Determinants of Educational Achievement in Public Schools

By: Geoffrey Koch

Introduction

Educational achievement is the precursor for success in any country. This study will

focus on the determinants of educational achievement for students in public schools. Since 90%

of children in the United States attend public schools, the economic future of our country largely

depends on the success of those institutions (Toma, 1996). According to James Heckmand and

Paul LaFontaine, the American High school graduation rate has steadily declined since the year

1969 (2007). This leaves one to wonder why students in American public schools are not

achieving at a higher rate. The hypothesis to be tested is the main determinant of educational

achievement is the amount of expenditures per pupil. For example, Ulster, New York spends

$12,482 per pupil and has an average SAT score of 1,032 while a lower funded district, Beaufort,

South Carolina, spends $9,278 per pupil and has average an SAT score of 971 (Settimi, 2007).

When public schools receive more funding, more money can be allocated to teacher salary,

school equipment, and the school buildings themselves. Educational achievement should

improve with better equipment and more qualified teachers.

This section will review the literature on the determinants of educational achievement.

Factors that have been found to influence educational achievement are the student-teacher ratio,

the location of the school, home environments, teacher’s salary and expenditures per pupil.

While all of these factors surely influence the educational achievement of students, the

expectation is that expenditures per pupil are the most influential factor in educational

achievement. [The studies reviewed have used educational production functions as a means to

explain the relationship between inputs, such as expenditures, and the amount of output, such as

test scores.]

Expenditures Per Pupil

Expenditures per pupil is expected to have a positive impact on educational achievement.

As expenditures increase, schools offer more courses to students to broaden their views and

increase their knowledge. Further, when schools have more money for expenditures, they can

attract more qualified teachers to the institution and purchase higher quality resources (such as

textbooks), improving educational achievement.

Eugenia Toma’s (1996) study on public school funding and private schooling found that

public funding was insignificant when it came to affecting educational achievement in public

schools. Even though Toma (1996) did not specifically test funding as a single variable, she

found that all interaction variables were insignificant. This implies that the effects of funding on

school achievement are independent of family socioeconomic status [since this is the case, and

private schools typically receive less funding per pupil than public schools, it can be said that

Toma found funding for schools does not matter]. In his study of Illinois public high schools,

entitled “Expenditures and Student Achievement in Illinois”, William Sander (1991) finds that

expenditures per pupil have a significant effect on educational achievement. However, he finds

that expenditures have a negative effect on achievement (Sander measures educational

achievement by ACT scores in both composite and mathematics). In Sander’s second study

(1998), entitled “Endogenous Expenditures and Student Achievement”, he once again collects

data from Illinois public schools, but measures student achievement by math test scores in third

and eighth grade. In this study, Sander finds that expenditures per pupil have a statistically

significant and positive effect on educational achievement. Another study, by Jonathan Klick

(2000), analyzes expenditures per pupil in Pennsylvania public schools. Klick cites that of the

top ten states that consistently rank highest in various student achievement tests, only one rated

in the top ten in terms of per pupil spending. In the study, Klick (2000) finds that expenditures

per pupil has a positive and significant impact on achievement, but the coefficient was so small

that schools would have to spend an impractical amount per pupil to increase test scores by 0.5.

In Rati Ram’s (2004) study entitled “School Expenditures and Student Achievement: Evidence

for the United States”, Ram uses panel data from the Digest of Education Statistics to test the

effects of expenditures per pupil on SAT scores. Ram finds that expenditures have a highly

significant positive effect on SAT scores. Finally, in Eric Hanushek’s (1986) study, out of 65

total studies done explaining the relationship between expenditures per pupil and educational

achievement, only 16 were found to be significant, while the remaining 49 were insignificant.

Student-Teacher Ratio

The student-teacher ratio is expected to have a negative impact on educational

achievement. As the ratio increases, teachers will be responsible for more students and will

therefore give less individual attention to each student, lowering the likelihood that all questions

about a subject can be answered.

Sander’s (1991) study analyzes the impact of student-teacher ratio on composite and

math ACT scores. Sander finds that student-teacher ratio has a significant and negative impact

on both composite and math scores. Sander (1998) uses a similar variable, average class size,

which he finds to have a negative and insignificant impact on achievement. In Eric Hanushek’s

(1986) report on production and efficiency in public schools, he examines the student-teacher

ratio in 112 studies. The ratio is found to have a positive and significant impact in 9 of those

studies, while 14 were found to have a negative and significant impact on educational

achievement. The other 89 studies found it to be insignificant.

