.03 -2.02 64 0.048
YEARSADOPT, β201 -0.01 0.006 -2.09 64 0.040
ADOPTION, β202 0.08 0.07 1.16 64 0.252
Random Effect Variance d.f. χ2 p-value
level-1, ε 81.27
School initial mean scores, e0 514.26 1900 21091.94 <0.001
School mean change rates, e1 9.53 1900 4001.75 <0.001
School mean acceleration rates, e2 0.05 1900 3727.72 <0.001
County initial mean scores, r00 59.08 64 337.72 <0.001
County mean change rates, r10 1.39 64 298.34 <0.001
County mean acceleration rates, r20 0.007 64 215.77 <0.001
155
A4-8. Results from the Model with Charter Policy Variables in Level 3 (8th grade; math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 301.17 2.59 116.18 64 <0.001
YEARSADOPT, β001 -0.62 0.49 -1.27 64 0.208
ADOPTION, β002 12.56 5.23 2.40 64 0.019
For YEAR slope, ψ1, ψ1
Overall mean change rate, β100 1.94 0.14 14.29 64 <0.001
YEARSADOPT, β101 0.08 0.03 2.47 64 0.016
ADOPTION, β102 -0.94 0.31 -3.04 64 0.003
Random Effect Variance d.f. χ2 p-value
level-1, ε 42.25
School initial mean scores, e0 444.15 666 21200.88 <0.001
School mean change rates, e1 1.31 666 3180.924 <0.001
County initial mean scores, r00 39.70 64 129.74 <0.001
County mean change rates, r10 0.19 64 141.93 <0.001
156
A4-9. Results from the Model with Charter Policy Variables in Level 3 (10th grade; math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 296.68 3.96 74.99 64 <0.001
YEARSADOPT, β001 -0.34 0.28 -1.25 64 0.216
ADOPTION, β002 6.48 4.75 1.36 64 0.177
For YEAR slope, ψ1, ψ1
Overall mean change rate, β100 3.61 0.37 9.79 64 <0.001
YEARSADO, β101 -0.11 0.06 -1.95 64 0.055
ADOPTION, β102 1.05 0.58 1.82 64 0.074
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.15 0.02 -6.82 64 <0.001
YEARSADOPT, β201 0.01 0.00 2.35 64 0.022
ADOPTION, β202 -0.09 0.04 -2.32 64 0.024
Random Effect Variance d.f. χ2 p-value
level-1, ε 47.28
School initial mean scores, e0 765.77 494 11687.43 <0.001
School mean change rates, e1 10.24 494 1437.87 <0.001
School mean acceleration rates, e2 0.05 494 1084.57 <0.001
County initial mean scores, r00 13.88 64 69.82 0.288
County mean change rates, r10 0.49 64 69.39 0.3
County mean acceleration rates, r20 0.00 64 65.35 0.43
157
A4-10. Results from the Model with Charter Policy Variables in Level 3 (5th grade; reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
Initial mean score, ψ0
Overall mean score, β000 293.27 2.58 113.54 64 <0.001
YEARSADOPT, β001 2.74 5.31 0.52 64 0.608
ADOPTION, β002 -0.08 0.47 -0.16 64 0.871
YEAR slope, ψ1, ψ1
Overall mean change rate, β100 -0.54 0.43 -1.27 64 0.208
YEARSADO, β101 -0.63 0.87 -0.73 64 0.471
ADOPTION, β102 0.03 0.07 0.40 64 0.692
YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.17 0.03 5.71 1597 <0.001
YEARSADOPT, β201 0.04 0.06 0.65 1597 0.519
ADOPTION, β202 0.00 0.01 -0.19 1597 0.852
Random Effect Variance d.f. χ2 p-value
level-1, ε 93.54
School initial mean scores, e0 403.82 1658 14968.62 <0.001
School mean change rates, e1 6.36 1658 2938.88 <0.001
School mean acceleration rates, e2 0.03 1724 2548.92 <0.001
County initial mean scores, r00 81.06 64 568.43 <0.001
County mean change rates, r10 0.24 64 624.68 <0.001
158
A4-11. Results from the Model with Charter Policy Variables in Level 3 (8th grade; reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 294.90 2.26 130.39 64 <0.001
YEARSADOPT, β001 -0.65 0.44 -1.48 64 0.143
ADOPTION, β002 9.24 4.93 1.87 64 0.066
For YEAR slope, ψ1, ψ1
Overall mean change rate, β100 -0.94 0.25 -3.68 64 <0.001
YEARSADOPT, β101 0.09 0.08 1.14 64 0.259
ADOPTION, β102 -0.32 0.84 -0.38 64 0.706
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.20 0.02 10.17 64 <0.001
YEARSADOPT, β201 0.00 0.01 -0.35 64 0.725
ADOPTION, β202 -0.03 0.06 -0.52 64 0.608
Random Effect Variance d.f. χ2 p-value
level-1, ε 53.38
School initial mean scores, e0 517.86 725 11481.01 <0.001
School mean change rates, e1 10.31 725 1917.65 <0.001
School mean acceleration rates, e2 0.04 725 1529.76 <0.001
County initial mean scores, r00 16.49 64 96.60 0.005
County mean change rates, r10 0.67 64 93.09 0.01
County mean acceleration rates, r20 0.00 64 105.62 0.001
159
A4-12. Results from the Model with Charter Policy Variables in Level 3 (10th grade; reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 291.22 4.39 66.30 64 <0.001
YEARSADOPT, β001 -0.76 0.27 -2.85 64 0.006
ADOPTION, β002 7.83 5.14 1.52 64 0.133
For YEAR slope, ψ1, ψ1
Overall mean change rate, β100 -1.55 0.46 -3.40 64 0.001
YEARSADOPT, β101 -0.12 0.07 -1.56 64 0.124
ADOPTION, β102 1.91 0.72 2.65 64 0.01
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.12 0.03 3.42 64 0.001
YEARSADOPT, β201 0.01 0.00 2.02 64 0.047
ADOPTION, β202 -0.13 0.05 -2.63 64 0.011
Random Effect Variance d.f. χ2 p-value
level-1, ε 68.68
School initial mean scores, e0 756.33 489 7421.27 <0.001
School mean change rates, e1 10.11 489 1048.09 <0.001
School mean acceleration rates, e2 0.04 489 908.64 <0.001
County initial mean scores, r00 12.17 64 64.75 0.45
County mean change rates, r10 1.03 64 92.83 0.011
County mean acceleration rates, r20 0.00 64 80.77 0.077
160
APPENDIX 5
RESULTS FROM THE MARKET COMPETITION MODELS
A5-1. Results from the Model with Charter Presence Dummy in Level 2 (5th grade; math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 313.41 1.89 165.83 45 <0.001
ANYCS25, β010 -9.16 2.06 -4.44 1584 <0.001
ANYCS50, β020 -3.37 1.70 -1.98 1584 0.048
For YEAR slope, ψ1
Overall mean change rate, β100 3.67 0.26 14.17 45 <0.001
ANYCS25, β110 0.22 0.31 0.72 1584 0.470
ANYCS50, β120 -0.35 0.28 -1.25 1584 0.212
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.12 0.02 -5.98 45 <0.001
ANYCS25, β210 0.00 0.02 0.01 1584 0.991
ANYCS50, β220 0.03 0.02 1.10 1584 0.271
Random Effect Variance d.f. χ2 p-value
level-1, ε 76.49
School initial mean scores, e0 428.42 1645 17226.61 <0.001
School mean change rate, e1 7.98 1645 3510.33 <0.001
School mean acceleration rate, e2 0.05 1645 3320.79 <0.001
County initial mean, r00 49.00 45 272.54 <0.001
County mean change rates, r10 1.90 45 377.02 <0.001
County mean acceleration rate, r20 0.01 45. 257.58 <0.001
161
A5-2. Results from the Model with Charter Presence Dummy in Level 2 (8th grade; math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 306.74 2.78 110.33 44 <0.001
ANYCS25, β010 -6.41 2.25 -2.85 525 0.004
ANYCS50, β020 0.88 3.51 0.25 525 0.801
For YEAR slope, ψ1
Overall mean change rate, β100 1.73 0.13 13.28 44 <0.001
ANYCS25, β110 -0.16 0.12 -1.39 525 0.166
ANYCS50, β120 0.03 0.12 0.27 525 0.786
Random Effect Variance d.f. χ2 p-value
level-1, ε
School initial mean scores, e0 538.78 567 21701.72 <0.001
School mean change rate, e1 1.22 567 2725.45 <0.001
County initial mean, r00 59.41 44 119.38 <0.001
County mean change rates, r10 0.26 44 164.14 <0.001
162
A5-3. Results from the Model with Charter Presence Dummy in Level 2 (10th grade; math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 300.98 2.85 105.72 39 <0.001
ANYCS25, β010 -2.60 3.08 -0.84 309 0.400
ANYCS50, β020 -5.00 3.99 -1.25 309 0.211
ANYCS100, β030 6.84 2.86 2.39 309 0.017
For YEAR slope, ψ1
Overall mean change rate, β100 4.62 0.37 12.54 39 <0.001
ANYCS25, β110 -0.24 0.29 -0.84 309 0.404
ANYCS50, β120 0.26 0.45 0.58 309 0.563
ANYCS100, β130 -1.08 0.45 -2.41 309 0.017
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.23 0.02 -9.93 39 <0.001
ANYCS25, β210 0.03 0.02 1.37 309 0.171
ANYCS50, β220 0.00 0.03 0.04 309 0.971
ANYCS100, β230 0.06 0.03 2.14 309 0.033
Random Effect Variance d.f. χ2 p-value
level-1, ε 38.99
School initial mean scores, e0 644.57 362 9129.65 <0.001
School mean change rate, e1 6.39 362 930.14 <0.001
School mean acceleration rate, e2 0.02 362 684.40 <0.001
County initial mean, r00 20.94 39 53.07 0.066
County mean change rates, r10 0.69 39 67.28 0.004
County mean acceleration rate, r20 0.00 39 66.99 0.004
163
A5-4. Results from the Model with Charter Presence Dummy in Level 2 (5th grade; reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 301.12 2.01 149.78 45 <0.001
ANYCS25, β010 -7.84 2.11 -3.71 1584 <0.001
ANYCS50, β020 -3.52 1.90 -1.85 1584 0.064
For YEAR slope, ψ1
Overall mean change rate, β100 -0.57 0.22 -2.55 45 0.014
ANYCS25, β110 -0.38 0.32 -1.16 1584 0.245
ANYCS50, β120 -0.13 0.29 -0.45 1584 0.653
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.17 0.02 10.62 45 <0.001
ANYCS25, β210 0.04 0.02 1.82 1584 0.069
ANYCS50, β220 0.01 0.02 0.29 1584 0.773
Random Effect Variance d.f. χ2 p-value
level-1, ε 89.89
School initial mean scores, e0 418.34 1627 14423.08 <0.001
School mean change rate, e1 5.44 1627 2551.12 <0.001
School mean acceleration rate, e2 0.02 1627 2191.12 <0.001
County initial mean, r00 72.00 45 383.29 <0.001
County mean change rates, r10 0.98 45 173.64 <0.001
County mean acceleration rate, r20 0.01 45 149.86 <0.001
164
A5-5. Results from the Model with Charter Presence Dummy in Level 2 (8th grade; reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 301.41 2.34 128.66 44 <0.001
ANYCS25, β010 -3.65 2.03 -1.79 477 0.074
ANYCS50, β020 0.57 2.54 0.22 477 0.824
For YEAR slope, ψ1
Overall mean change rate, β100 -0.74 0.29 -2.58 44 0.013
ANYCS25, β110 -1.17 0.37 -3.12 477 0.002
ANYCS50, β120 0.33 0.44 0.75 477 0.456
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.17 0.02 8.23 44 <0.001
ANYCS25, β210 0.07 0.03 2.93 477 0.004
ANYCS50, β220 -0.03 0.03 -0.87 477 0.387
Random Effect Variance d.f. χ2 p-value
level-1, ε 44.75
School initial mean scores, e0 415.87 545 8793.96 <0.001
School mean change rate, e1 6.47 545 1281.25 <0.001
School mean acceleration rate, e2 0.03 545 1108.11 <0.001
County initial mean, r00 39.98 44 108.03 <0.001
County mean change rates, r10 0.59 44 74.22 0.003
County mean acceleration rate, r20 0.00 44 79.14 0.001
165
A5-6. Results from the Model with Charter Presence Dummy in Level 2 (10th grade; reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 298.15 2.21 134.81 39 <0.001
ANYCS25, β010 0.05 3.25 0.01 311 0.989
ANYCS50, β020 -2.21 3.34 -0.66 311 0.508
For YEAR slope, ψ1
Overall mean change rate, β100 -0.28 0.36 -0.79 39 0.437
ANYCS25, β110 -0.86 0.29 -2.93 311 0.004
ANYCS50, β120 -0.28 0.40 -0.70 311 0.486
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.05 0.02 2.00 39 0.053
ANYCS25, β210 0.04 0.03 1.68 311 0.095
ANYCS50, β220 0.03 0.03 1.02 311 0.310
Random Effect Variance d.f. χ2 p-value
level-1, ε 57.16
School initial mean scores, e0 588.07 360 5040.50 <0.001
School mean change rate, e1 9.79 360 838.31 <0.001
School mean acceleration rate, e2 0.04 360 665.68 <0.001
County initial mean, r00 22.28 39 53.49 0.061
County mean change rates, r10 0.83 39 60.02 0.017
County mean acceleration rate, r20 0.00 39 59.72 0.018
166
A5-7. Results from the Model with Charter Numbers in Level 2 (5th grade; math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 311.30 1.27 244.43 45 <0.001
