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Measuring Between-School Segregationin an Open Enrollment System: The Caseof Rio de JaneiroTiago Lisboa Bartholo aa Federal University of Rio de Janeiro , Rio de Janeiro , BrazilPublished online: 05 Sep 2013.

To cite this article: Tiago Lisboa Bartholo (2013) Measuring Between-School Segregation in an OpenEnrollment System: The Case of Rio de Janeiro, Journal of School Choice: International Research andReform, 7:3, 353-371, DOI: 10.1080/15582159.2013.808937

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Journal of School Choice, 7:353–371, 2013Copyright © Taylor & Francis Group, LLCISSN: 1558-2159 print/1558-2167 onlineDOI: 10.1080/15582159.2013.808937

Measuring Between-School Segregationin an Open Enrollment System: The Case

of Rio de Janeiro

TIAGO LISBOA BARTHOLOFederal University of Rio de Janeiro, Rio de Janeiro, Brazil

Recent research in Rio de Janeiro public schools has brought tolight a “Hidden Quasi-Market” that combines purported freedom ofchoice for parents with school control over their pupil intake. Thearticle analyzes patterns of segregation among schools, from 2004to 2010, according to three indicators of potentially disadvan-taged pupils: Ethnic Background, Poverty, and Parents’ Education.Segregation was assessed utilizing the Dissimilarity Index and theSegregation Index. The segregation trends over time, using differ-ent pupil characteristics, show distinctive trajectories, which mightsuggest at least two different segregation processes. Initial find-ings reinforce the need to track segregation by multiple pupilcharacteristics.

KEYWORDS school segregation, life chance, poverty, parents’education, ethnicity

INTRODUCTION

This article’s central theme is the distribution of educational opportunities inRio de Janeiro Municipal Public Schools and how it relates to social inequalityin Brazil. It uses figures at school level for all Municipal Schools and presentstwo different indices of between-school segregation, the Dissimilarity Indexand the Segregation Index, using three different indicators related to poten-tially disadvantaged pupils: (a) Poverty, (b) Parents’ Education, and (c) EthnicBackground.

Address correspondence to Tiago Lisboa Bartholo, Rua Viúva Lacerda 128, Apartment102, Humaitá, Rio de Janeiro 22261-050, Brazil. E-mail: tiagobartholo@gmail.com

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Segregation here is referred to as the product of an uneven distribu-tion of pupils with similar characteristics across a school system. During the1950s, several indices of residential segregation were created, initially con-cerned with the racial division in the United States, later to be extended toother fields, including the public school admission patterns. Social segrega-tion among schools has to be considered as a consequence of residentialsegregation, admission policies, and parental choice, which are presumed tocorrelate with social, economic, and cultural isolation (Harris, 2012).

The debate about the social impact of clustering pupils has differentcharacteristics depending on the country of interest. In the United States, forexample, the main concern has been with segregation by Ethnic Background,more specifically with Black Pupils (Goldhaber, 1999; Hill & Lake, 2010;Sikkink & Emerson, 2008; Saporito, 2003). European researchers from differ-ent countries, such as England or The Netherlands, have been more focusedon segregation by First (or Home) Language and Poverty (Gorard, Taylor, &Fitz 2003; Gramberg, 1998). In Brazil, the concern with school segregationis not recent, although previous studies always used to analyze a very smallnumber of schools, mainly focused on clustering by Poverty (Consorte, 1959;Costa, 2008).

Understanding segregation levels and how they occur are important forfuture public policies aiming to achieve more equitable educational systems.Clustering pupils that live in shantytowns or those from poorer, less edu-cated, or Black families, in a subset of schools has possible implications fortheir future academic aspirations and outcomes, such as attainment, subse-quent compulsory participation and the academic performance of the mostdisadvantaged groups (Gorard & Smith, 2010; Gorard, See, & Davies, 2011).It is also an affront.

The contribution of this article is to measure, for the first time, the seg-regation levels considering all the Rio de Janeiro municipal public schools.Previous studies had analyzed a limited number of schools, in small areas,which did not allow any extrapolation of results that would reflect the realityof the public network. Using the segregation indices, future analyses willestimate the “school mix effect” (Gorard, 2006), trying to clarify one of thekey questions in the educational field: “After all, does it matter who goes toschool with whom?”

Despite the fact that there is very little evidence that clustering pupilswith similar characteristics produces any overall results for the school sys-tem (Gorard, 2009a; Haahr, Nielsen, Hansen, & Jakobsen, 2005), it is notuncommon to find educational policies that select pupils by their abilities(tracking systems), from a very early age, thus creating a segregated system.Very often, the practical result of such policies is an educational system thatreproduces social inequalities (high correlation between social backgroundand academic achievement), with pupils from different social backgroundsattending separate schools. Clustering pupils with similar characteristics is an

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important wider phenomenon, also observed in educational systems that donot formally implement tracking policies.