Teacher’s Salary

Teacher salary is expected to have a positive effect on educational achievement. When

teachers receive more pay, they will have a more positive outlook on their job and will truly want

to educate students. If teachers receive relatively low pay, going to work everyday will seem

more of a chore than a pleasant activity. Higher salaries will also attract more qualified teachers.

William Sander (1991) finds that teacher’s salary has a significant and positive effect on

educational achievement in both ACT composite and mathematics scores but an insignificant

impact on graduation rates. Sander’s (1998) second study also indicates that teacher’s salary has

a significant and positive effect on both third grade and eighth grade test scores. Eric Hanushek’s

(1986) report found quite the opposite. Hanushek examines the research on the economics of

education that has been done up to the year 1986. In 65 studies that estimated the effect of

teacher’s salary on educational achievement, 13 found that salary had a positive and significant

impact while only 3 found a significant and negative effect. 49 other studies found teacher’s

salary to have an insignificant effect on educational achievement.

Location of School

The location of the school is typically identified as being in an urban or rural setting. If a

school is located in an urban setting, this will have a negative effect on educational achievement

because of the increased population in the area and the likelihood of a higher crime rate.

Conversely, schools in a rural setting will have a positive effect on achievement because of a

lower population and lower crime rate.

Jonathan Klick (2000) measures size of school district by average daily attendance in a

school. He uses this variable to measure the effects of economies and diseconomies of scale in

the education process. Klick found that the size of a school district did not have a consistently

significant impact on educational achievement. Sander (1991) measures school size for districts

in Illinois and finds that it has a significant and positive impact on ACT composite and

mathematics scores and percentage college-bound. Sander’s (1998) second study finds that

school size is negatively correlated, but is insignificant in both third grade and eighth grade test

scores.

Percentage Poor

The percentage of poor in a certain area is a proxy for the educational achievement of

parents in the area. If the parents of a child are poorly educated, and therefore have a paltry

salary, they cannot help their child with schoolwork and most likely cannot afford to have their

child enrolled in any extracurricular activities which would help enrich their education.

Sander (1991) finds that percentage of poor have a significant and negative effect on

ACT composite and math scores. The percentage of poor also has a significant and negative

effect on the graduation rate. Sander’s (1998) second study also finds that the variable “low

income” has a significant and negative effect on third grade and eighth grade test scores. Klick

(2000) tests 90 functional forms of his model with the variable “poor’. Out of the 90 different

forms, the variable was found to be significant and negative in every specification.

Percentage Taking ACT

The percentage of students taking the ACT exam is a proxy for the amount of students

planning on attending college. Percentage taking ACT is expected to have a positive relationship

with educational achievement. Students who do well in school are more likely to take the ACT

exam than those who do poorly.

The only study that focuses on the percentage of students taking the ACT exam is

William Sander’s 1991 study. In it, he found that the percentage taking the ACT exam is

significantly and positively related to higher test scores.

Summary

This study focuses on the determinants of educational achievement in public schools.

Several variables have been found to affect the educational achievement of students. The study

will focus on random samples from high school districts in West Virginia, Virginia, and

Maryland public schools. These three states each provide different characteristics that will help

in finding the determinants of educational achievement such as differing populations, incomes,

and locations for students. The variables which will be examined in this study include

expenditures per pupil, the student-teacher ratio, teacher’s salary, the location of the school, the

percentage of poor, and the percentage of students taking the ACT exam.

Theory Section

This study focuses on the factors that impact the educational achievement of students

attending public schools. The hypothesis to be tested is that an increase in funding will positively

affect the educational achievement of students. Other factors that have been found to influence

educational achievement range from the student-teacher ratio to crime rates.

In this section, the effect of funding and other economic and demographic factors on

educational achievement will be analyzed using a production function. In the equation and graph

below, educational achievement is seen as a function of various inputs. These inputs can consist

of funding (Fund), student-teacher ratio (Ra), teacher salary (Sal), location of the school (Loc),

the percentage poor (Poor), and percentage taking the ACT (%ACT).

Educational Achievement = f (Fund, Ra, Sal, Loc, Poor, % ACT)

Typically, when inputs are added to this function, the educational achievement of

students should increase. However, the production function is subject to diminishing marginal

returns. So, when one input is increased, holding all other inputs constant, educational

achievement will increase at a decreasing rate.

One factor likely to have an impact on educational achievement is the amount of funding

a school receives, or expenditures per pupil. With more money, schools are able to hire better

teachers and purchase higher quality textbooks. More money for schools will also grant them the

ability to perform any other activity necessary to educate students. When funding increases for a

school, educational achievement is expected to increase.