RAD25, β010 -4.43 1.09 -4.08 1584 <0.001
RAD50, β020 -2.38 0.61 -3.91 1584 <0.001
For YEAR slope, ψ1
Overall mean change rate, β100 3.49 0.23 14.97 45 <0.001
RAD25, β110 0.31 0.15 2.06 1584 0.039
RAD50, β120 -0.07 0.07 -1.10 1584 0.273
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.10 0.02 -6.02 45 <0.001
RAD25, β210 -0.01 0.01 -0.97 1584 0.334
RAD50, β220 0.00 0.00 0.92 1584 0.359
Random Effect Variance d.f. χ2 p-value
level-1, ε
School initial mean scores, e0 415.01 1645 16532.36 <0.001
School mean change rate, e1 7.98 1645 3507.00 <0.001
School mean acceleration rate, e2 0.05 1645 3325.68 <0.001
County initial mean, r00 54.57 45 309.28 <0.001
County mean change rates, r10 1.86 45 369.74 <0.001
County mean acceleration rate, r20 0.01 45 247.60 <0.001
167
A5-8. Results from the Model with Charter Numbers in Level 2 (8th grade; math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 308.19 1.80 171.55 44 <0.001
RAD25, β010 -0.26 2.06 -0.13 525 0.899
RAD50, β020 -4.27 1.03 -4.16 525 <0.001
For YEAR slope, ψ1
Overall mean change rate, β100 1.61 0.09 17.81 44 <0.001
RAD25, β110 -0.30 0.15 -2.02 525 0.044
RAD50, β120 0.20 0.05 3.78 525 <0.001
Random Effect Variance d.f. χ2 p-value
level-1, ε 41.99
School initial mean scores, e0 519.79 567 20517.82 <0.001
School mean change rate, e1 1.20 567 2671.18 <0.001
County initial mean, r00 58.55 44 108.34 <0.001
County mean change rates, r10 0.23 44 135.16 <0.001
168
A5-9. Results from the Model Charter Numbers in Level 2 (10th grade; math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 303.06 2.12 143.20 39 <0.001
RAD25, β010 -1.27 3.31 -0.38 312 0.702
RAD50, β020 -0.24 2.15 -0.11 312 0.913
For YEAR slope, ψ1
Overall mean change rate, β100 3.99 0.25 15.86 39 <0.001
RAD25, β110 -0.21 0.41 -0.51 312 0.613
RAD50, β120 -0.13 0.17 -0.77 312 0.442
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.19 0.02 -11.73 39 <0.001
RAD25, β210 0.01 0.04 0.23 312 0.815
RAD50, β220 0.03 0.02 1.60 312 0.112
Random Effect Variance d.f. χ2 p-value
level-1, ε 39.02
School initial mean scores, e0 646.66 363 9163.00 <0.001
School mean change rate, e1 6.51 363 943.61 <0.001
School mean acceleration rate, e2 0.02 363 693.14 <0.001
County initial mean, r00 28.53 39 57.34 0.029
County mean change rates, r10 0.73 39 67.47 0.003
County mean acceleration rate, r20 0.00 39 65.54 0.005
169
A5-10. Results from the Model with Charter Numbers in Level 2 (5th grade; reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 299.52 1.36 220.08 45 <0.001
RAD25, β010 -3.74 0.98 -3.80 1584 <0.001
RAD50, β020 -2.74 0.65 -4.19 1584 <0.001
For YEAR slope, ψ1
Overall mean change rate, β100 -0.76 0.20 -3.78 45 <0.001
RAD25, β110 -0.06 0.11 -0.57 1584 0.569
RAD50, β120 -0.03 0.07 -0.42 1584 0.673
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.19 0.02 12.25 45 <0.001
RAD25, β210 0.02 0.01 1.39 1584 0.164
RAD50, β220 0.00 0.00 0.30 1584 0.763
Random Effect Variance d.f. χ2 p-value
level-1, ε 89.90
School initial mean scores, e0 400.93 1627 13756.59 <0.001
School mean change rate, e1 5.47 1627 2552.61 <0.001
School mean acceleration rate, e2 0.02 1627 2190.48 <0.001
County initial mean, r00 67.66 45 343.467 <0.001
County mean change rates, r10 0.97 45 168.6209 <0.001
County mean acceleration rate, r20 0.01 45 152.2838 <0.001
170
A5-11. Results from the Model with Charter Numbers in Level 2 (8th grade; reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 303.51 1.44 210.81 44 <0.001
RAD25, β010 0.29 1.93 0.15 477 0.880
RAD50, β020 -4.32 0.92 -4.67 477 <0.001
For YEAR slope, ψ1
Overall mean change rate, β100 -1.03 0.20 -5.17 44 <0.001
RAD25, β110 -0.36 0.31 -1.16 477 0.246
RAD50, β120 0.16 0.16 1.04 477 0.297
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.18 0.02 12.14 44 <0.001
RAD25, β210 0.00 0.02 0.12 477 0.906
RAD50, β220 0.00 0.01 -0.11 477 0.916
Random Effect Variance d.f. χ2 p-value
level-1, ε 44.76
School initial mean scores, e0 398.52 545 8197.56 <0.001
School mean change rate, e1 6.72 545 1288.53 <0.001
School mean acceleration rate, e2 0.03 545 1110.33 <0.001
County initial mean, r00 28.88 44 82.94 <0.001
County mean change rates, r10 0.45 44 66.67 0.015
County mean acceleration rate, r20 0.00 44 79.35 0.001
171
A5-12. Results from the Model with Charter Numbers in Level 2 (10th grade; reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 298.26 1.85 161.16 39 <0.001
RAD25, β010 1.30 2.79 0.47 308 0.641
RAD50, β020 1.06 1.76 0.61 308 0.546
RAD100, β030 -1.88 0.80 -2.36 308 0.019
For YEAR slope, ψ1
Overall mean change rate, β100 -0.71 0.30 -2.38 39 0.022
RAD25, β110 -0.65 0.51 -1.26 308 0.207
RAD50, β120 -0.09 0.38 -0.23 308 0.816
RAD100, β130 0.16 0.11 1.43 308 0.153
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.07 0.02 3.13 39 0.003
RAD25, β210 0.01 0.04 0.31 308 0.755
RAD50, β220 0.00 0.03 0.08 308 0.934
RAD100, β230 0.01 0.01 0.73 308 0.469
Random Effect Variance d.f. χ2 p-value
level-1, ε 57.17
School initial mean scores, e0 590.49 359 5038.14 <0.001
School mean change rate, e1 10.00 359 849.73 <0.001
School mean acceleration rate, e2 0.04 359 667.32 <0.001
County initial mean, r00 14.87 39 45.83 0.210
County mean change rates, r10 0.88 39 61.79 0.012
County mean acceleration rate, r20 0.00 39 58.94 0.021
172
A5-13. Results from the Model with the Minimum Distance in Level 2 (5th grade; math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 304.94 2.27 134.51 45 <0.001
MINDST, β010 0.34 0.20 1.71 1587 0.087
For YEAR slope, ψ1
Overall mean change rate, β100 3.47 0.30 11.76 45 <0.001
MINDST, β130 0.01 0.02 0.35 1587 0.728
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.10 0.02 -4.60 45 <0.001
MINDST, β230 0.00 0.00 -0.18 1587 0.856
Random Effect Variance d.f. χ2 p-value
level-1, ε 76.50
School initial mean scores, e0 450.00 1646 17914.38 <0.001
School mean change rate, e1 8.00 1646 3514.90 <0.001
School mean acceleration rate, e2 0.05 1646 3325.61 <0.001
County initial mean, r00 52.34 45 314.08 <0.001
County mean change rates, r10 1.90 45 376.87 <0.001
County mean acceleration rate, r20 0.01 45 244.68 <0.001
173
A5-14. Results from the Model with the Minimum Distance in Level 2 (8th grade; math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 305.09 2.08 146.33 44 <0.001
MINDST, β010 -0.05 0.09 -0.48 527 0.632
For YEAR slope, ψ1
Overall mean change rate, β100 1.57 0.13 12.12 44 <0.001
MINDST, β130 0.01 0.01 1.35 527 0.179
Random Effect Variance d.f. χ2 p-value
level-1, ε 41.96
School initial mean scores, e0 545.62 568 21984.79 <0.001
School mean change rate, e1 1.22 568 2733.50 <0.001
County initial mean, r00 64.39 44 130.03 <0.001
County mean change rates, r10 0.27 44 166.30 <0.001
174
A5-15. Results from the Model with the Minimum Distance in Level 2 (10th grade; math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 303.27 1.71 177.53 39 <0.001
MINDST, β010 -0.03 0.03 -1.08 315 0.282
For YEAR slope, ψ1
Overall mean change rate, β100 3.77 0.25 14.79 39 <0.001
MINDST, β130 0.01 0.01 0.64 315 0.523
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.17 0.02 -9.84 39 <0.001
MINDST, β230 0.00 0.00 -0.26 315 0.796
Random Effect Variance d.f. χ2 p-value
level-1, ε 39.01
School initial mean scores, e0 646.97 364 9175.78 <0.001
School mean change rate, e1 6.52 364 937.15 <0.001
School mean acceleration rate, e2 0.03 364 696.50 <0.001
County initial mean, r00 26.56 39 59.27 0.020
County mean change rates, r10 0.69 39 66.73 0.004
County mean acceleration rate, r20 0.00 39 68.19 0.003
175
A5-16. Results from the Model with the Minimum Distance in Level 2 (5th grade; reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 292.68 2.74 106.68 45 <0.001
MINDST, β010 0.39 0.23 1.70 1587 0.089
For YEAR slope, ψ1
Overall mean change rate, β100 -0.79 0.23 -3.46 45 0.001
MINDST, β130 0.00 0.02 -0.12 1587 0.904
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.20 0.02 11.78 45 <0.001
MINDST, β230 0.00 0.00 -0.13 1587 0.893
Random Effect Variance d.f. χ2 p-value
level-1, ε 89.90
School initial mean scores, e0 433.20 1628 14813.65 <0.001
School mean change rate, e1 5.47 1628 2554.57 <0.001
School mean acceleration rate, e2 0.02 1628 2195.85 <0.001
County initial mean, r00 79.14 45 434.83 <0.001
County mean change rates, r10 0.96 45 161.08 <0.001
County mean acceleration rate, r20 0.01 45 152.61 <0.001
176
A5-17. Results from the Model with the Minimum Distance in Level 2 (8th grade; reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 300.35 1.74 172.74 44 <0.001
MINDST, β010 -0.01 0.07 -0.14 480 0.891
For YEAR slope, ψ1
Overall mean change rate, β100 -0.99 0.23 -4.39 44 <0.001
MINDST, β130 0.00 0.01 -0.39 480 0.694
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.17 0.02 8.84 44 <0.001
MINDST, β230 0.00 0.00 1.06 480 0.291
Random Effect Variance d.f. χ2 p-value
level-1, ε 44.75
School initial mean scores, e0 417.11 546 8833.31 <0.001
School mean change rate, e1 6.75 546 1293.25 <0.001
School mean acceleration rate, e2 0.03 546 1109.30 <0.001
County initial mean, r00 43.85 44 116.89 <0.001
County mean change rates, r10 0.50 44 67.58 0.013
County mean acceleration rate, r20 0.00 44 79.99 <0.001
177
A5-18. Results from the Model with the Minimum Distance in Level 2 (10th grade; reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 297.46 1.61 185.27 39 <0.001
MINDST, β010 -0.02 0.04 -0.65 314 0.516
For YEAR slope, ψ1
Overall mean change rate, β100 -0.74 0.29 -2.56 39 0.015
MINDST, β130 0.00 0.01 0.10 314 0.918
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.07 0.02 3.55 39 0.001
MINDST, β230 0.00 0.00 0.70 314 0.487
Random Effect Variance d.f. χ2 p-value
level-1, ε 57.17
School initial mean scores, e0 585.90 361 5000.63 <0.001
School mean change rate, e1 10.06 361 846.16 <0.001
School mean acceleration rate, e2 0.04 361 677.36 <0.001
County initial mean, r00 24.23 39 56.77 0.033
County mean change rates, r10 0.94 39 62.06 0.011
County mean acceleration rate, r20 0.00 39 59.00 0.021
178
A5-19. Results from the Model with School Choice in Level 3 (5th grade; Math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 313.38 4.88 64.24 42 <0.001
PCHARTER, β001 -0.23 0.37 -0.63 42 0.533
PPVTHE, β002 -0.39 0.31 -1.27 42 0.211
PCSMED,β003 0.48 3.48 0.14 42 0.890
For YEAR slope, ψ1, ψ1
Overall mean change rate, β100 2.00 0.79 2.53 42 0.015
PCHARTER, β101 -0.12 0.07 -1.71 42 0.095
PPVTHE, β102 0.11 0.05 2.28 42 0.028
PCSMED,β103 0.90 0.58 1.56 42 0.126
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.01 0.05 -0.10 42 0.922
PCHARTER, β201 0.01 0.01 2.04 42 0.047
PPVTHE, β202 -0.01 0.00 -2.14 42 0.039
PCSMED,β203 -0.08 0.04 -2.02 42 0.050
Random Effect Variance d.f. χ2 p-value
level-1, ε 76.49