In the case of Rio de Janeiro, despite the fact that policy-makers didnot implement formal tracking or school choice policies, previous researchhas shown strong parental pressure on the most prestigious schools andalso calls for different pupil selection strategies and criteria on the part ofthe educational bureaucracy. This singular scenario, combining purportedfreedom of parental choice with school control over their pupil intake, hasbeen termed “Hidden-Quasi-Market” (Bruel & Bartholo, 2012; Costa, 2008;Costa & Koslinski, 2011).

The Rio de Janeiro public school enrollment legislation allows parentsto choose any school. Nevertheless, the possibility to choose does not guar-antee that the authorities will grant the family’s first option. The legislationraises many questions. For example, what happens to schools with oversub-scription? Who decides who gets in or is left out in such a situation? After fill-ing all the vacancies, what will be the criteria to determine pupil allocation tothe “school shifts” (morning, afternoon, or night)? Lack of transparency mighttrigger two distinctive, but complementary, phenomena. On the one hand,members of the educational bureaucracy actively select pupils based on dif-ferent criteria. On the other, parents use different strategies to try to increasetheir child’s chances of being admitted to the most prestigious public schools.

This article is divided into six sections, including this introduction.Section two presents a brief debate about the recent concern about stratifi-cation within public schools in Brazil, and the misuse of the concept “schoolchoice” in the public network. Section three formally presents the conceptof between-school segregation and how it should be measured. Section fourpresents the database provided by the Rio de Janeiro Municipal EducationalDepartment, and the different attempts to deal with the problem of miss-ing data. Section five presents the Segregation Index and the DissimilarityIndex considering all public schools. Section six summarizes the findingsand highlights future use of the Segregation Index for educational policy.

SCHOOL CHOICE IN THE BRAZILIAN PUBLICSYSTEM: MISUSE OF CONCEPTS

The educational system in this country is currently divided into three differentschooling levels of: (a) Preschool–children aged 4–5, not compulsory; (b)Fundamental Education–compulsory, catering for pupils aged 6–14, usuallydivided into 5 initial grades (first segment) and 4 upper grades (secondsegment); (c) High School–not compulsory, for pupils aged 15–17.

Rio de Janeiro city has the largest public school network in Brazil. Thereare around 1,300 schools providing Preschool and Fundamental Education.This article focuses on the only mandatory educational level, Fundamental

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School, analyzing the total population—around 700,000 pupils in a total of900 schools. Despite the fact that there is data available about Preschool, theywill not be included in this analysis, mainly because this type of educationhas not reached universal attendance.

It is also important to mention that around 18% of the pupils in thewhole country are enrolled in private schools. In Rio de Janeiro, this numberis even higher, reaching 25%. Unfortunately, there is no data available forthe private schools to allow a more robust analysis considering the entirepupil population in Fundamental Education. Because the private schools aremainly frequented by the middle class and elite, it is reasonable to assumethat the segregation levels presented in this article are underestimated. Thereason is simple. The data available deals with a more homogeneous part ofthe population and, therefore, it is most likely that the part of the variationthat would influence the indices used to measure segregation is left out ofthe analysis.

The educational system in Brazil has experienced important changessince the beginning of the 1990s. Possibly, the two most significant achieve-ments have been the universal attendance in Fundamental Education andthe growth in the number of grades completed. Nonetheless, another impor-tant accomplishment has been the establishment of a National Pupil Census,along with a National Assessment System of pupil proficiency in Mathematicsand Language (with standardized tests). For the first time, researchers haveaccess to reliable comparable data to analyze the overall levels of attainmentfor both the private and public sectors. Along with these changes, Brazil hasalso started to participate in international assessment tests (like PISA) thatallow international comparison (Veloso, 2009).

All these figures highlight two problems: an “old” one (widely dis-cussed in previous research) and perhaps a “new” one. The achievementgap between the private and public sector was clear in the standardizedtests. Good private schools in Brazil have outcomes comparable to those ofany of the high performance schools in the top ranking countries in PISA.However, the overall level in the public sector is among the lowest, not onlyin comparison to South America as a whole, but also to any other develop-ing country. Brazil lies at the bottom in any international assessment, whichsuggests not only failure of the public schools, but also high levels of socialstratification.

Nonetheless, the standardized national tests have allowed the researcherto observe an underestimated public sector problem. Analyzing only pub-lic schools, it was also possible to observe big differences in their overalloutcomes, which triggered new interest in understanding why some pub-lic schools were better than others. Once again, as observed previously inthe public versus private sector dichotomy, a major part of the variation inthe overall achievement levels in public schools could be explained by their

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pupil intakes. Immediately, researchers started to address two complemen-tary questions: (a) How do parents choose their child’s school? (b) What isthe role of the educational legislation in the overall segregation levels?

Most of the research conducted so far has been in major cities like Riode Janeiro, São Paulo, and Belo Horizonte, all urban areas with large, well-established public networks. It is important to note that in Brazil, each Statehas autonomy to legislate regarding its enrollment policies, which makescomparison more complex.