Another factor likely to have an impact on educational achievement is the student-teacher

ratio. When teachers have a small number of students to teach, they can focus their efforts on

individuals more often. Consequently, students in smaller classes are more likely to be noticed if

they are struggling and are more likely to get assistance. So, when the student-teacher ratio

increases, educational achievement is likely to decrease.

Teacher salary is also expected to have an impact on the educational achievement of

students in public schools. It is expected to have a direct relationship with educational

achievement. As teacher salary increases, other things constant, teachers will be more

encouraged about their job and will have a positive outlook on the day. In turn, students will be

able to learn more from a teacher with a positive outlook, rather than a negative one. Teacher

salary is expected to behave similarly to expenditures per pupil. That is, when the teacher salary

for a school increases, educational achievement will also increase. Once again, however, this is

subject to diminishing marginal returns.

The location of a school will affect the educational achievement of a student. Schools in

urban areas are more likely to have problems with overpopulation. Urban areas also have higher

crime rates, which can negatively effect educational achievement. When a school is located in a

rural environment, students are more likely to receive attention at home from parents when help

is needed. Schools located in urban areas are expected to have students with lower educational

achievement than those located in rural areas.

The percentage poor is expected to have an inverse relationship with educational

achievement. This is a measure of the human capital available for students when they are at

home and also the educational achievement of adults in the area. A poor household is less likely

to support a student with school supplies which would further their education. Also, students in a

poor household are less likely to have parents available to provide support and help with their

schoolwork. As the percentage poor increases, educational achievement is expected to decrease.

The percentage of pupils taking the ACT exam is expected to have a direct relationship

with educational achievement. When students take an ACT exam, they are more than likely

preparing for college. Students planning on attending college are expected to have higher grades,

and therefore will have higher educational achievement. When the percentage of pupils taking

the ACT increases, educational achievement will also increase.

Summary

This study will focus on the determinants of educational achievement in public schools.

An educational production function is used in order to find educational achievement. Six

variables will be used in this study to estimate the impact each have on educational achievement.

The first variable, expenditures per pupil, is expected to have a positive relationship with

educational achievement. The next variable, student-teacher ratio, is expected to have a negative

relationship. Teacher salary is expected to have a positive relationship with educational

achievement, while the location of the school is expected to affect it also. If a school is located in

an urban district, achievement is expected to be less than if a school is in a rural district. The next

variable examined is the percentage of poor in the school district, which is expected to have a

negative relationship with educational achievement. Lastly, the percentage of students taking the

ACT is expected to have a positive relationship.

Empirical Analysis

The purpose of this study is to investigate the determinants of educational achievement.

The hypothesis to be tested is that the amount of expenditures per pupil is the main determinant

in educational achievement. An increased amount of expenditures per pupil should result in an

increase educational achievement.

The regression equation to be estimated in this section is:

+

ACHIEVEMENT is defined as the average ACT score in a district, FUND is the amount of

expenditures per pupil, RATIO is the student-teacher ratio, SAL is the average teacher salary,

LOC is whether the school district is in an urban or rural area, POOR is the percentage below the

poverty line, and %ACT is the percentage of students taking the ACT exam.

As funding increases, schools will be able to hire better teachers and purchase higher-

quality materials for students. Schools with increased funding will also have the ability to pursue

any other necessary activity in order to educate students. The expected sign of the funding

coefficient (β1) is positive.

The coefficient on the student-teacher ratio variable, β2, is expected to have a negative

sign. When the student-teacher ratio increases, achievement is expected to decrease. As class size

increases, individual students are no longer the primary focus of the teacher. With a smaller class

size, a teacher can devote more time to each student, increasing educational achievement.

The expected sign of the teacher salary coefficient (β3) is expected to be positive. As

average teacher salary increases, teachers’ attitudes toward their job will become more positive.

A student who has a teacher with a positive attitude will learn more than they would if they had a

teacher with a negative attitude.

The location of a school is categorized as either rural or urban. Schools located in an

urban district are more likely to be overpopulated, while schools located in a rural district are

less likely to be overpopulated. Urban areas are more likely to have a high crime rate, which can

lead to an increased number of gangs, lowering the educational achievement of students in the

area. A dummy variable is assigned, with 0 being rural and 1 being urban.

The expected sign of the poor coefficient, β5, is negative. This is a proxy for the

educational achievement of adults in the area. Students in poor households are less likely to

receive help from adults with regards to their schoolwork. As the percentage of the population

below the poverty line increases, educational achievement is expected to decrease.