School initial mean scores, e0 453.46 1647 18098.27 <0.001
School mean change rates, e1 8.00 1647 3515.97 <0.001
School mean acceleration rates, e2 0.05 1647 3326.67 <0.001
County initial mean scores, r00 50.45 42 296.42 <0.001
County mean change rates, r10 1.43 42 252.35 <0.001
County mean acceleration rates, r20 0.01 42 172.76 <0.001
179
A5-20. Results from the Model with School Choice in Level 3 (8th grade; Math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 314.76 4.26 73.90 41 <0.001
PCHARTER, β001 -0.38 0.63 -0.60 41 0.552
PPVTHE, β002 -0.55 0.28 -2.00 41 0.052
PCSMED,β003 -2.23 5.68 -0.39 41 0.696
For YEAR slope, ψ1, ψ1
Overall mean change rate, β100 1.10 0.25 4.45 41 <0.001
PCHARTER, β101 -0.02 0.05 -0.44 41 0.659
PPVTHE, β102 0.04 0.02 2.08 41 0.043
PCSMED,β103 0.39 0.33 1.18 41 0.246
Random Effect Variance d.f. χ2 p-value
level-1, ε 41.98
School initial mean scores, e0 546.80 569 21973.58 <0.001
School mean change rates, e1 1.23 569 2736.44 <0.001
County initial mean scores, r00 50.63 41 103.60 <0.001
County mean change rates, r10 0.19 41 113.81 <0.001
180
A5-21. Results from the Model with School Choice in Level 3 (10th grade; Math)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 309.72 3.78 81.93 36 <0.001
PCHARTER, β001 0.20 0.30 0.66 36 0.511
PPVTHE, β002 -0.23 0.29 -0.80 36 0.430
PCSMED,β003 -8.27 3.40 -2.43 36 0.020
For YEAR slope, ψ1, ψ1
Overall mean change rate, β100 3.98 0.68 5.87 36 <0.001
PCHARTER, β101 -0.08 0.06 -1.53 36 0.135
PPVTHE, β102 0.01 0.04 0.37 36 0.716
PCSMED,β103 -0.23 0.40 -0.57 36 0.570
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 -0.21 0.05 -4.42 36 <0.001
PCHARTER, β201 0.01 0.00 1.56 36 0.129
PPVTHE, β202 0.00 0.00 0.01 36 0.990
PCSMED,β203 0.05 0.03 1.96 36 0.057
Random Effect Variance d.f. χ2 p-value
level-1, ε 38.99
School initial mean scores, e0 650.67 365 9202.21 <0.001
School mean change rates, e1 6.51 365 942.69 <0.001
School mean acceleration rates, e2 0.03 365 697.59 <0.001
County initial mean scores, r00 9.76 36 43.29 0.188
County mean change rates, r10 0.63 36 63.20 0.004
County mean acceleration rates, r20 0.00 36 57.48 0.013
181
A5-22. Results from the Model with School Choice in Level 3 (5th grade; Reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 303.57 5.08 59.74 42 <0.001
PCHARTER, β001 -0.58 0.39 -1.49 42 0.144
PPVTHE, β002 -0.45 0.32 -1.40 42 0.170
PCSMED,β003 0.28 4.13 0.07 42 0.945
For YEAR slope, ψ1, ψ1
Overall mean change rate, β100 -1.25 0.67 -1.87 42 0.068
PCHARTER, β101 -0.09 0.04 -2.06 42 0.046
PPVTHE, β102 0.04 0.04 0.87 42 0.392
PCSMED,β103 0.46 0.45 1.03 42 0.310
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.21 0.05 4.19 42 <0.001
PCHARTER, β201 0.01 0.00 2.84 42 0.007
PPVTHE, β202 0.00 0.00 -0.57 42 0.571
PCSMED,β203 -0.03 0.03 -0.82 42 0.417
Random Effect Variance d.f. χ2 p-value
level-1, ε 89.90
School initial mean scores, e0 437.31 1629 15009.04 <0.001
School mean change rates, e1 5.46 1629 2554.46 <0.001
School mean acceleration rates, e2 0.02 1629 2196.16 <0.001
County initial mean scores, r00 75.98 42 422.82 <0.001
County mean change rates, r10 0.89 42 148.51 <0.001
County mean acceleration rates, r20 0.01 42 151.72 <0.001
182
A5-23. Results from the Model with School Choice in Level 3 (8th grade; Reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 309.88 3.20 96.95 41 <0.001
PCHARTER, β001 -0.37 0.46 -0.79 41 0.435
PPVTHE, β002 -0.51 0.20 -2.49 41 0.017
PCSMED,β003 -2.58 4.74 -0.54 41 0.590
For YEAR slope, ψ1, ψ1
Overall mean change rate, β100 -1.07 0.65 -1.64 41 0.108
PCHARTER, β101 -0.07 0.07 -0.98 41 0.332
PPVTHE, β102 0.01 0.03 0.25 41 0.801
PCSMED,β103 0.49 0.61 0.81 41 0.421
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.14 0.05 2.70 41 0.010
PCHARTER, β201 0.01 0.01 1.10 41 0.278
PPVTHE, β202 0.00 0.00 0.59 41 0.561
PCSMED,β203 -0.02 0.05 -0.35 41 0.731
Random Effect Variance d.f. χ2 p-value
level-1, ε 44.76
School initial mean scores, e0 417.48 547 8831.35 <0.001
School mean change rates, e1 6.72 547 1292.95 <0.001
School mean acceleration rates, e2 0.03 547 1109.14 <0.001
County initial mean scores, r00 33.24 41 90.94 <0.001
County mean change rates, r10 0.49 41 67.39 0.006
County mean acceleration rates, r20 0.00 41 78.23 <0.001
183
A5-24. Results from the Model with School Choice in Level 3 (10th grade; Reading)
Fixed Effect Coefficient SE t-ratio d.f. p-value
For Initial mean score, ψ0
Overall mean score, β000 301.91 3.98 75.94 36 <0.001
PCHARTER, β001 0.23 0.32 0.70 36 0.487
PPVTHE, β002 -0.04 0.26 -0.16 36 0.877
PCSMED,β003 -9.53 3.02 -3.16 36 0.003
For YEAR slope, ψ1, ψ1
Overall mean change rate, β100 -0.91 0.78 -1.17 36 0.248
PCHARTER, β101 -0.06 0.07 -0.84 36 0.406
PPVTHE, β102 0.05 0.05 1.13 36 0.267
PCSMED,β103 -0.80 0.44 -1.83 36 0.075
For YEARSQ slope, ψ2
Overall mean acceleration rate, β200 0.09 0.05 1.76 36 0.087
PCHARTER, β201 0.00 0.00 0.52 36 0.609
PPVTHE, β202 0.00 0.00 -1.38 36 0.176
PCSMED,β203 0.08 0.03 2.93 36 0.006
Random Effect Variance d.f. χ2 p-value
level-1, ε 44.76
School initial mean scores, e0 589.47 362 5017.36 <0.001
School mean change rates, e1 9.94 362 847.34 <0.001
School mean acceleration rates, e2 0.04 362 674.49 <0.001
County initial mean scores, r00 4.45 36 39.64 0.311
County mean change rates, r10 0.73 36 53.95 0.027
County mean acceleration rates, r20 0.00 36 47.44 0.096
184
APPENDIX 6
RESULTS FROM CHARTER-SCHOOL MODELS AND SOCIAL
INEQUALITY MODELS
A6-1. Results from both models (5th grade; math)
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For INTRCPT1, ψ0 INTRCPT3, β000 301.55 3.63 83.04 62 <0.001 364.21 11.88 30.66 50 <0.001
ADOPTION, β001 6.22 4.88 1.27 62 0.208 8.00 2.99 2.67 50 0.010 YEARSADOPT, β
0.37 0.49 0.75 62 0.456 -0.13 0.31 -0.41 50 0.681 PCSMED, β003 2.34 3.23 0.72 62 0.472 -0.52 2.22 -0.23 50 0.816
PPVTHE, β004 -0.06 0.30 -0.19 62 0.852 -0.15 0.26 -0.59 50 0.557 PPSM,β005
0.00 0.00 -1.31 50 0.196 GRADRATE,β006
-0.09 0.14 -0.68 50 0.498
PABSNT21,β007 -0.61 0.46 -1.35 50 0.183
PPEREG,β008 0.00 0.00 -0.32 50 0.751
PCLSOOFT,β009 0.10 0.14 0.71 50 0.484
MINCOME,β0010 0.00 0.00 -2.24 50 0.029
PPOOR517,β0011 -0.97 0.52 -1.86 50 0.069
HSOVER,β0012 -0.47 0.31 -1.48 50 0.145
BAOVER,β0013 0.14 0.17 0.85 50 0.402
CPBLK,β0014 -0.16 0.09 -1.82 50 0.075
CPHISP,β0015 0.03 0.18 0.17 50 0.869
CPELL,β0016 -0.38 0.39 -0.97 50 0.339
CHARTER, β010 3.79 7.05 0.54 1452 0.591 -3.13 3.99 -0.79 1413 0.432 ANYCS25, β020 -3.72 1.44 -2.58 1452 0.010 0.32 0.82 0.39 1413 0.699
ANYCS50, β030 -1.19 1.65 -0.72 1452 0.470 1.45 0.93 1.57 1413 0.118 RAD25, β040 -3.64 0.99 -3.67 1452 <0.001 -1.23 0.56 -2.18 1413 0.029 RAD50, β050 -0.92 1.02 -0.90 66 0.371 0.51 0.48 1.06 66 0.295
CLSSZG5, β060 -0.58 0.08 -6.92 1413 <0.001
MEMBER, β070 0.00 0.00 -2.46 1413 0.014
PDABD, β080 -0.37 0.06 -6.37 1413 <0.001
PADVDG, β090 0.07 0.04 1.93 1413 0.054
AVGYREXP, β0100 0.25 0.12 2.14 1413 0.032
PPEREG, β0110 0.00 0.00 -2.19 1413 0.029
PINSTSTF, β0120 -0.01 0.07 -0.21 1413 0.833
PFRL, β0130 -0.61 0.03 -22.64 1413 <0.001
STABRATE, β0140 0.10 0.17 0.58 1413 0.566
SUBURBAN, β0150 0.33 0.66 0.50 1413 0.615
PBLK, β0160 -0.20 0.03 -7.95 1413 <0.001
PHSP, β0170 0.00 0.03 -0.03 1413 0.980
PELL, β0180 0.03 0.03 0.98 1413 0.325
185
A6-1.- continued
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For YEAR12 slope,ψ1 INTRCPT2,π10, β100 2.87 0.65 4.40 62 <0.001 4.64 3.62 1.28 50 0.205
ADOPTION, β101 -1.40 0.87 -1.61 62 0.112 -2.42 0.91 -2.66 50 0.011
YEARSADOPT, β
0.16 0.09 1.81 62 0.076 0.11 0.09 1.19 50 0.241
PCSMED, β103 -0.08 0.55 -0.14 62 0.889 0.27 0.65 0.41 50 0.681
PPVTHE, β104 0.06 0.05 1.17 62 0.245 0.03 0.08 0.43 50 0.667
PPSM,β105 0.00 0.00 0.85 50 0.398
GRADRATE,β106 0.10 0.04 2.42 50 0.019
PABSNT21,β107 -0.08 0.14 -0.60 50 0.552
PPEREG,β108 0.00 0.00 0.21 50 0.837
PCLSOOFT,β109 -0.02 0.04 -0.60 50 0.550
MINCOME,β1010 0.00 0.00 0.63 50 0.531
PPOOR517,β1011 0.11 0.16 0.67 50 0.504
HSOVER,β1012 0.00 0.09 -0.05 50 0.963
BAOVER,β1013 0.06 0.05 1.15 50 0.254
CPBLK,β1014 0.02 0.03 0.90 50 0.374
CPHISP,β1015 -0.04 0.05 -0.66 50 0.512
CPELL,β1016 0.07 0.12 0.63 50 0.531
CHARTER, β110 0.04 1.33 0.03 1452 0.978 -0.13 1.28 -0.10 1413 0.919
ANYCS25, β120 -0.03 0.27 -0.10 1452 0.920 -0.16 0.26 -0.61 1413 0.543
ANYCS50, β130 -0.48 0.30 -1.61 1452 0.108 -0.39 0.29 -1.32 1413 0.186
RAD25, β140 0.32 0.19 1.72 1452 0.086 0.22 0.18 1.22 1413 0.223
RAD50, ,β150 -0.03 0.09 -0.32 1452 0.746 -0.05 0.09 -0.54 1413 0.588
CLSSZG5, β160 -0.01 0.03 -0.48 1413 0.634
MEMBER, β170 0.00 0.00 0.02 1413 0.988
PDABD, β180 -0.16 0.02 -8.39 1413 <0.001
PADVDG, β190 -0.01 0.01 -0.66 1413 0.510
AVGYREXP, β1100 -0.05 0.04 -1.27 1413 0.204
PPEREG, β1110 0.00 0.00 2.32 1413 0.021
PINSTSTF, β1120 0.01 0.02 0.25 1413 0.801
PFRL, β1130 0.03 0.01 3.17 1413 0.002
STABRATE, β1140 0.23 0.05 4.13 1413 <0.001
SUBURBAN, β1150 0.11 0.21 0.52 1413 0.603
PBLK, β1160 0.00 0.01 0.11 1413 0.913
PHSP, β1170 -0.03 0.01 -3.02 1413 0.003
PELL, β1180 0.01 0.01 0.94 1413 0.349
186
A6-1.- continued
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For YEARSQ slope,ψ2 INTRCPT2,π20, β200 -0.03 0.05 -0.69 62 0.493 -0.49 0.27 -1.79 50 0.079
ADOPTION, β201 0.08 0.07 1.24 62 0.219 0.18 0.07 2.55 50 0.014
YEARSADOPT, β
-0.01 0.01 -2.04 62 0.046 -0.01 0.01 -1.53 50 0.132
PCSMED, β203 0.01 0.04 0.22 62 0.823 0.00 0.05 -0.10 50 0.921
PPVTHE, β204 0.00 0.00 -0.87 62 0.386 0.00 0.01 -0.09 50 0.930
PPSM,β205 0.00 0.00 -0.22 50 0.826
GRADRATE,β206 -0.01 0.00 -2.25 50 0.029
PABSNT21,β207 0.01 0.01 0.66 50 0.513
PPEREG,β208 0.00 0.00 0.06 50 0.955
PCLSOOFT,β209 0.00 0.00 -0.33 50 0.743
MINCOME,β2010 0.00 0.00 0.60 50 0.550
PPOOR517,β2011 0.00 0.01 0.39 50 0.695
HSOVER,β2012 0.00 0.01 0.15 50 0.883
BAOVER,β2013 -0.01 0.00 -1.65 50 0.106
CPBLK,β2014 0.00 0.00 -0.49 50 0.628
CPHISP,β2015 0.00 0.00 1.06 50 0.294
CPELL,β2016 -0.01 0.01 -0.84 50 0.408
CHARTER, β210 0.05 0.11 0.50 1452 0.618 0.09 0.10 0.85 1413 0.396
ANYCS25, β220 0.01 0.02 0.50 1452 0.618 0.01 0.02 0.64 1413 0.521
ANYCS50, β230 0.03 0.02 1.42 1452 0.155 0.02 0.02 0.97 1413 0.330
RAD25, β240 -0.01 0.01 -0.90 1452 0.371 -0.01 0.01 -0.59 1413 0.558
RAD50, β250 0.00 0.01 0.12 1452 0.902 0.00 0.01 -0.22 1413 0.824
CLSSZG5, β260 0.00 0.00 1.24 1413 0.216
MEMBER, β270 0.00 0.00 0.07 1413 0.946
PDABD, β280 0.01 0.00 9.21 1413 <0.001
PADVDG, β290 0.00 0.00 1.07 1413 0.284
AVGYREXP, β2100 0.00 0.00 0.93 1413 0.353
PPEREG, β2110 0.00 0.00 -0.85 1413 0.394
PINSTSTF, β2120 0.00 0.00 0.20 1413 0.841
PFRL, β2130 0.00 0.00 -2.21 1413 0.027
STABRATE, β2140 -0.02 0.00 -3.48 1413 <0.001
SUBURBAN, β2150 -0.01 0.02 -0.78 1413 0.435
PBLK, β2160 0.00 0.00 0.75 1413 0.452
PHSP, β2170 0.00 0.00 3.08 1413 0.002
PELL, β2180 0.00 0.00 -0.94 1413 0.345
187
A6-2. Results from both models (8th grade; math)
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For INTRCPT1, ψ0 INTRCPT3, β000 301.14 3.85 78.12 62 <0.001 351.95 11.26 31.25 50 <0.001
ADOPTION, β001 0.23 0.55 0.42 62 0.674 0.35 0.28 1.25 50 0.218
YEARSADOPT, β002 9.61 5.54 1.73 62 0.088 -0.74 2.99 -0.25 50 0.806
PCSMED, β003 -2.16 3.04 -0.71 62 0.479 -3.29 1.49 -2.21 50 0.032
PPVTHE, β004 -0.32 0.29 -1.10 62 0.274 -0.23 0.22 -1.06 50 0.294
PPSM,β005 0.00 0.00 1.09 50 0.28
GRADRATE,β006 0.12 0.11 1.07 50 0.29
PABSNT21,β007 -0.03 0.24 -0.12 50 0.906
PPEREG,β008 0.00 0.00 -1.10 50 0.278
PCLSOOFT,β009 0.10 0.11 0.93 50 0.357
MINCOME,β0010 0.00 0.00 -3.37 50 0.001
PPOOR517,β0011 -1.02 0.45 -2.27 50 0.028
HSOVER,β0012 0.48 0.14 3.32 50 0.002
BAOVER,β0013 -0.55 0.29 -1.89 50 0.064
CPBLK,β0014 -0.35 0.08 -4.19 50 <0.001
CPHISP,β0015 -0.24 0.13 -1.87 50 0.068
CPELL,β0016 1.23 0.46 2.64 50 0.011
CHARTER, β010 -16.54 13.03 -1.27 216 0.205 -7.06 6.09 -1.16 256 0.248
ANYCS25, β020 -1.51 2.70 -0.56 216 0.576 -0.42 1.23 -0.34 256 0.734
ANYCS50, β030 0.63 2.72 0.23 216 0.816 0.83 1.28 0.65 256 0.515
RAD25, β040 1.94 3.10 0.63 66 0.534 2.74 1.04 2.64 256 0.009
RAD50, β050 -3.56 1.58 -2.25 66 0.028 0.57 0.71 0.80 66 0.428
CLSSZG5, β060 0.08 0.17 0.44 256 0.659
MEMBER, β070 -0.01 0.00 -3.64 256 <0.001
PDABD, β080 -0.73 0.11 -6.69 256 <0.001
PADVDG, β090 0.23 0.05 4.34 256 <0.001
AVGYREXP, β0100 0.42 0.17 2.43 256 0.016
PPEREG, β0110 0.00 0.00 -1.56 256 0.120
PINSTSTF, β0120 0.00 0.13 -0.03 256 0.979
PFRL, β0130 -0.52 0.05 -10.54 256 <0.001
STABRATE, β0140 0.66 0.26 2.58 66 0.012
SUBURBAN, β0150 0.17 0.89 0.20 256 0.845
PBLK, β0160 -0.22 0.04 -5.53 256 <0.001
PHSP, β0170 0.06 0.05 1.09 256 0.278
PELL, β0180 -0.29 0.15 -1.99 256 0.048
188
A6-2 - continued
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For YEAR12slope,ψ1 INTRCPT2,π10, β100 1.66 0.21 7.81 62 <0.001 2.65 1.30 2.05 50 0.046
ADOPTION, β101 0.00 0.03 0.06 62 0.951 -0.01 0.03 -0.20 50 0.845
YEARSADOPT, β102 -0.62 0.31 -2.02 62 0.048 -0.37 0.34 -1.11 50 0.271
PCSMED, β103 0.33 0.16 2.12 62 0.038 0.21 0.16 1.31 50 0.196
PPVTHE, β104 0.04 0.02 2.24 62 0.029 0.00 0.02 0.16 50 0.875
PPSM,β105 0.00 0.00 -0.26 50 0.793
GRADRATE,β106 0.00 0.01 -0.34 50 0.739
PABSNT21,β107 -0.03 0.03 -1.20 50 0.236
PPEREG,β108 0.00 0.00 1.50 50 0.139
PCLSOOFT,β109 -0.01 0.01 -1.25 50 0.217
MINCOME,β1010 0.00 0.00 1.45 50 0.153
PPOOR517,β1011 0.03 0.05 0.65 50 0.516
HSOVER,β1012 -0.02 0.02 -1.32 50 0.194
BAOVER,β1013 0.02 0.03 0.69 50 0.494
CPBLK,β1014 0.03 0.01 2.65 50 0.011
CPHISP,β1015 0.01 0.01 0.60 50 0.552
CPELL,β1016 -0.05 0.05 -1.03 50 0.308
CHARTER, β110 0.77 0.78 0.99 216 0.325 0.60 0.76 0.80 256 0.425
ANYCS25, β120 -0.07 0.16 -0.41 216 0.684 -0.19 0.15 -1.23 256 0.221
ANYCS50, β130 -0.15 0.16 -0.97 216 0.335 -0.13 0.16 -0.81 256 0.421
RAD25, β140 -0.45 0.19 -2.43 66 0.018 -0.25 0.13 -1.94 256 0.054
RAD50, ,β150 0.20 0.06 3.14 216 0.002 0.10 0.06 1.60 256 0.111
CLSSZG5, β160 -0.02 0.02 -1.06 256 0.288
MEMBER, β170 0.00 0.00 1.04 256 0.299
PDABD, β180 -0.02 0.01 -1.60 256 0.111
PADVDG, β190 -0.01 0.01 -2.24 256 0.026
AVGYREXP, β1100 -0.04 0.02 -1.90 256 0.059
PPEREG, β1110 0.00 0.00 2.60 256 0.010
PINSTSTF, β1120 0.01 0.02 0.70 256 0.487
PFRL, β1130 0.01 0.01 1.40 256 0.162
STABRATE, β1140 0.03 0.02 1.38 256 0.168
SUBURBAN, β1150 -0.02 0.11 -0.20 256 0.840
PBLK, β1160 0.01 0.00 1.96 256 0.051
PHSP, β1170 0.00 0.01 -0.73 256 0.468
PELL, β1180 0.01 0.02 0.31 256 0.759
189
A6-3. Results from both models (10th grade; math)
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For INTRCPT1, ψ0 INTRCPT3, β000 303.77 3.21 94.59 62 <0.001 321.52 12.17 26.42 50 <0.001
ADOPTION, β001 10.02 4.06 2.47 62 0.016 -1.49 2.83 -0.53 50 0.602
YEARSADOPT, β
0.35 0.56 0.62 62 0.540 -0.15 0.37 -0.39 50 0.696
PCSMED, β003 -4.76 4.05 -1.18 62 0.244 2.21 2.93 0.75 50 0.454
PPVTHE, β004 -0.19 0.26 -0.76 62 0.452 0.14 0.24 0.58 50 0.562
PPSM,β005 0.00 0.00 0.75 50 0.455
GRADRATE,β006 0.39 0.14 2.77 50 0.008
PABSNT21,β007 -0.25 0.15 -1.62 50 0.112
PPEREG,β008 0.00 0.00 -0.40 50 0.691
PCLSOOFT,β009 0.10 0.14 0.70 50 0.491
MINCOME,β0010 0.00 0.00 -1.49 50 0.143
PPOOR517,β0011 -0.21 0.51 -0.41 50 0.681
HSOVER,β0012 -0.02 0.33 -0.05 50 0.963
BAOVER,β0013 0.16 0.18 0.87 50 0.387
CPBLK,β0014 -0.24 0.09 -2.61 50 0.012
CPHISP,β0015 -0.02 0.14 -0.17 50 0.862
CPELL,β0016 0.20 0.56 0.35 50 0.728
CHARTER, β010 5.77 9.60 0.60 164 0.549 13.11 5.75 2.28 125 0.024
ANYCS25, β020 -7.91 3.16 -2.50 164 0.013 -3.03 1.86 -1.63 125 0.106
ANYCS50, β030 4.62 2.77 1.67 164 0.097 4.94 1.67 2.96 125 0.004
RAD25, β040 5.47 3.86 1.42 164 0.159 5.09 2.27 2.24 125 0.027
RAD50, β050 -6.88 1.90 -3.62 164 <0.001 -3.66 1.17 -3.14 125 0.002
CLSSZG5, β060 0.14 0.26 0.53 125 0.594
MEMBER, β070 0.00 0.00 0.45 125 0.653
PDABD, β080 -0.22 0.17 -1.32 125 0.191
PADVDG, β090 0.27 0.07 3.97 125 <0.001
AVGYREXP, β0100 -0.21 0.24 -0.87 125 0.385
PPEREG, β0110 0.00 0.00 -0.01 125 0.992
PINSTSTF, β0120 0.30 0.14 2.09 125 0.038
PFRL, β0130 -0.35 0.07 -4.84 125 <0.001
STABRATE, β0140 1.73 0.23 7.58 125 <0.001
SUBURBAN, β0150 -0.92 1.18 -0.78 125 0.440
PBLK, β0160 -0.29 0.05 -5.79 125 <0.001
PHSP, β0170 -0.02 0.07 -0.28 125 0.784
PELL, β0180 -0.32 0.21 -1.56 125 0.122
190
A6-3 - continued
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For YEAR12slope,ψ1 INTRCPT2,π10, β100 3.62 0.52 6.98 62 <0.001 8.10 2.94 2.76 50 0.008
ADOPTION, β101 0.12 0.66 0.18 62 0.861 0.30 0.69 0.43 50 0.667
YEARSADOPT, β
0.03 0.09 0.30 62 0.762 0.04 0.09 0.42 50 0.678
PCSMED, β103 -0.74 0.68 -1.09 62 0.279 -0.84 0.70 -1.20 50 0.237
PPVTHE, β104 0.01 0.04 0.21 62 0.837 -0.03 0.06 -0.49 50 0.625
PPSM,β105 0.00 0.00 0.20 50 0.842
GRADRATE,β106 0.00 0.03 0.06 50 0.955
PABSNT21,β107 0.04 0.04 1.09 50 0.280
PPEREG,β108 0.00 0.00 0.02 50 0.987
PCLSOOFT,β109 0.00 0.04 -0.04 50 0.966
MINCOME,β1010 0.00 0.00 0.27 50 0.791
PPOOR517,β1011 -0.11 0.12 -0.92 50 0.363
HSOVER,β1012 -0.03 0.08 -0.37 50 0.713
BAOVER,β1013 0.01 0.04 0.13 50 0.899
CPBLK,β1014 0.02 0.02 0.85 50 0.398
CPHISP,β1015 -0.01 0.03 -0.16 50 0.875
CPELL,β1016 0.11 0.13 0.79 50 0.432
CHARTER, β110 -4.58 1.54 -2.98 164 0.003 -6.03 1.45 -4.16 125 <0.001
ANYCS25, β120 -0.06 0.49 -0.12 164 0.904 0.02 0.45 0.05 125 0.962
ANYCS50, β130 -0.54 0.43 -1.26 164 0.211 -0.33 0.40 -0.81 125 0.420
RAD25, β140 0.04 0.59 0.06 164 0.952 0.00 0.55 0.01 125 0.994
RAD50, ,β150 0.39 0.30 1.32 164 0.189 0.23 0.28 0.82 125 0.415
CLSSZG5, β160 -0.05 0.06 -0.78 125 0.438
MEMBER, β170 0.00 0.00 -2.38 125 0.019
PDABD, β180 -0.23 0.04 -5.62 125 <0.001
PADVDG, β190 -0.01 0.02 -0.53 125 0.600
AVGYREXP, β1100 0.05 0.06 0.87 125 0.385
PPEREG, β1110 0.00 0.00 -0.71 125 0.481
PINSTSTF, β1120 0.00 0.04 0.11 125 0.913
PFRL, β1130 0.03 0.02 1.88 125 0.062
STABRATE, β1140 0.00 0.06 0.02 125 0.983
SUBURBAN, β1150 -0.05 0.29 -0.18 125 0.855
PBLK, β1160 0.01 0.01 0.98 125 0.330
PHSP, β1170 0.01 0.02 0.61 125 0.541
PELL, β1180 -0.11 0.05 -2.19 125 0.031
191
A6-3 – continued
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For YEARSQ slope,ψ2 INTRCPT2,π20, β200 -0.17 0.04 -4.73 62 <0.001 -0.57 0.20 -2.77 50 0.008
ADOPTION, β201 -0.02 0.04 -0.50 62 0.621 -0.01 0.05 -0.24 50 0.813
YEARSADOPT, β
-0.01 0.01 -0.91 62 0.367 0.00 0.01 -0.76 50 0.449
PCSMED, β203 0.10 0.04 2.29 62 0.026 0.08 0.05 1.72 50 0.091
PPVTHE, β204 0.00 0.00 0.02 62 0.987 0.00 0.00 0.65 50 0.520
PPSM,β205 0.00 0.00 -0.50 50 0.622
GRADRATE,β206 0.00 0.00 -0.27 50 0.790
PABSNT21,β207 0.00 0.00 -1.58 50 0.121
PPEREG,β208 0.00 0.00 -0.34 50 0.733
PCLSOOFT,β209 0.00 0.00 -0.53 50 0.600
MINCOME,β2010 0.00 0.00 0.42 50 0.677
PPOOR517,β2011 0.01 0.01 1.61 50 0.113
HSOVER,β2012 0.00 0.01 0.78 50 0.437
BAOVER,β2013 0.00 0.00 -0.81 50 0.420
CPBLK,β2014 0.00 0.00 -0.46 50 0.651
CPHISP,β2015 0.00 0.00 0.65 50 0.516
CPELL,β2016 -0.01 0.01 -0.97 50 0.339
CHARTER, β210 0.38 0.12 3.13 164 0.002 0.45 0.11 3.98 125 <0.001
ANYCS25, β220 0.02 0.04 0.59 164 0.559 0.01 0.03 0.25 125 0.804
ANYCS50, β230 0.02 0.03 0.68 164 0.495 0.01 0.03 0.42 125 0.677
RAD25, β240 -0.02 0.04 -0.35 164 0.728 -0.01 0.04 -0.28 125 0.783
RAD50, β250 0.00 0.02 0.00 164 0.996 0.00 0.02 0.07 125 0.943
CLSSZG5, β260 0.00 0.00 0.53 125 0.601
MEMBER, β270 0.00 0.00 1.84 125 0.068
PDABD, β280 0.02 0.00 5.29 125 <0.001
PADVDG, β290 0.00 0.00 0.44 125 0.662
AVGYREXP, β2100 0.00 0.00 -0.79 125 0.431
PPEREG, β2110 0.00 0.00 0.58 125 0.564
PINSTSTF, β2120 0.00 0.00 -1.06 125 0.290
PFRL, β2130 0.00 0.00 -1.66 125 0.101
STABRATE, β2140 0.00 0.00 -0.92 125 0.359
SUBURBAN, β2150 0.00 0.02 0.04 125 0.967
PBLK, β2160 0.00 0.00 -0.31 125 0.759
PHSP, β2170 0.00 0.00 -0.79 125 0.432
PELL, β2180 0.01 0.00 2.58 125 0.011
192
A6-4 . Results from both models (5th grade; reading)
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For INTRCPT1, ψ0 INTRCPT3, β000 293.85 3.61 81.42 62 <0.001 333.92 10.35 32.27 50 <0.001
ADOPTION, β001 2.92 4.85 0.60 62 0.550 4.79 2.66 1.80 50 0.078
YEARSADOPT, β
0.40 0.48 0.83 62 0.410 0.04 0.25 0.16 50 0.877
PCSMED, β003 0.71 3.10 0.23 62 0.819 -1.18 1.62 -0.73 50 0.470
PPVTHE, β004 -0.05 0.29 -0.19 62 0.852 -0.04 0.20 -0.21 50 0.837
PPSM,β005 0.00 0.00 0.19 50 0.853
GRADRATE,β006 -0.05 0.11 -0.45 50 0.657
PABSNT21,β007 -0.25 0.41 -0.60 50 0.555
PPEREG,β008 0.00 0.00 0.08 50 0.938
PCLSOOFT,β009 0.11 0.11 1.03 50 0.308
MINCOME,β0010 0.00 0.00 -1.92 50 0.061
PPOOR517,β0011 -0.35 0.45 -0.78 50 0.437
HSOVER,β0012 -0.14 0.26 -0.51 50 0.611
BAOVER,β0013 0.07 0.14 0.54 50 0.591
CPBLK,β0014 -0.26 0.07 -3.59 50 <0.001
CPHISP,β0015 0.11 0.14 0.77 50 0.446
CPELL,β0016 -0.97 0.31 -3.17 50 0.003
CHARTER, β010 -0.40 7.17 -0.06 1386 0.956 -4.34 4.05 -1.07 1347 0.285
ANYCS25, β020 -2.49 1.45 -1.72 1386 0.086 0.78 0.82 0.95 1347 0.343
ANYCS50, β030 -2.63 1.72 -1.52 1386 0.128 0.46 0.95 0.48 1347 0.633
RAD25, β040 -3.51 1.00 -3.52 1386 <0.001 -0.87 0.56 -1.55 1347 0.122
RAD50, β050 0.10 1.67 0.06 66 0.955 1.02 0.77 1.34 66 0.186
CLSSZG5, β060 -0.02 0.09 -0.18 1347 0.860
MEMBER, β070 -0.01 0.00 -3.19 1347 0.001
PDABD, β080 -0.24 0.06 -4.18 1347 <0.001
PADVDG, β090 0.09 0.04 2.62 1347 0.009
AVGYREXP, β0100 0.64 0.11 5.61 1347 <0.001
PPESCH, β0110 0.00 0.00 -2.02 1347 0.044
PINSTSTF, β0120 0.02 0.07 0.31 1347 0.756
PFRL, β0130 -0.59 0.03 -21.05 1347 <0.001
STABRATE, β0140 0.01 0.17 0.09 1347 0.930
SUBURBAN, β0150 0.15 0.65 0.23 1347 0.816
PBLK, β0160 -0.21 0.03 -8.38 1347 <0.001
PHSP, β0170 -0.04 0.03 -1.258 1347 0.209
PELL, β0180 0.02 0.03 0.69 1347 0.493
193
A6-4 - continued
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For YEAR12 slope,ψ1 INTRCPT2,π10, β100 -1.27 0.59 -2.18 62 0.033 0.75 2.93 0.26 50 0.799
ADOPTION, β101 -0.45 0.79 -0.57 62 0.574 -1.56 0.76 -2.05 50 0.045
YEARSADO, β102 0.04 0.07 0.48 62 0.633 -0.01 0.07 -0.20 50 0.842
PCSMED, β103 0.02 0.39 0.05 62 0.960 0.45 0.39 1.16 50 0.254