When students prepare to continue on to college, they are more likely to have achieved

more in school than those who are not planning on continuing their education. As the percentage

of students taking the ACT exam increases, educational achievement is expected too, also. The

expected sign of the %ACT coefficient, β6, is positive.

The above regression equation will be estimated using data on a sample of 38 school

districts in West Virginia, Virginia, and Maryland after 2 outliers were found in the data and had

to be removed. The districts were randomly chosen from the website www.schooldatadirect.org.

The dependent variable, ACHIEVEMENT, is the average ACT score for the district as reported

on the website. Student-teacher ratio (RATIO), expenditures per student (FUND), and the

percentage taking the ACT exam (%ACT) were also taken from this website. Teacher salary,

SAL, is measured by the average teacher salary for a school district. This was found on the West

Virginia, Virginia, and Maryland department of education websites. All salary data was recorded

for 2007. All data for the location variable, LOC, was found on the Economic Research Service

United States Department of Agriculture website. This data was recorded for 2004 and counties

were classified as either metropolitan or non-metropolitan. Counties which were classified as

metropolitan were classified with a dummy variable of 1 while non-metropolitan counties were

0. POOR is the percentage of the population in a county below the poverty line. This data was

taken from the U.S. Census Bureau and are recorded for 2007.

The regression equation was estimated using SPSS. The estimated regression equation is:

=18.217+.000 +.109 +2.265 +.208 +-.105* +-.008% (.616) (.746) (.374) (.460) (-2.225) (-.411)

The numbers in parentheses are the computed t-scores. Estimated coefficients that are

statistically significant at a 10 percent level of significance are starred (*). The coefficient of

multiple determination is .457, indicating that only 45.7 percent of the variation in the average

ACT score is explained by the estimated regression equation. The complete regression results

appear in Appendix 2.

As expected, the estimated coefficient on the POOR variable is negative and statistically

significant. Students living in poverty have less help at home than students living in a relatively

upscale neighborhood do. Also, with more poverty, crime is likely to be higher, which can cause

distractions for many students. As the percentage of citizens living in poverty increases,

educational achievement decreases by .105. POOR is the only variable hypothesized correctly.

The variable FUND, measuring expenditures per pupil, was found to be statistically

insignificant. The estimated coefficient was found to be .000, meaning it would take a substantial

increase in expenditures per pupil in order to affect the average ACT score of a student. The

estimated coefficient on the RATIO variable was expected to be negative, but was instead found

to be positive. According to the estimate, an increase in the student-teacher ratio would result in

an increase of .109 in the average ACT score, everything else constant. The estimated

coefficient for the SAL variable is positive, but insignificant. The location variable, LOC, was

also found to be insignificant. The percent taking the ACT, %ACT, was found to be insignificant

but negatively related. When the percentage of students taking the ACT exam increases, the

average ACT score decreases by .008 on average.

Summary

As expected, the estimated sign of the POOR coefficient was negative and statistically

significant. This was the only variable found to be statistically significant. The expected sign of

the FUND coefficient was positive; however, after running a regression, the variable was found

to be statistically insignificant while the coefficient was rounded to .000 in SPSS, showing that

expenditures per pupil has a negligent effect on educational achievement. The expected sign of

the RATIO coefficient was negative, but was found to be positive in the estimated regression

equation. The RATIO variable was also found to be statistically insignificant. Teacher salary,

location, and the percentage taking the ACT were all found to be statistically insignificant also,

with SALARY and LOC fulfilling expectations of coefficients with a positive sign while the

expected sign of the %ACT coefficient was positive and turned out to be negative.

Conclusion

The educational achievement of students should be of utmost importance to the country.

The debate, however, is how exactly do we improve a student’s educational achievement? After

reviewing literature to determine proper independent variables, six were determined to have an

effect on the level of educational achievement. With these variables, an education production

function was developed with the hypothesis that the main determinant of educational

achievement was the amount of funding a school receives. With the help of SPSS and multiple

data sources, this study found that the level of income in an area is the main determinant in

educational achievement. Therefore, the null hypothesis, the amount of funding a school receives

is not the main determinant of educational achievement, must be accepted. However, with only

38 samples from three states, this study did not have a very large sample size. Therefore, more

school districts and more variables should be used to further determine variables that effect

educational achievement. Another problem arose with the data for the percentage of students

taking the ACT. In many cases, very few students in Virginia and Maryland took the ACT

because the majority take the SAT exam. This caused the variable %ACT to effect educational

achievement negatively. Regardless, this study shows there are many variables that influence the

educational achievement of a student. One must wonder if all of those variables will ever be

found.