PPVTHE, β104 0.06 0.04 1.32 62 0.192 0.06 0.05 1.05 50 0.298
PPSM,β105 0.00 0.00 -1.86 50 0.069
GRADRATE,β106 0.08 0.03 2.84 50 0.006
PABSNT21,β107 -0.07 0.12 -0.61 50 0.543
PPEREG,β108 0.00 0.00 -0.72 50 0.473
PCLSOOFT,β109 -0.05 0.03 -1.81 50 0.076
MINCOME,β1010 0.00 0.00 1.32 50 0.192
PPOOR517,β1011 0.23 0.13 1.81 50 0.077
HSOVER,β1012 0.07 0.07 1.01 50 0.318
BAOVER,β1013 0.02 0.04 0.65 50 0.517
CPBLK,β1014 0.04 0.02 1.88 50 0.066
CPHISP,β1015 -0.02 0.04 -0.63 50 0.533
CPELL,β1016 0.11 0.08 1.37 50 0.179
CHARTER, β110 -0.26 1.29 -0.20 1386 0.843 -0.96 1.18 -0.82 1347 0.415
ANYCS25, β120 -0.42 0.26 -1.63 1386 0.103 -0.35 0.24 -1.47 1347 0.141
ANYCS50, β130 -0.20 0.29 -0.68 1386 0.499 0.00 0.27 0.01 1347 0.989
RAD25, β140 0.05 0.18 0.30 1386 0.764 0.00 0.16 -0.03 1347 0.980
RAD50, ,β150 -0.04 0.10 -0.44 66 0.664 -0.05 0.10 -0.44 66 0.660
CLSSZG5, β160 -0.22 0.03 -7.87 1347 <0.001
MEMBER, β170 0.00 0.00 -0.19 1347 0.851
PDABD, β180 -0.16 0.02 -9.36 1347 <0.001
PADVDG, β190 0.00 0.01 0.44 1347 0.663
AVGYREXP, β1100 -0.09 0.03 -2.68 1347 0.007
PPESCH, β1110 0.00 0.00 1.16 1347 0.248
PINSTSTF, β1120 0.00 0.02 -0.06 1347 0.955
PFRL, β1130 -0.01 0.01 -1.53 1347 0.126
STABRATE, β1140 0.26 0.05 5.17 1347 <0.001
SUBURBAN, β1150 0.08 0.19 0.44 1347 0.663
PBLK, β1160 0.02 0.01 2.37 1347 0.018
PHSP, β1170 -0.02 0.01 -2.15 1347 0.032
PELL, β1180 -0.01 0.01 -1.25 1347 0.211
194
A6-4 - continued
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For YEARSQ slope,ψ2 INTRCPT2,π20, β200 0.22 0.04 5.06 62 <0.001 0.001 0.22 0.01 50 0.996
ADOPTION, β201 0.03 0.06 0.51 62 0.613 0.13 0.06 2.34 50 0.023
YEARSADOPT, β
0.00 0.01 -0.57 62 0.574 0.00 0.01 -0.19 50 0.847
PCSMED, β203 0.02 0.03 0.52 62 0.602 -0.02 0.03 -0.69 50 0.493
PPVTHE, β204 0.00 0.00 -1.15 62 0.254 0.00 0.00 -0.70 50 0.490
PPSM, β205 0.00 0.00 1.97 50 0.054
GRADRATE, β206 -0.01 0.00 -2.71 50 0.009
PABSNT21, β207 0.00 0.01 0.40 50 0.693
PPEREG, β208 0.00 0.00 0.91 50 0.369
PCLSOOFT, β209 0.00 0.00 0.59 50 0.556
MINCOME, β2010 0.00 0.00 -0.46 50 0.649
PPOOR517, β2011 -0.01 0.01 -1.36 50 0.179
HSOVER, β2012 -0.01 0.01 -1.62 50 0.112
BAOVER, β2013 0.00 0.00 -0.73 50 0.467
CPBLK, β2014 0.00 0.00 -1.66 50 0.104
CPHISP, β2015 0.00 0.00 0.28 50 0.783
CPELL, β2016 0.00 0.01 -0.47 50 0.638
CHARTER, β210 0.11 0.10 1.07 1386 0.285 0.17 0.09 1.85 1347 0.064
ANYCS25, β220 0.03 0.02 1.70 1386 0.090 0.03 0.02 1.60 1347 0.110
ANYCS50, β230 0.01 0.02 0.59 1386 0.553 -0.01 0.02 -0.31 1347 0.757
RAD25, β240 0.01 0.01 0.57 1386 0.569 0.01 0.01 0.64 1347 0.520
RAD50, β250 0.00 0.01 -0.44 1386 0.663 0.00 0.01 -0.69 1347 0.493
CLSSZG5, β260 0.02 0.00 7.38 1347 <0.001
MEMBER, β270 0.00 0.00 0.46 1347 0.648
PDABD, β280 0.01 0.00 9.97 1347 <0.001
PADVDG, β290 0.00 0.00 -0.08 1347 0.936
AVGYREXP, β2100 0.00 0.00 0.76 1347 0.449
PPESCH, β2110 0.00 0.00 0.85 1347 0.396
PINSTSTF, β2120 0.00 0.00 0.85 1347 0.397
PFRL, β2130 0.00 0.00 1.30 1347 0.195
STABRATE, β2140 -0.02 0.00 -4.39 1347 <0.001
SUBURBAN, β2150 -0.01 0.01 -1.03 1347 0.302
PBLK, β2160 0.00 0.00 -1.74 1347 0.082
PHSP, β2170 0.00 0.00 2.22 1347 0.027
PELL, β2180 0.00 0.00 1.64 1347 0.101
195
A6-5. Results from both models (8th grade; reading)
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For INTRCPT1, ψ0 INTRCPT3, β000 297.25 2.66 111.66 272 <0.001 333.57 10.18 32.77 50 <0.001
ADOPTION, β001 -0.14 0.36 -0.39 272 0.700 0.23 0.24 0.98 50 0.330
YEARSADO, β002 9.31 3.78 2.46 272 0.014 0.50 2.71 0.18 50 0.856
PCSMED, β003 -1.07 1.91 -0.56 272 0.577 -3.58 1.19 -3.02 50 0.004
PPVTHE, β004 -0.09 0.19 -0.47 272 0.636 0.04 0.19 0.20 50 0.844
PPSM,β005 0.00 0.00 0.17 50 0.866
GRADRATE,β006 0.06 0.09 0.67 50 0.503
PABSNT21,β007 0.01 0.21 0.05 50 0.965
PPEREG,β008 0.00 0.00 0.39 50 0.697
PCLSOOFT,β009 0.03 0.09 0.38 50 0.708
MINCOME,β0010 0.00 0.00 -3.80 50 <0.001
PPOOR517,β0011 -1.09 0.41 -2.69 50 0.010
HSOVER,β0012 0.35 0.13 2.75 50 0.008
BAOVER,β0013 -0.38 0.27 -1.44 50 0.156
CPBLK,β0014 -0.35 0.07 -4.65 50 <0.001
CPHISP,β0015 -0.27 0.11 -2.47 50 0.017
CPELL,β0016 1.11 0.39 2.82 50 0.007
CHARTER, β010 -19.96 11.68 -1.71 272 0.088 -7.00 5.96 -1.17 237 0.242
ANYCS25, β020 1.82 2.37 0.77 272 0.443 2.16 1.21 1.79 237 0.074
ANYCS50, β030 2.12 2.36 0.90 272 0.371 0.50 1.26 0.39 237 0.695
RAD25, β040 -2.37 2.42 -0.98 66 0.330 1.14 1.02 1.12 237 0.262
RAD50, β050 -3.11 1.38 -2.25 66 0.028 -0.61 0.93 -0.66 66 0.512
CLSSZG5, β060 0.28 0.17 1.63 237 0.104
MEMBER, β070 -0.01 0.00 -4.04 237 <0.001
PDABD, β080 -0.73 0.10 -7.16 237 <0.001
PADVDG, β090 0.23 0.05 4.65 237 <0.001
AVGYREXP, β0100 0.79 0.17 4.72 237 <0.001
PPESCH, β0110 0.00 0.00 -3.70 237 <0.001
PINSTSTF, β0120 -0.10 0.12 -0.80 237 0.425
PFRL, β0130 -0.31 0.04 -7.05 237 <0.001
STABRATE, β0140 1.04 0.11 9.23 237 <0.001
SUBURBAN, β0150 0.35 0.85 0.41 237 0.685
PBLK, β0160 -0.19 0.04 -5.18 237 <0.001
PHSP, β0170 -0.01 0.05 -0.26 237 0.794
PELL, β0180 -0.28 0.14 -2.00 237 0.047
196
A6-5 - continued
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For YEAR12 slope,ψ1 INTRCPT2,π10, β100 -1.32 0.53 -2.51 62 0.015 6.34 2.90 2.19 50 0.033
ADOPTION, β101 0.00 0.08 0.01 62 0.994 -0.02 0.07 -0.34 50 0.732
YEARSADOPT, β
-0.07 0.76 -0.09 62 0.927 -0.69 0.76 -0.92 50 0.362
PCSMED, β103 0.30 0.42 0.72 62 0.473 0.65 0.38 1.73 50 0.089
PPVTHE, β104 0.00 0.04 0.04 62 0.967 -0.12 0.06 -2.10 50 0.041
PPSM,β105 0.00 0.00 1.67 50 0.102
GRADRATE,β106 0.06 0.03 2.05 50 0.046
PABSNT21,β107 -0.02 0.06 -0.37 50 0.712
PPEREG,β108 0.00 0.00 -0.68 50 0.503
PCLSOOFT,β109 0.00 0.03 -0.17 50 0.868
MINCOME,β1010 0.00 0.00 -0.08 50 0.936
PPOOR517,β1011 0.07 0.11 0.57 50 0.572
HSOVER,β1012 -0.01 0.04 -0.21 50 0.836
BAOVER,β1013 0.13 0.07 1.82 50 0.075
CPBLK,β1014 0.06 0.02 2.86 50 0.006
CPHISP,β1015 0.05 0.03 1.56 50 0.125
CPELL,β1016 -0.10 0.12 -0.81 50 0.423
CHARTER, β110 0.48 1.94 0.25 272 0.805 0.48 1.67 0.29 237 0.773
ANYCS25, β120 -0.84 0.39 -2.15 272 0.033 -0.95 0.34 -2.80 237 0.005
ANYCS50, β130 -0.04 0.39 -0.11 272 0.913 0.06 0.34 0.19 237 0.851
RAD25, β140 0.06 0.33 0.19 272 0.849 0.19 0.29 0.66 237 0.511
RAD50, ,β150 0.07 0.15 0.48 272 0.633 0.31 0.14 2.20 237 0.029
CLSSZG5, β160 -0.08 0.05 -1.55 237 0.122
MEMBER, β170 0.00 0.00 0.37 237 0.712
PDABD, β180 -0.14 0.03 -4.54 237 <0.001
PADVDG, β190 -0.02 0.01 -1.52 237 0.129
AVGYREXP, β1100 -0.12 0.05 -2.48 237 0.014
PPESCH, β1110 0.00 0.00 2.50 237 0.013
PINSTSTF, β1120 0.03 0.04 0.92 237 0.360
PFRL, β1130 -0.04 0.01 -2.76 237 0.006
STABRATE, β1140 0.12 0.04 2.74 237 0.007
SUBURBAN, β1150 -0.12 0.24 -0.50 237 0.616
PBLK, β1160 0.01 0.01 0.48 237 0.634
PHSP, β1170 0.02 0.01 1.27 237 0.204
PELL, β1180 -0.18 0.04 -4.50 237 <0.001
197
A6-5 - continued
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For YEARSQ slope,ψ2 INTRCPT2,π20, β200 0.21 0.04 5.18 62 <0.001 -0.26 0.22 -1.19 50 0.239
ADOPTION, β201 0.00 0.01 0.13 62 0.896 0.00 0.01 -0.07 50 0.944
YEARSADOPT, β
-0.03 0.06 -0.56 62 0.579 0.04 0.06 0.70 50 0.487
PCSMED, β203 0.00 0.03 -0.14 62 0.890 -0.02 0.03 -0.91 50 0.367
PPVTHE, β204 0.00 0.00 0.32 62 0.751 0.01 0.00 2.08 50 0.043
PPSM, β205 0.00 0.00 -1.43 50 0.160
GRADRATE, β206 0.00 0.00 -1.63 50 0.110
PABSNT21, β207 0.00 0.00 -0.54 50 0.594
PPEREG, β208 0.00 0.00 1.08 50 0.287
PCLSOOFT, β209 0.00 0.00 -0.52 50 0.603
MINCOME, β2010 0.00 0.00 0.72 50 0.473
PPOOR517, β2011 0.00 0.01 -0.16 50 0.876
HSOVER, β2012 0.00 0.00 -0.42 50 0.677
BAOVER, β2013 -0.01 0.01 -1.88 50 0.065
CPBLK, β2014 0.00 0.00 -1.72 50 0.092
CPHISP, β2015 0.00 0.00 -0.92 50 0.364
CPELL, β2016 0.00 0.01 0.32 50 0.753
CHARTER, β210 0.04 0.14 0.26 272 0.794 0.02 0.12 0.17 237 0.866
ANYCS25, β220 0.05 0.03 1.67 272 0.096 0.06 0.03 2.25 237 0.025
ANYCS50, β230 -0.01 0.03 -0.37 272 0.710 -0.01 0.03 -0.39 237 0.699
RAD25, β240 -0.02 0.02 -0.73 272 0.467 -0.03 0.02 -1.53 237 0.127
RAD50, β250 0.01 0.01 0.68 272 0.496 -0.02 0.01 -1.56 237 0.121
CLSSZG5, β260 0.00 0.00 1.07 237 0.287
MEMBER, β270 0.00 0.00 0.30 237 0.763
PDABD, β280 0.01 0.00 4.67 237 <0.001
PADVDG, β290 0.00 0.00 0.97 237 0.334
AVGYREXP, β2100 0.00 0.00 0.56 237 0.580
PPESCH, β2110 0.00 0.00 -0.76 237 0.449
PINSTSTF, β2120 0.00 0.00 -0.51 237 0.613
PFRL, β2130 0.00 0.00 2.11 237 0.036
STABRATE, β2140 -0.01 0.00 -2.34 237 0.020
SUBURBAN, β2150 0.01 0.02 0.38 237 0.703
PBLK, β2160 0.00 0.00 0.22 237 0.829
PHSP, β2170 0.00 0.00 -1.18 237 0.239
PELL, β2180 0.02 0.00 5.20 237 <0.001
198
A6-6. Results from both models (10th grade; reading)
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For INTRCPT1, ψ0 INTRCPT3, β000 302.45 2.43 124.45 160 <0.001 306.55 9.72 31.53 109 <0.001
ADOPTION, β001 8.84 3.03 2.92 160 0.004 -0.81 2.20 -0.37 109 0.714
YEARSADOPT, β
-0.09 0.39 -0.23 160 0.819 -0.29 0.28 -1.01 109 0.314
PCSMED, β003 -2.32 2.67 -0.87 160 0.384 3.50 2.22 1.58 109 0.117
PPVTHE, β004 -0.14 0.18 -0.74 160 0.461 0.22 0.19 1.16 109 0.248
PPSM,β005 0.00 0.00 0.29 109 0.771
GRADRATE,β006 0.33 0.11 3.14 109 0.002
PABSNT21,β007 -0.11 0.12 -0.91 109 0.365
PPEREG,β008 0.00 0.00 -0.99 109 0.323
PCLSOOFT,β009 0.14 0.11 1.31 109 0.195
MINCOME,β0010 0.00 0.00 -1.76 109 0.081
PPOOR517,β0011 0.07 0.40 0.19 109 0.854
HSOVER,β0012 0.08 0.26 0.32 109 0.751
BAOVER,β0013 0.12 0.14 0.82 109 0.413
CPBLK,β0014 -0.20 0.07 -2.92 109 0.004
CPHISP,β0015 -0.04 0.10 -0.35 109 0.728
CPELL,β0016 0.23 0.41 0.57 109 0.573
CHARTER, β010 -5.62 8.37 -0.67 160 0.503 -1.15 5.18 -0.22 109 0.825
ANYCS25, β020 -5.60 2.76 -2.03 160 0.044 -2.08 1.69 -1.23 109 0.220
ANYCS50, β030 1.92 2.49 0.77 160 0.442 3.44 1.61 2.14 109 0.034
RAD25, β040 4.24 3.40 1.25 160 0.213 4.97 2.06 2.41 109 0.018
RAD50, β050 -2.70 2.07 -1.31 66 0.196 -1.85 1.59 -1.17 66 0.248
CLSSZG5, β060 -0.10 0.24 -0.42 109 0.678
MEMBER, β070 0.00 0.00 -0.69 109 0.491
PDABD, β080 -0.35 0.15 -2.38 109 0.019
PADVDG, β090 0.26 0.06 4.53 109 <0.001
AVGYREXP, β0100 0.32 0.21 1.52 109 0.132
PPESCH, β0110 0.00 0.00 -1.64 109 0.104
PINSTSTF, β0120 0.09 0.13 0.72 109 0.474
PFRL, β0130 -0.31 0.06 -4.84 109 <0.001
STABRATE, β0140 1.52 0.21 7.40 109 <0.001
SUBURBAN, β0150 -1.12 1.05 -1.07 109 0.289
PBLK, β0160 -0.19 0.04 -4.38 109 <0.001
PHSP, β0170 -0.02 0.06 -0.25 109 0.805
PELL, β0180 -0.33 0.19 -1.77 109 0.080
199
A6-6 - continued
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For YEAR12 slope,ψ1 INTRCPT2,π10, β100 -2.46 0.57 -4.34 62 <0.001 9.02 3.00 3.00 50 0.004
ADOPTION, β101 1.26 0.71 1.76 62 0.083 -0.03 0.69 -0.04 50 0.965
YEARSADOPT, β
0.06 0.10 0.60 62 0.554 0.02 0.09 0.27 50 0.786
PCSMED, β103 -1.52 0.69 -2.20 62 0.032 -0.95 0.70 -1.36 50 0.180
PPVTHE, β104 0.06 0.04 1.29 62 0.201 -0.03 0.06 -0.60 50 0.552
PPSM,β105 0.00 0.00 1.45 50 0.153
GRADRATE,β106 0.01 0.03 0.20 50 0.842
PABSNT21,β107 0.01 0.04 0.28 50 0.780
PPEREG,β108 0.00 0.00 -0.09 50 0.931
PCLSOOFT,β109 -0.02 0.03 -0.56 50 0.577
MINCOME,β1010 0.00 0.00 -0.53 50 0.599
PPOOR517,β1011 -0.19 0.12 -1.55 50 0.126
HSOVER,β1012 0.02 0.08 0.29 50 0.773
BAOVER,β1013 0.01 0.04 0.13 50 0.900
CPBLK,β1014 0.02 0.02 0.96 50 0.344
CPHISP,β1015 0.00 0.03 0.06 50 0.952
CPELL,β1016 0.05 0.13 0.35 50 0.731
CHARTER, β110 -0.86 1.85 -0.47 160 0.641 -1.96 1.57 -1.24 109 0.216
ANYCS25, β120 -0.80 0.58 -1.38 160 0.170 -0.37 0.47 -0.78 109 0.437
ANYCS50, β130 -0.42 0.51 -0.83 160 0.410 -0.14 0.43 -0.33 109 0.743
RAD25, β140 0.46 0.70 0.66 160 0.513 0.39 0.58 0.68 109 0.497
RAD50, ,β150 0.12 0.35 0.34 160 0.735 0.24 0.30 0.79 109 0.429
CLSSZG5, β160 0.06 0.07 0.84 109 0.405
MEMBER, β170 0.00 0.00 -1.12 109 0.267
PDABD, β180 -0.29 0.04 -6.71 109 <0.001
PADVDG, β190 -0.01 0.02 -0.36 109 0.722
AVGYREXP, β1100 -0.10 0.06 -1.60 109 0.112
PPESCH, β1110 0.00 0.00 2.16 109 0.033
PINSTSTF, β1120 0.06 0.04 1.59 109 0.115
PFRL, β1130 0.01 0.02 0.28 109 0.780
STABRATE, β1140 0.08 0.06 1.31 109 0.193
SUBURBAN, β1150 0.38 0.30 1.26 109 0.210
PBLK, β1160 -0.01 0.01 -1.11 109 0.271
PHSP, β1170 0.00 0.02 0.12 109 0.907
PELL, β1180 -0.23 0.05 -4.41 109 <0.001
200
A6-6 - continued
Fixed Effect Coef SE t-ratio d.f. p-val Coef SE t-tatio d.f. p-val
For YEARSQ slope,ψ2 NTRCPT2,π20, β200 0.20 0.04 4.90 62 <0.001 -0.56 0.23 -2.45 50 0.018
ADOPTION, β201 -0.07 0.05 -1.42 62 0.160 0.02 0.05 0.29 50 0.771
YEARSADO, β202 0.00 0.01 -0.52 62 0.604 0.00 0.01 -0.35 50 0.727
PCSMED, β203 0.13 0.05 2.52 62 0.014 0.07 0.05 1.39 50 0.171
PPVTHE, β204 -0.01 0.00 -1.75 62 0.085 0.00 0.00 0.76 50 0.449
PPSM, β205 0.00 0.00 -1.83 50 0.074
GRADRATE, β206 0.00 0.00 0.10 50 0.923
PABSNT21, β207 0.00 0.00 -1.15 50 0.257
PPEREG, β208 0.00 0.00 0.26 50 0.794
PCLSOOFT, β209 0.00 0.00 -0.78 50 0.441
MINCOME, β2010 0.00 0.00 1.27 50 0.210
PPOOR517, β2011 0.02 0.01 2.35 50 0.023
HSOVER, β2012 0.00 0.01 0.12 50 0.904
BAOVER, β2013 0.00 0.00 -0.71 50 0.483
CPBLK, β2014 0.00 0.00 -1.15 50 0.254
CPHISP, β2015 0.00 0.00 0.52 50 0.604
CPELL, β2016 0.00 0.01 -0.33 50 0.744
CHARTER, β210 0.06 0.15 0.44 160 0.661 0.11 0.13 0.85 109 0.397
ANYCS25, β220 0.04 0.04 0.97 160 0.334 0.03 0.04 0.77 109 0.445
ANYCS50, β230 0.03 0.04 0.77 160 0.440 0.02 0.03 0.70 109 0.487
RAD25, β240 -0.03 0.05 -0.64 160 0.524 -0.03 0.05 -0.67 109 0.506
RAD50, β250 0.00 0.03 -0.11 160 0.917 0.00 0.02 -0.15 109 0.879
CLSSZG5, β260 -0.01 0.01 -1.12 109 0.267
MEMBER, β270 0.00 0.00 -0.10 109 0.919
PDABD, β280 0.02 0.00 4.97 109 <0.001
PADVDG, β290 0.00 0.00 0.97 109 0.333
AVGYREXP, β2100 0.00 0.01 0.41 109 0.683
PPESCH, β2110 0.00 0.00 -2.39 109 0.019
PINSTSTF, β2120 -0.01 0.00 -1.77 109 0.080
PFRL, β2130 0.00 0.00 -1.16 109 0.247
STABRATE, β2140 0.00 0.00 -0.05 109 0.962
SUBURBAN, β2150 -0.04 0.02 -1.54 109 0.127
PBLK, β2160 0.00 0.00 0.32 109 0.750
PHSP, β2170 0.00 0.00 -0.07 109 0.945
PELL, β2180 0.02 0.00 4.13 109 <0.001
201
APPENDIX 7
RESULTS FROM ANALYSES OF CHARTER SCHOOL DIS
A7-1. Results from the Model for DIs of black Students
Fixed Effect Coefficient Standard t-ratio Approx. p-value
For the initial mean DI,π00 INTRCPT3,β000 14.76 8.45 1.75 34 0.09
YEARSADOPT,β001 -1.58 0.71 -2.22 34 0.033
PPEREG,β002 -0.01 0.00 -1.87 34 0.07
PPSM,β003 0.00 0.00 0.08 34 0.935
MINCOME,β004 0.00 0.00 1.66 34 0.106
HSOVER,β005 -0.23 0.52 -0.43 34 0.669
DROPOUT,β006 -1.28 1.11 -1.16 34 0.255
RAD100CS, π01 -0.07 0.45 -0.16 196 0.87
MAXBLK, π02 0.13 0.05 2.81 196 0.006
DIFRL, π03 0.46 0.05 9.00 196 <0.001
MEMBER, π04 0.00 0.00 -0.12 196 0.905
METRO, π05 13.78 3.60 3.83 196 <0.001
SUBURBAN, π06 -1.04 3.20 -0.33 196 0.745
ELT, π07 7.99 3.52 2.27 196 0.024
MID, π08 3.83 3.46 1.11 196 0.27
For SCHAGE slope,ψ1 INTRCPT3,β000 0.27 0.63 0.43 196 0.668
YEARSADOPT,β001 0.01 0.05 0.12 196 0.902
PPEREG,β002 0.00 0.00 1.10 196 0.274
PPSM,β003 0.00 0.00 -0.96 196 0.338
MINCOME,β004 0.00 0.00 0.64 196 0.524
HSOVER,β005 0.02 0.04 0.63 196 0.53
DROPOUT,β006 0.12 0.08 1.57 196 0.119
RAD100CS, π01 0.08 0.04 2.07 196 0.04
MAXBLK, π02 0.00 0.00 0.11 196 0.913
DIFRL, π03 0.00 0.00 -0.71 196 0.48
MEMBER, π04 0.00 0.00 -1.15 196 0.252
METRO, π05 -0.43 0.26 -1.65 196 0.1
SUBURBAN, π06 -0.10 0.23 -0.44 196 0.658
ELT, π07 -1.03 0.27 -3.86 196 <0.001
MID, π08 -0.18 0.26 -0.70 196 0.483
Random Effect
Variance d.f. χ2 p-value
level-1,e
7.64
School initial mean, r0 354.16 173 24738.49 <0.001
School mean change rate, r1 0.91 213 1071.61 <0.001
County initial mean, u00 0.19 34 25.68 >.500
202
A7-2. Results from the Model for DIs of white Students
Fixed Effect Coefficient Standard t-ratio Approx. p-value
For the initial mean DI,π00 INTRCPT3,β000 -20.94 7.74 -2.71 34 0.011
YEARSADOPT,β001 1.78 0.66 2.69 34 0.011
PPEREG,β002 0.00 0.00 1.36 34 0.183
PPSM,β003 0.00 0.00 -0.79 34 0.436
MINCOME,β004 0.00 0.00 -1.38 34 0.177
HSOVER,β005 0.73 0.48 1.52 34 0.138
DROPOUT,β006 1.29 1.01 1.28 34 0.21
RAD100CS, π01 -0.71 0.35 -2.02 196 0.045
MAXWHT, π02 -0.01 0.04 -0.22 196 0.83
DIFRL, π03 -0.49 0.05 -10.52 196 <0.001
MEMBER, π04 0.00 0.00 -1.04 196 0.298
METRO, π05 -5.87 3.27 -1.80 196 0.074
SUBURBAN, π06 2.75 2.92 0.94 196 0.347
ELT, π07 -4.33 3.24 -1.34 196 0.182
MID, π08 -0.71 3.16 -0.23 196 0.822
For SCHAGE slope,ψ1 INTRCPT3,β000 0.35 0.75 0.47 196 0.638
YEARSADOPT,β001 -0.07 0.06 -1.11 196 0.269
PPEREG,β002 0.00 0.00 0.06 196 0.956
PPSM,β003 0.00 0.00 0.35 196 0.73
MINCOME,β004 0.00 0.00 -0.59 196 0.559
HSOVER,β005 0.02 0.04 0.36 196 0.716
DROPOUT,β006 0.03 0.09 0.33 196 0.744
RAD100CS, π01 -0.04 0.04 -1.01 196 0.312
MAXWHT, π02 0.00 0.00 0.10 196 0.923
DIFRL, π03 0.00 0.00 1.10 196 0.271
MEMBER, π04 0.00 0.00 -0.11 196 0.913
METRO, π05 0.28 0.31 0.92 196 0.36
SUBURBAN, π06 0.09 0.27 0.33 196 0.739
ELT, π07 0.78 0.32 2.46 196 0.015
MID, π08 -0.06 0.31 -0.20 196 0.842
Random Effect
Variance d.f. χ2
p-value
level-1,e
11.55
School initial mean, r0 289.30 173 12057.44 <0.001
School mean change rate, r1 1.30 213 1186.25 <0.001
County initial mean, u00 0.11 34 34.97 0.422
203
A7-3. Results from the Model for DIs of Hispanic Students
Fixed Effect Coefficient Standard t-ratio Approx. p-value
For the initial mean DI,π00 INTRCPT3,β000 2.48 6.20 0.40 34 0.691
YEARSADOPT,β001 -0.41 0.53 -0.77 34 0.445
PPEREG,β002 0.00 0.00 1.47 34 0.152
PPSM,β003 0.00 0.00 0.80 34 0.429
MINCOME,β004 0.00 0.00 -1.82 34 0.078
HSOVER,β005 1.01 0.43 2.36 34 0.024
DROPOUT,β006 0.06 0.82 0.08 34 0.938
RAD100CS, π01 -0.58 0.31 -1.85 196 0.066
MAXHSP, π02 0.32 0.05 6.98 196 <0.001
DIFRL, π03 0.09 0.04 2.33 196 0.021
MEMBER, π04 0.00 0.00 0.81 196 0.418
METRO, π05 -6.36 2.65 -2.39 196 0.018
SUBURBAN, π06 -2.77 2.35 -1.18 196 0.241
ELT, π07 -3.01 2.62 -1.15 196 0.252
MID, π08 -2.43 2.55 -0.95 196 0.342
For SCHAGE slope,ψ1 INTRCPT3,β000 -0.58 0.61 -0.95 196 0.342
YEARSADOPT,β001 0.04 0.05 0.80 196 0.423
PPEREG,β002 0.00 0.00 -0.90 196 0.367
PPSM,β003 0.00 0.00 0.42 196 0.676
MINCOME,β004 0.00 0.00 -0.09 196 0.93
HSOVER,β005 -0.02 0.04 -0.55 196 0.583
DROPOUT,β006 -0.14 0.07 -1.80 196 0.073
RAD100CS, π01 -0.07 0.03 -2.07 196 0.04
MAXHSP, π02 0.01 0.00 1.46 196 0.147
DIFRL, π03 0.00 0.00 -0.26 196 0.793
MEMBER, π04 0.00 0.00 1.35 196 0.18
METRO, π05 0.05 0.25 0.21 196 0.836
SUBURBAN, π06 -0.14 0.22 -0.63 196 0.527
ELT, π07 0.47 0.26 1.80 196 0.074
MID, π08 0.37 0.25 1.47 196 0.144
Random Effect
Variance d.f. χ2
p-value
level-1,e
8.07
School initial mean, r0 188.84 173 12497.22 <0.001
School mean change rate, r1 0.83 213 1127.41 <0.001
County initial mean, u00 0.12 34 36.14 0.369
204
A7-4. Results from the Model for DIs of FRL Students
Fixed Effect Coefficient Standard t-ratio Approx. p-value
For the initial mean DI,π00 INTRCPT3,β000 -19.55 8.79 -2.23 34 0.033
YEARSADOPT,β001 1.44 0.78 1.85 34 0.073
PPEREG,β002 0.00 0.01 0.71 34 0.481
PPSM,β003 -0.01 0.00 -2.31 34 0.027
MINCOME,β004 0.00 0.00 -1.12 34 0.272
HSOVERCT,β005 0.56 0.70 0.81 34 0.426
DROPOUT,β006 -0.01 1.49 -0.01 34 0.993
RAD100CS, π01 0.40 0.41 0.98 194 0.327
DIBLK, π02 1.05 0.27 3.86 194 <0.001
DIWHT, π03 0.42 0.28 1.52 194 0.132
DIHSP, π04 0.88 0.28 3.18 194 0.002
MEMBER, π05 -0.01 0.00 -2.31 194 0.022
METRO, π06 2.10 3.40 0.62 194 0.537
SUBURBAN, π07 5.01 2.94 1.71 194 0.09
ELT, π08 -9.81 3.28 -2.99 194 0.003
MID, π09 -4.56 3.10 -1.47 194 0.143
For SCHAGE slope,ψ1 INTRCPT3,β000 -0.61 1.16 -0.53 194 0.599
YEARSADOPT,β001 0.07 0.10 0.68 194 0.499
PPEREG,β002 0.00 0.00 -0.68 194 0.5
PPSM,β003 0.00 0.00 0.96 194 0.339
MINCOME,β004 0.00 0.00 -0.67 194 0.506
HSOVERCT,β005 -0.06 0.06 -0.97 194 0.333
DROPOUT,β006 -0.10 0.15 -0.69 194 0.49
RAD100CS, π01 0.04 0.06 0.69 194 0.494
DIBLK, π02 0.08 0.09 0.85 194 0.398
DIWHT, π03 0.05 0.09 0.60 194 0.551
DIHSP, π04 0.09 0.09 0.97 194 0.332
MEMBER, π05 0.00 0.00 -0.21 194 0.834
METRO, π06 -0.63 0.50 -1.27 194 0.205
SUBURBAN, π07 -0.67 0.42 -1.58 194 0.116
ELT, π08 0.65 0.51 1.27 194 0.204
MID, π09 1.24 0.49 2.55 194 0.012
Random Effect
Variance d.f. χ2
p-value
level-1,e
96.56 School initial mean, r0
221.42 172 1215.63 <0.001
School mean change rate, r1 1.60 212 387.76 <0.001
County initial mean, u00 54.00 34 88.88 <0.001
205
APPENDIX 8
RESULTS FROM THE ONE-WAY ANOVA HMLM MODELS
A8-1. Results from the Model for DIs of Elementary School
Fixed Effect Estimate SE d.f. t-ratio Sig.
DIBLK 3.95 0.69 1377 5.75 .000
DIWHT -2.46 0.55 1377 -4.47 .000
DIHSP -1.28 0.51 1377 -2.53 .012
Random Effect Coefficient SE Wald Z Sig.
DIBLK Var(1) 648.17 24.70 26.24 .000
DIWHT Var(2) 416.01 15.85 26.24 .000
DIHSP Var(3) 356.33 13.58 26.24 .000
Corr(2,1) -0.67 0.01 -45.69 .000
Corr(3,1) -0.57 0.02 -31.16 .000
Corr(3,2) -0.22 0.03 -8.47 .000
Pair-wise Comparisons
Dissimilarity Index Mean Diff. SE d.f. Sig.a
DIBLK DIWHT 6.40 1.13 1377 .000
DIBLK DIHSP 5.23 1.06 1377 .000
DIWHT DIHSP -1.17 0.83 1377 .469
206
A8-2. Results from the Model for DIs of Middle School
Fixed Effect Coefficient SE d.f. t-ratio Sig.
DIBLK 3.94 1.07 418 3.68 .000
DIWHT -2.69 0.84 418 -3.19 .002
DIFRL -1.15 0.81 418 -1.43 .154
Covariance Parameter Coefficient SE Wald Z Sig.
DIBLK Var(1) 481.48 33.30 14.46 .000
DIWHT Var(2) 296.76 20.53 14.46 .000
DIFRL Var(3) 272.90 18.88 14.46 .000
Corr(2,1) -0.66 0.03 -23.82 .000
Corr(3,1) -0.60 0.03 -19.44 .000
Corr(3,2) -0.19 0.05 -4.10 .000
Pair-wise Mean Comparisons
DI Mean Diff. SE d.f. Sig.a
DIBLK DIWHT 6.63 1.75 418 .001
DIBLK DIHSP 5.10 1.69 418 .008
DIWHT DIHSP -1.53 1.28 418 .690
207
A8-3. Results from the Model for DIs of High School
Fixed Effect Coefficient SE d.f. t-ratio Sig.
DIBLK 3.90 1.26 442 3.10 .002
DIWHT -2.91 0.99 429 -2.93 .004
DIHSP -1.02 0.93 458 -1.09 .277
Covariance Parameter Coefficient SE Wald Z Sig.
DIBLK Var(1) 368.16 24.76 14.87 .000
DIWHT Var(2) 228.57 15.60 14.65 .000
DIFRL Var(3) 202.65 13.40 15.12 .000
Corr(2,1) -0.67 0.00 -358.79 .000
Corr(3,1) -0.59 0.00 . .
Corr(3,2) -0.19 0.00 . .
Pair-wise Mean Comparisons
DI Mean Diff. SE d.f. Sig.