APPENDIX 1

DistrictACT Score Expenditures Ratio Salary Location Poor TakingACT

Alleghany 21.1 11038 11.6 44095 0 11.9 18Augusta 21.7 7844 11.8 43075 0 7.2 9.8Botetourt 21.8 8322 10.8 46561 1 6.2 10.8Campbell 20.2 7689 11.2 41324 1 11.6 11.5Charlotte 19.8 8198 10.7 40530 0 18.1 11.5Culpeper 19.9 8169 13.2 44565 0 8.3 4.4Fairfax 22.9 11909 12.3 60593 1 4.9 16.6Frederick 21.4 9012 10.5 45481 1 6.6 8.7Hanover 21.8 7802 11 44609 1 5.1 13.6Isle of Wight 19.6 8488 13.7 45989 1 8.3 10.1Louisa 20.5 8561 11.9 47347 1 9.7 22.1Mecklenburg 19.3 7790 10.4 40432 0 16 6.6Nelson 19.7 9930 9.6 42627 1 11.4 12Northumberland 19.2 8857 10.9 46644 0 13.6 17.4Pittsylvania 19.3 7527 11.2 41202 1 12.1 8Prince George 20.9 7833 12.6 45720 1 9.3 6.9Rockingham 22.5 8268 11.3 43154 1 8.3 8.9Smyth 22.6 8195 10.8 36969 0 17.1 5.2Wythe 20.3 8413 11.3 41164 0 12.2 3.5Boone 20.1 9539 17.3 42922 1 18.2 53.6Calhoun 20.3 9061 17.1 40447 0 22.1 40.8Gilmer 20.5 8988 16.5 40149 0 22.8 54.1Hancock 21.7 8504 18.9 43400 1 12.7 55.7Jefferson 21.3 7895 17.3 40437 1 8.3 46.7Logan 19.8 8185 17.2 42000 0 22.2 52.6McDowell 17.8 9449 17.5 42263 0 34.7 41.2Monongalia 22 8339 16.1 42229 1 16.4 64.7Ohio 20.6 9139 16.4 43860 1 16.9 52.4Preston 20.5 7592 18.1 41863 1 16.5 60.3Ritchie 19.5 8699 17.1 42742 0 17.1 66Tucker 19.2 8523 17.5 40961 0 16.4 68.2Webster 19 8682 16 40713 0 25.2 52.6Wyoming 20.2 9221 16.4 42879 0 23.5 45.8Baltimore 20.7 9865 14.3 57639 1 7.6 6.6Cecil 23.4 9126 14.4 53406 1 9.3 1.1Garrett 22.5 10019 12.7 55083 0 12.9 4.1Montgomery 23.6 12255 14.3 70011 1 5.1 15.9Worcester 21.1 11856 12.2 57361 0 9.2 7.3

APPENDIX 2 Regression

Variables Entered/Removedb

ModelVariables Entered

Variables Removed Method

1 takingACT, Location, Expenditures, Poor, Salary, Ratioa

. Enter

a. All requested variables entered.

b. Dependent Variable: ACTscore

Model Summary

Model R R SquareAdjusted R

SquareStd. Error of the Estimate

1 .673a .452 .346 1.07009

a. Predictors: (Constant), takingACT, Location, Expenditures, Poor, Salary, Ratio

ANOVAb

ModelSum of Squares df Mean Square F Sig.

1 Regression 29.316 6 4.886 4.267 .003a

Residual 35.498 31 1.145

Total 64.814 37

a. Predictors: (Constant), takingACT, Location, Expenditures, Poor, Salary, Ratiob. Dependent Variable: ACTscore

Coefficientsa

Model Unstandardized Coefficients

Standardized Coefficients

t Sig.

Variables Entered/Removedb

ModelVariables Entered

Variables Removed Method

1 takingACT, Location, Expenditures, Poor, Salary, Ratioa

. Enter

B Std. Error Beta

1 (Constant) 18.217 1.889 9.646 .000

Expenditures .000 .000 .153 .616 .543

Ratio .109 .146 .232 .746 .461

Salary 2.265E-5 .000 .115 .374 .711

Location .208 .451 .079 .460 .649

Poor -.105 .047 -.525 -2.225 .033

takingACT -.008 .019 -.131 -.411 .684

a. Dependent Variable: ACTscore

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