DIBLK DIWHT 6.81 2.06 436 .003
DIBLK DIHSP 4.92 1.96 459 .038
DIWHT DIHSP -1.90 1.49 460 .608
208
APPENDIX 9
DEFINITIONS OF THE VARIABLES USED THE ANALYSES IN THIS STUDY
A9-1. Dependent and School Level Variables
Variable Source Year Definition
Dep
enden
t Variab
le
FCAT FDOE 98-10
The Florida Comprehensive Assessment Test is a criterion-referenced assessments measuring selected benchmarks in mathematics, reading, science, and writing Sunshine State Standards (FDOE)***. The FCAT reading scores of years prior to 2001-02 in the dataset in this study are for grades 4.
MSS FDOE 98-10 School's mean scale score ranging from 100 to 500.
DIBLK CCD 98-09 The dissimilarity index calculated by subtracting the coundty mean percentage from the percentage of a certain demographic group in a public school. BLK stands for black student, WHT for white student, HSP for Hispanic student, and FRL for students eligible for free/reduced lunch program.
DIWHT CCD 98-09
DIHSP CCD 98-09
DIFRL CCD 98-09
Charter-sch
ool-related
variab
le
YEAR /SCHAGE
CCD 98-09 Year set as zero in 1998/ Years after school information was reported to CCD database since 1998.
CHARTER CCD 98-09 Charter school. A school that provides free elementary and/or secondary education to eligible students under a specific charter granted by the state legislature or other appropriate authority.*
Dummy
ANYCS(N) CCD 98-09 The presence and the number of charter schools within a certain radius, and the distance to the nearest charter school from a TPS calculated by MS EXCEL program using CCD latitude and longitude information.
Dummy
RAD(N) CCD 98-09
MINDST CCD 98-09
NRST(D/G) CCD 2009 The percentage of a certain demographic group in the charter school nearest to a given public school.
MAX(D/G) CCD 2009 The maximum percentage of a certain demographic group among the nearest and the second nearest charter school.
Note: One asterisk (*) means that the definitions come from this source: Sable, J., Gaviola, N., and Garofano, A. (2007). Documentation to the NCES
Common Core of Data Public Elementary/Secondary School Universe Survey: School Year 2005–-06 (NCES 2007-365). U.S. Department of Education. Washington, DC: National Center for Education Statistics. Two asterisks (**) means that the definitions come from the Florida Department of Education Website: http://www.fldoe.org/eias/eiaspubs/description.asp. visited on February 16, 2012. Three asterisks (*** ) means the source of Florida Department of Education Website: http://www.fldoe.org/faq/default.asp?Dept=179&ID=984#Q984 visited on February 16, 2012.
209
Variable Source Year Definition
Educatio
nal V
ariable
CLSSZ(G-N) FSIR 98-01 Class size for a given grade and subject. The class size of grade 5 is shown as a single average for all classes. ESE classes, ESOL classes, and Dropout Prevention classes are not included in figures for represented schools.**
AVGYREXP FSIR 98-06 The average number of years of teaching experience for teachers at the school. Both in-state and out-of-state experience is counted.**
PADVDG FSIR 98-06 The percentage of teachers with a master’s degree, a doctorate, or a specialist’s degree. For purposes of this indicator, teachers are defined as professionals who are paid on the instructional salary schedule negotiated by a Florida school district.**
PINSTSTF FSIR 98-06 The percentage of instrudtional staff among three categories: instructional staff, administrative staff, and support staff.
PPESCH FSIR 98-06 Per-pupil costs for school operations shown for regular program area.
PELL FSIR 98-06 The percentage of the school’s students who are ELL students served in English for Speakers of Other Languages (ESOL) programs.**
PDABD FSIR 98-06 The percentage of students from the October membership count in exceptional student education (ESE) programs, excluding gifted students.**
MEMBER CCD 98-09 The count of students on the current roll taken on the school day closest to October 1, by using either the sum of original entries and re-entries minus total withdrawals or the sum of the total present and the total absent.*
METRO CCD 98-09 A principal city of a metropolitan core based statistical area (CBSA).* Dummy
SUBURBAN CCD 98-09 Any incorporated place, Census designated place, or non-place territory within a metropolitan CBSA of a large city and defined as urban by the Census Bureau.*
Dummy
ELT CCD 98-09 Elementary school from grade 1 to grade 5 Dummy
MID CCD 98-09 Middle school from grade 6 to grade 8 Dummy
Dem
ograp
hic
Variab
le
STABRATE FSIR 98-06 The percentage of students from the October membership count who are still present in the second semester (February count).**
PFRL CCD 98-09 The proportion of total count of students eligible to participate in the Free/Reduced Price Lunch Program under the ational School Lunch Act.*
PBLK CCD 98-09 The percentage of students in a public school having origins in any of the black racial groups of Africa.*
PHSP CCD 98-09 The percentage of students of Mexican, Puerto Rican, Cuban, Central or South American, or other Spanish culture or origin, regardless of race.*
210
A9-2. County Level Variables
Variable Source Year Definition
Charter-sch
ool-related
variab
le
ADOPTION CCD 98-09 An indicator of the existence of charter schools in a given county and year. Dummy
YEARADOPT CCD 98-09 The year count since the first charter school opened in a county.
PCHARTER CCD 98-09 The percentage of charter-school students that is a aggregated number of charter-school membership in a county.
PSCMED CCD 98-09 An indicator of county that has a higher percentage of charter-school students than the median percentage.
Dummy
PPVTHE FSA 98-09 The percentage of private school and home education students which is not classified by school level.
Educatio
nal v
ariable
PCLSOOFT FSIR 02-06 The percentage of classes in core academic courses being taught by classroom teachers who are teaching out of field.**
PPEREG FSIR 98-06 County per-pupil-expenditure for regualr program area. State-mean-centered.
DROPOUT FSIR 98-06 The percentage calculated by dividing (a) the number of students in grades 9-12 for whom a dropout withdrawal reason was reported by (b) the year's total enrollment for grades 9-12.**
GRADRATE FSIR 98-06
The percentage of students who have graduated within four years of entering ninth grade for the first time. A graduate is defined as a student who receives a standard diploma, a special diploma, or a diploma awarded after successful completion of the GED examination. Certificate recipients are not included.**
PABSNT21 FSIR 98-06 The percentage of students from the total enrollment who were absent 21 or more days during the school year.**
CPELL FSIR 98-06 The percentage of ELL students. D
emo
grap
hic v
ariable
PPSM FSA 98-09 Per-Square-Mile population of a county.
CPBLK CCD 98-06 The county percentage of a certain demographic student calculated by aggregating the regular public school's membership.
CPHISP CCD 98-06
HSOVER CENSUS 05-09 The percent of high school graduate or higher among persons 25 years and over. State-mean-centered.
BAOVER CENSUS 05-09 The percent of bachelor's degree or higheramong persons 25 years and over. State-mean-centered.
MINCOME FSA 98-09 County's household median income. State-mean-centered.
PPOOR517 FSA 98-09 Percentage of 5-year-old to 17-year-old children in poverty.
APPENDIX 10
STUDIES ON THE CS COMPETITION IMPACTS ON STUDENT ACHIEVEMENT IN TPSS
Area Author Pub. Year
Pub. Type
Data Year
Unit Estimation method Dependent Variable Competition Measure Direction of Effect
grade
Arizona Hoxby 2003 Working
Paper 92-93~ 99-00
School Regression
(School/Year FE26
)
Productivity27
Share of CS28
students in districts Dummy (>6%) in district
Positive
G4/ G7
Change in Productivity Positive
National percentile rank Positive
Change in Scores Positive
Cali- fornia
Zimmer& Buddin/
Buddin& Zimmer
2009 /2005
Journal Article/
Working Paper
97-98 ~
01-02 Student
Regression (Student/School/
Year FE)
Stanford 9 test score gains
D to the nearest CS No effect
P: HR29
E M H
Existence of CS within 2.5m No effect P: MM4
Number of CS within 2.5m No effect
Share of CS student within 2.5m No effect N: ER4
Lost(%) to CS In t-1 within 2.5m No effect
Florida
Sass 2006 Journal Article
99-00 ~
02-03 Student
Regression (Student/School FE)
Student Achievement Gains in TPSs
Existence of CS
Within 2.5m/5m/10m
No effect (Positive on Math only within 2.5-mile)
G3- G10
Number of CS
Share of CS Students
Ertas 2007 Diss. 95 ~
2000 School Regression
Florida Writing Assessment Program
Existence of CS in a district Existence of CS within 5-mile Share of CS student (Dummy charter student >= county with median % of public student)
No effect (Positive on only 4th with market share measure)
G4/ G10
26 Fixed effects estimation
27 Michigan Educational Assessment Program scale scores/PPE in $1000
28 Charter school
29 P: HR - Positive effects on high school reading scores; P: MM – Positive effects on middle school math scores, N: ER - Negative effect on elementary reading scores
212
Area Author Pub. Year
Pub. Type
Data Year
Unit Estimation method Dependent Variable Competition Measure Direction
of Effect Grade
Michigan
Bettinger 2005 /2000 /1999
Journal Article/ Diss./
Working Paper
96-97 ~
98-99 School
Diff-in-Diff regression (District FE)
MEAP30
Average of Schools Number of CS
Within 5m from TPS
No effect G4
Any CS
Regression (District FE)
Lagged dependent variable Number of CS
MEAP scores (IV31
)
Eberts Hollenbeck
2001 Working
Paper 96-97~ 98-99
Student Regression
(Student/District FE) MEAP Scores Existence of CS In a district No effects
G4/ G5
Hoxby 2003 Working
Paper
92-93 ~
00-01 School
Regression (School/Year FE)
Productivity
Share of CS Students in Districts
Dummy (>6%) in district
Positive
G4/ G7
Change in Productivity Positive
MEAP scale scores Positive
Changes in MAEP scores
Positive
Ni 2009 Journal Article
94 ~ 04
(Reading 94 ~
02)
School Pooled
Regression
Regression MAEP
Average Student achievement of Schools
the 6% of student lost to CS in each district
Short-run(=<3y) Negative32
G4/ G7
Medium-run(4-5y) No effect
Long-run (>5yrs)
School FE Short /Medium /Long
Negative FD33
FE/FD
Lee 2009 Journal Article
1994/ 1999
District
Chi-square analysis Changes in efficiency
Index
Dummy variable (>6%) for share of CS students in districts
No difference
G4/ G7 Regression
First differecing Changes in share No effect
First differecing Changes in pass rates Changes in share No effect
30 Michigan Educational Assessment Program
31 Instrumental variable estimation
32 Negative on G4 and No effect on G7
33 First differencing
213
Area Author Pub. Year
Pub. Type
Data Year
Unit Estimation method Dependent Variable Competition Measure Direction of
Effect grade
Chicago Zimmer
et al. 2009
Report (RAND)
97~ 06
Student Regression
(Student/School FE) ITBS
34 score gains
Number of CS within 2.5m Distiance to the nearest CS
Neutral G8- 12
Denver Zimmer
et al. 2009
Report (RAND)
01~ 05
Student Regression
(Student/School FE) Test score gains
Number of CS within 2.5m Distiance to the nearest CS
Neutral G3- 10
Mil- waukee
Greene Forster
2002 Report 96-97~ 00-01
School Regression WKCE35
(Z-score) An index of the distance between the
school and the three nearest charter
schools
No Effect G8
Positive G10
Lavertu Witte
2008 Working
Paper 00-01
~06-07 Student
Regression (Student/school FE)
WKCE (Z score gains)
Number of CS within 2.5m No Effect G3- G10 D to the nearest CS No Effect
Zimmer
et al. 2009
Report (RAND)
2000~ 06
Student Regression
(Student/School fixed effects) WKCE (Z-score)
Number of CS within 2.5m Distance to the nearest CS
No Effect G3- G10
New
York
City Winters 2009 Report
05~ 08
Student Regression
(Student/School FE) Test scores (Math,
English Language Arts) Lost (%) to CS No effect
G3- G8
North Carolina
Holmes et
al. 2006 /2003
Journal Article/
Working Paper
96-97 ~
99-00 School Regression
Cross-sectional Model by year
NDCPI36
scores - school level
performance composite
Existence of CS within 10km/20km
Positive
G3- G8
Existence of CS In the district Positive
IV Panel Model Existence of CS
within 5/10/ 15/20/25km
Positive
in county No effect
ML Model Existence of CS 5/10/15/20/25km Positive
Bifulco Ladd
2006 Journal Article
97-98 ~
01-02 Student Regression
Student/ Student & school
FE
End of Grade
developmental scale score
Dummy for the distance to the nearest
CS(2.5m/2.5m-5m/5m-10m) No effect
G3- G8 Dummy for the number of CS
(1 CS/2 CS/>2 CS within 5m) No effect
34 Iowa Tests of Basic Skills 35 Wisconsin Knowledge and Concepts Examination 36 North Carolina Department of Public Instruction
214
Area Author Pub. Year
Pub. Type
Data Year
Unit Estimation method Dependent Variable Competition Measure Direction of Effect
grade
Ohio
Carr Ritter
2007 Working
Paper 02~ 06
School Pooled Regression School proficiency
passage rates Existence of CS in the District Negative
G4/G6/ G12
Ertas 2007 Dissertation 95~ 01
School Regression School Passing Rates Existence of CS in a district Existence of CS within 5-mile Share of CS student (Dummy)
Negative G4/6/ 8/10
Zimmer et al.
2009 Report
(RAND) 04~ 07
Student Regression
(Student/School FE) Normalized test core
gains Number of CS within 2.5m Distance to the nearest CS
No Effect G3- G8
San Diego
Zimmer et al.
2009 Report
(RAND) 97~ 06
Student Regression
(Student/School FE) Test score gains
(California DOE) Number of CS within 2.5m Distance to the nearest CS
No Effect G2- G11
Texas
Bohte 2004 Journal Article
96~ 02
County Pooled Regression County Pass rate on
TAAS37
exam
Percent of CS student in a Conuty Positive G10 Presence of CS in a county
Gross- kopf et al.
2004 Working
Paper 95~ 01
District Regression
(IV estimation)
Productivity Index of a district Share of CS Students
(n-mile radius) Relative CS enrollment
No effect
G6 Relative Efficiency
38 of
districts Positive
Booker et al.
2008 /2006 /2004
Journal Article/
Working Paper/ Diss.
93-94 ~
03-04 Student
Regression (Student/School FE)
Rank-Based Z Scores (transformed TAAS
scores)
Share of CS students in the district
Positive G3- G8
Number of CS within 0-5m/6-10m
Number of CS students (1000) within 0-5m/6-10m
interactions (CS share*year)
Interactions (Number of CS*year)
Zimmer et al.
2009 Report
(RAND) 94~ 03
Student Regression
(Student/School FE) Rank-based Z-scores
(TAAS, TAKS) Number of CS within Distance to the nearest CS
Positive G3- G8
Ertas 2007 Dissertation 95~ 01
School Regression TASS Scores Existence of CS in a district Existence of CS within 5-mile Share of CS student (Dummy)
Positive G3- G8/ G10
37 Texas Assessment of Academic Skills
38 Relative efficiency = Productivity / Technical efficiency
215
Area Author Pub. Year
Pub. Type
Data Year
Unit Estimation method Dependent Variable Competition Measure Direction of
Effect grade
Phila- delphia
Zimmer
et al. 2009
Report (RAND)
00~ 06
Student Regression
(Student/School FE) Rank-Based Z Scores
Number of CS within 2.5m Distance to the nearest CS
No Effect G1- G10
ALUSD-
SW39
Imber- Man
2009 Working
Paper/ Dissertation
93-94 ~
04-05 Student
Regression Student FE
the Stanford Achievement
Test Score Share of CS student
in the same grade within 1m/1.5m
Negative G1-
G12 Student/School FE No effect
Regression
(2SLS)
Baseline Negative
Interaction (CS Share*G1-5)
Negative G1-G5
Interaction (CS Share*G6-11)
No effect G6-
G-11
Regression Student FE
Difference
(Value-added)
Share of CS student
in the same grade within 1m/1.5m
No Effect G1-
G12 Student/School FE No effect
Regression
(2SLS)
Baseline Negative
Interaction (CS Share*G1-5)
Negative G1-
G5
Interaction (CS Share*G6-11)
No effect G6-
G-11
39 Anonymous large urban school district in the southwest
REFERENCES
Allen, J., Consoletti, A., & Kerwin, K. (2009). The Accountability Report. Washington: The Center for Education Reform.
Baumler, E. R., Harrist, R. B., & Carvajal, S. (2003). Analysis of repeated measures data. In S. P. Reise & N. Duan (Eds.), Multilevel Modeling: Methodological Advances, Issues,
and Applications (pp. 140-156). Mahwah, New Jersey: Lawrence Erlbaum Associates.
Belfield, C. R., & Levin, H. M. (2002). The effects on competition between schools on educational outcomes: A review for the United States. Review of Educational
Research, 72(2), 279-341.
Bettinger, E. P. (2005). The effect of charter schools on charter students and public schools. Economics of Education Review, 24, 133-147.
Betts, J. R., & Tang, Y. E. (2011). The effect of charter schools on student achievement. Seattle: National Charter School Research Project.
Bifulco, R., & Ladd, H. F. (2006a). The impacts of charter schools on student achievement: Evidence from North Carolina. Education Finance and Policy, 50-90.
Bifulco, R., & Ladd, H. F. (2006b). School choice, racial segregation, and test-score gaps: Evidence from North Carolina's charter school program. Journal of Policy Analysis
and Management, 26(1), 31-56.
Bohte, J. (2004). Examinig the Impact of Charter Schools on Performance in Traditional Public Schools. The Policy Studies Journal, 32(4), 501-520.
Booker, Gilpatric, Gronberg, & Jansen (2008). The effect of charter schools on traditional public school students in Texas: Are children who stay behind left behind? Journal of
Urban Economics, 64, 123-145.
Borman, K. M., Eitle, T. M., Michael, D., Eitle, D. J., Lee, R., Johnson, L., et al. (2004). Accountability in a postsegregation era: The contibuing significance of racial segregation in Florida's schools. American Educational Research Journal, 41, 605-631.
Braun, H., Jenkins, F., & Grigg, W. (2006). A closer look at charter schools using
hierarchical linear modeling (No. NCES 2006-460). Washington, DC: U.S. Department of Education, Natinal Center for Education Statistics, Institute of Education Sciences.
Buckley, J., & Schneider, M. (2007). Charter Schools: Hope or Hype? Princeton: Princeton University Press.
Budde, R. (1988). Education by charter: Restructuring school districts. Key to long-term
contituing improvement in American education. Andover: Regional Laboratory for Educational Improvement of the Northeast & Islands.
217
Bulkley, K., & Fisler, J. (2003). A decade of charter schools: From theory to practice. Educational Policy, 17(3), 317-342.
Carnoy, M. (2000). School choice? or is it privatization? Educational Researcher, 29(7), 15-20.
Carr, M., & Ritter, G. (2007). Measuring the Competitive Effect on Charter Schools on Student Achievement in Ohio's Traditional Public Schools. Paper submitted to National Center for Study of Privatization in Education. NY: Columbia University.
Chen, H.-T., & Rossi, P. H. (1980). The multi-goal, theory-driven approach to evaluation: A model linking basic and applied social science. Social Forces, 59(1), 106-122.
Chubb, J. E. (2006). The private can be public. In P. E. Peterson (Ed.), Choice and
Competition in American Education (pp. 13-22). New York: Rowman and Littlefield Publishers.
Chubb, J. E., & Moe, T. M. (1990). Politics, Markets, America's Schools. Washington, D.C.: The Brookings Institution.
Chung, J. Y., Shin, I.-S., & Lee, H. (2009). The effectiveness of charter school: Synthesizing standardized mean-changes. KEDI Journal of Educational Policy, 6(1), 61-80.
Clark, D. (2005). Politics, markets and schools: Quasi-experimental evidence on the impact of autonomy and competition from a truly revolutionary UK reform. Center for Labor Economics, University of California, Berkeley.
Clotfelter, C. T. (1999). Public School Segregation in Metropolitan Areas. Land Economics,
75(4), 487-504.
Clotfelter, C. T. (2001). Are Whites Still Fleeing? Racial Patterns and Enrollment Shifts in Urban Public Schools, 1987-1996. Journal of Policy Analysis and Management, 20(2), 199-221.
Cobb, C. D., Glass, G. V., & Crockett, C. (2000). The U.S. Charter School Movement and Ethnic Segregation. The American Educational Research Association.
Coleman, J. S., Campbell, E. Q., Hobson, C. J., McPartland, J., Mood, A. M., Weinfeld, F. D., et al. (1966). Equality of Educational Opportunity. Washington: National Center for Educational Statistics.
CREDO (2009). Multiple choice: Charter school performance in 16 states. Stanford: Center for Research on Education Outcomes.
Crew, R. E., & Anderson, M. R. (2003). Accountability and Performance in Charter Schools in Florida: A Theory-based Evaluation. American Journal of Evaluation, 24, 189-212.
Crockett, C. M. (1999). California Charter Schools: The Issue of Racial/Ethnic Segregation. Unpublished Dissertation, Arizona State University.
Dee, T. S., & Fu, H. (2004). Do charter schools skim students or drain resources? Economics
of Education Review, 23, 259-271.
218
deHaven-Smith, L. (1988). Philosophical Critiques of Policy Analysis: Lindblom, Habermas,
and The Great Society. Gainesville: University of Florida Press.
Eberts, R. W., & Hollenbeck, K. (2001). An Examination of Student Achievement in Michigan Charter Schools. Unpublished Working Paper. Upjohn Institute.
Education, N. C. o. E. i. (1984). A Nation at Risk. Cambridge, Massachusetts: USA Research.
Ertas, N. (2007). Public School Responses to Charter SChool. Unpublished Dissertation, Georgia State University, Atlanta, GA.
FDOE (2006). Florida's Charter Schools: A Decade of Progress. Tallahassee: Florida Department of Education.
FLDOE (2004). Florida charter schools: 2002-2003 annual accountability report. Tallahassee: Florida Department of Education.
FLDOE (2006). Student achievement in Florida's charter schools: A decades of progress. Tallahassee: Florida Department of Education.
FLDOE (2009). Student achievement in Florida's charter schools: A comparison with
achievement in traditional public schools. Tallahassee: Florida Department of Education.
FLDOE (2010). Student achievement in Florida's charter schools: A comparison with
achievement in traditional public schools. Tallahassee: Florida Department of Education.
Frankenberg, E., & Lee, C. (2003). Charter schools and race: The lost opportunity for
integrated education (Reports). Cambridge, MA: Harvard Civil Rights Project at Harvard University.
Frankenberg, E., Lee, C., & Orfield, G. (2003). A Multiracial Society With Segregated
Schools: Are We Losing the Dream? (Reports). Cambridge, MA: Harvard Civil Rights Project.
Friedman, M. (1955). The role of government in education. Capitalism and Freedom, 71(2), 85-107.
Friedman, M. (1997). Public schools: Make them private. Education Economics, 5(3), 341-344.
Fuller, B., Elmore, R. F., & Orfield, G. (1996). Policy-making in the dark. In B. Fuller, R. F. Elmore & G. Orfield (Eds.), Who Chooses? Who Loses? (pp. 1-24). New York: Teachers College, Columbia University.
Garcia, D. R. (2008). The Impact of School Choice on Racial Segregation in Charter Schools. Educational Policy, 22(6), 805-829.
Gleason, P., Clark, M., Tuttle, C. C., & Dwoyer, E. (2010). The evaluation of charter school
impacts: Final report (No. NCEE 2010-4029). Washington, D.C.: National Center for
219
Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.
Glomm, G., Harris, D., & Lo, T.-F. (2005). Charter school location. Economics of Education
Review, 24, 451-457.
Greene, J., & Forster, G. (2002). Rising to the Challenge: The effect of school choice on
public schools in Milwaukee and San Antonio. New York: Manhattan Institute, Center for Civic Innovation.
Greene, J. P., Forster, G., & Winters, M. A. (2003). Apples to apples: An evaluation of charter schools serving general student populations. Manhattan Institute for Policy Research.
Grosskopf, S., Hayes, K. J., & Taylor, L. L. (2004). Competition and Efficiency: The Impact of Charter Schools on Public School Performance. Oregon State University.
Hanushek, E. A., Kain, J. F., & Rivkin, S. G. (2009). New Edivence about Brown v. Board of
Education: The Complex Effects of School Racial Composition on Achievement. Journal of Labor Economics, 27(3).
Hanushek, E. A., & Rivkin, S. (2006). School Quality and The Black-White Achievement Gap. National Bureau of Economic Research.
Hassel, B. C., Terrell, M. G., & Kowal, J. (2006). Florida charter schools: Hot and humid
with passing storms. Washington, D.C.: Education Sector.
Heck, R. H., Thomas, S. L., & Tabata, L. N. (2010). Multilevel and Longitudinal Modeling
with IBM SPSS. New York: Toutledge.
Henig, J. R. (1996). The Local Dynamics of Choice: Ethnic Preferences and Institutional Responses. In B. Fuller, R. F. Elmore & G. Orfield (Eds.), Who Chooses? Who
Loses?: Culture, Institutions, and the Unequal Effects of School Choice (pp. 95-117). New York: Teachers College Press.
Henig, J. R. (2008). Spin Cycle: how research is used in policy debates: the case of charter
schools. New York: Russell Sage Foundation.
Holmes, G. M., DeSimone, J., & Rupp, N. G. (2003). Does school choice increase school quality? Unpublished Working Paper 9683. National Bureau of Economic Research.
Horn, J., & Miron, G. (1999). Evaluation of the Michigan Public School Academy Initiative. Kalamazoo: The Evaluation Center, Western Michigan University.
Hoxby, C. M. (2002a). How School Choice Affects the Achievement of Public School Students. Alliance for School Choice.
Hoxby, C. M. (2002b). School Choice and School Productivity (or Could School Choice be a Tide that Lifts All Boats?). National Bureau of Economic Research.
Hoxby, C. M. (2003). School choice and school competition: Evidence from the United States. Swedish Economic Policy Review, 10, 11-67.
220
Hoxby, C. M. (2004). Achievement in Charter Schools and Regular Public Schools in the United States: Understanding the Differences.
Imberman, S. A. (2009). The effect of charter schools on achievement and behavior of public school students. Social Science Research Network.
Kolderie, T. (1990). Beyond Choice to New Public Schools: Withdrawing the Exclusive
Franchise in Public Education (No. Policy Report No. 8). Washington, D.C.: Progressive Policy Institute.
Lacireno-Paquet, N., Holyoke, T. T., Moser, M., & Henig, J. R. (2002). Creaming versus cropping: Charter school enrollment practices in response to market incentives. Educational Evaluation and Policy Analysis, 24(2), 145-158.
Lavertu, S., & Witte, J. (2008). A Multifaceted Analysis of Milwaukee Charter Schools. Paper presented at the The 2008 Annual Meeting of the American Political Science Association.
Lee, K. (2009). Do charter schools spur improved efficiency in tratiditional public schools in Michigan? Journal of Educational Policy, 6(1), 41-59.
Levin, H. R. (2009). An economic perspective on school choice. In M. Berends, M. G. Springer, D. Ballou & H. J. Walberg (Eds.), Handbook of Research on School Choice (pp. 19-34). New York: Routledge.
Loveless, T. (2002). The 2002 Brown Center Report on American Education: How well are
american students learing? Washington, D.C.: The Brookings Institution.
Lubienski, C. (2001). Redefining "public" education: Charter schools, common schools, and the rhetoric of reform. Teachers College Record, 103(4), 634-666.
Lubienski, C. (2005a). Public schools in marketized environments: Shifting incentives and unintended consequences of competition-based educational reforms. Chicago
Journals, 111(4), 464-486.
Lubienski, C. (2005b). School Choice as a Civil Right: District Responses to Competition and Equal Educational Opportunity. Equity & Excellence in Education, 38(4), 331-341.
Lubienski, S. T., & Lubienski, C. (2006). School sector and academic achievement: A multilevel analysis of NAEP mathmatics data. Educational Research Journal, 43(4), 651-698.
MacCallum, R. C., & Kim, C. (2000). Modeling Multivariate Change. In T. D. Little, K. U. Schnabel & J. Baumert (Eds.), Modeling Longitudinal and Multilevel Data: Practical
Issues, Applied Approaches and Specific Examples (pp. 51-68). Nahwah, New Jersey: Lawrence Erlbaum Associates.
Miron, G., & Horn, J. (2002). Evaluation of Connecticut Charter Schools and the Charter
School Initiative. Kalamazoo, MI: The Evaluation Center, Western Michigan University.
221
Miron, G., Urschel, J. L., Mathis, W., J., & Tornquist, E. (2010). Schools without Diversity: Education Management Orgainzaitons, Charter Schools and the Demographic Stratification of the American School System. Education and the Public Interest Center
Eduction Policy Research Unit.
NAPCS (2009). Charter school achievement: What we know. Washington, D.C.: The National Alliance for Public Charter Schools.
NCES (2003). America's Charter Schools: Results From the NAEP 2003 Pilot study (No. NCES 2005-456). Washington.
Nelson, F. H., Rosenberg, B., & Meter, N. V. (2004). Charter school achievement on the 2003
National Assessment of Educational Progress. Washington, D.C.: American Federation of Teachers.
Ni, Y. (2009). The impact of charter schools on the efficiency of traditional public schools: Evidence from Michigan. Economics of Education Review, 28, 571-584.
North, D. C. (1990). Institutions, Institutional Change and Economic Performance. New York: Cambridge University Press.
Orfield, G. (2001). Schools More Segregated: Consequences of a Decade of Resegregation. Cambridge, MA: Harvard University.
Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and
Data Analysis Methods (Second Edition ed.). Thousand Oaks: Sage Publications.
Renzulli, L. A. (2006). District segregation, race legislation, and black enrollment in charter schools. Social Science Quarterly, 87(3), 618-637.
Renzulli, L. A., & Evans, L. (2005). School choice, charter schools, and white flight. Social
Problems, 52(3), 398-418.
Reville, P., Coggins, C., & Candon, J. (2004). Massachusetts charter schools and their feeder
districts: A demographic analysis. Boston: Rennie Center for Education Research and Policy.
Rivkin, S. G. (1994). Residential segregation and school integration. Sociology of Education,
67(4), 279-292.
Roy, J., & Mishel, L. (2005). Advantage none: Re-examining Hoxby's findings of charter
school benefits. Washington, D.C.: Economic Policy Institute.
Rumberger, R. W., & Palardy, G. J. (2005). Does Segregation Still Matter? The Impact of Student Composition on Academic Achievement in High School. Teachers College
Record, 107(9), 1999-2045.
Sass, T. R. (2006). Charter Schools and Student Achievement in Florida. Education Finance
and Policy, 1(1), 91-122.
222
Teske, P., Schneider, M., Buckley, J., & Clark, S. (2000). Does charter school competition
improve traditional public schools? Civic report.
Tiebout, C. M. (1956). A pure theory of local expenditure. The Journal of Political Economy,
64(5), 416-424.
USDOE (2004a). America's Charter Schools: Results From the NAEP 2003 Pilot study (No. NCES 2005-456). Washington: National Center for Education Statistics.
USDOE (2004b). Evaluation of the Public Charter Schools Program: Final Report. Washington, D.C.: Office of Under Secretary.
Weiher, G. R., & Tedin, K. L. (2001). Does Choice Lead to Racially Distinctive School? Charter schools and Household Preferences. Journal of Policy Analysis and
Management, 21(1), 79-92.
Winters, M. A. (2009). Everyone Wins: How Charter Schools Benefit All New York City
Public School Students. New York: Manhattan Institute.
Zimmer, R., & Buddin, R. (2009). Is charter school competition in California improving the performance of traditional public schools? Public Administration Review, 69(5), 831-845.
Zimmer, R., Gill, B., Booker, K., Lavertu, S., Sass, T. R., & Witte, J. F. (2009). Chater Schools in Eight States: Effects on Achievement, Attainment, Integration, and Competition. Rand Corporation.
Zoloth, B. S. (1974). An investigation of alternative measures of school segregation. Institution for Research on Poverty, Wisconsin University.
Zoloth, B. S. (1976). Alternative measures of school segregation. Land Economics, 52(3), 278-298.
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BIOGRAPHICAL SKETCH
EDUCATION
M.B.A. from Aju University, South Korea, 2004
B.B. A. from Seoul University, South Korea, 2005
TEACHING EXPERIENCE
PAD3003-01 Public Administration in Society, Fall 2010 – Spring 2011, Askew
School of Public Administration and Policy, FSU
PROFESSIONAL SERVICE
Assistant Director, 1995-1996, Kunsan Labor Office, Ministry of Labor, Korea
Deputy Director, 1996-2006, Ministry of Education, Korea
Director, 2007-2008, Kyungbuk & Pusan National University, Korea