Recent research regarding stratification in public schools in Rio deJaneiro and São Paulo has used the concept of School Choice and Quasi-Markets in an attempt to analyze the distribution of educational opportunitiesand different school segregation patterns (Costa & Koslinski, 2011, 2012).Despite the fact that there are no formal School Choice policies in Brazil,some cities present specific legislation that, in theory, allows parents to exer-cise choice (open enrollment). Some additional policies, such as free publictransport for pupils, potentially increase the possibility of attending a schoolfar from home. The results suggest two key elements related to school seg-regation: (a) first enrollment policies; (b) unfettered movement of pupilsamong schools (Bruel & Bartholo, 2012).

Admission policies that combine social selection with patrimonialisticpractices by civil servants have been analyzed in Rio de Janeiro since 1950(Consorte, 1959), and, even today, researchers are trying to understand differ-ent pupil mobility patterns among public schools (Costa & Koslinski, 2008).Findings by Bruel and Bartholo (2012), analyzing the transition between thefirst (1st–5th grade) and second (6th–9th grade) segments, of a limited num-ber of pupils in Rio de Janeiro public schools, suggest that variables, suchas, Parents’ Education and pupils’ Ethnic Background have an impact on thechances of access to the most prestigious schools. The same study showsthat the previous school in the first segment is the most important variable topredict access to a high performance school (good reputation) in the secondsegment.

Empirical analyses considering large datasets were interpreted with thetheoretical framework of School Choice. The concept of “Hidden-Quasi-Markets” was created to characterize Rio de Janeiro educational policy(Costa & Koslinski, 2011). However, it is important to make some commentsabout the limitations of the use of school choice theory to characterize edu-cational systems that do not have per pupil funding and, most importantly,the fact that the school staff (represented by the school principal) decidewhose preference (parental choice) will be honored.

The Rio de Janeiro educational legislation allows parents to chooseany school. There is a specific calendar with key dates for first enrollment,confirmation of school registration and formal requests to change school.Recently, the Educational Department has provided information about theperformance of all public schools in an attempt to better inform parents

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(schools “performance” table). So far, there is no solid evidence of howparents are using this new information in their decision-making process.

If it is true that parents purportedly exercise freedom of choice, it is alsocrucial to highlight that school staff (usually represented by the principal)have control over their intake, especially in the case of oversubscription.Because schools have different reputations, it is more likely that oversub-scription occurs mainly in two scenarios: (a) highly dense regions with alimited supply of public schools. Just a few areas of the city could be put intothis category of Fundamental and High School education (Alves, Lange, &Bonamino, 2010); (b) schools that have a good reputation–so-called highperformance (Bruel & Bartholo, 2012).

Logic suggests that schools with better reputations would, on average,present higher oversubscription rates and, therefore, could potentially selecttheir pupils. A vicious circle where: (a) school intakes are correlated to schoolreputation, and (b) the potential to select pupils is also correlated to schoolreputation.

The policy of not funding schools according to enrollment does notstimulate schools to compete for pupils. The only type of funding truly linkedto each pupil is the money for lunch, to which all pupils in public schoolsare entitled. Any other resources are not directly linked to the number ofpupils enrolled. This increases the power of the educational staff to simplydeny access to potentially disadvantaged pupils, because there will be noreal consequences—including school funding. Table 1 presents a summarycomparing the Rio de Janeiro educational legislation with that of other citiesthat formally implement school choice policies.

Future research should reconsider the use of concepts, such as SchoolChoice or Hidden-Quasi-Markets to characterize the educational system inRio de Janeiro or São Paulo. It could be argued that it is the absence of aschool market, and not the existence of one, that characterizes such educa-tional systems. Evidence suggests that, in the case of Rio de Janeiro, familiescompete for schools with good reputations, but schools do not seem tocompete for pupils. In reality, the data indicates more of a collaboration pro-cess, where schools “exchange pupils” based on specific criteria (Costa &

TABLE 1 Comparison of Educational Legislation in Rio de Janeiroand Formal School Choice Policy

Rio de JaneiroPolicy

Formal SchoolChoice Policy

Open enrollment X XSchools select pupils XInformation about quality

of schoolsX X

Price mechanism(funding per capita)

X

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Koslinski, 2012). Perhaps, the concept of “Market Ecology” would be morehelpful in characterizing a system where collaboration among schools seemsto be more prevalent than competition (Yair, 1996).

WHAT IS SEGREGATION AND HOW SHOULDWE MEASURE IT?

The concept of segregation is widely used both in academia, more specif-ically in the social sciences, and in publications in general newspapers,magazines, books. However, its popularity, instead of making the mean-ing of the concept clearer, actually has the opposite effect, a multiplicity ofdefinitions and uses.

Massey, White, and Phua (1996) identify five dimensions of segre-gation: evenness, exposure, concentration, centralization, and clustering.In this research, the concepts of interest are: evenness and exposure.My segregation measure is the uneven distribution of pupils with similarcharacteristics across different schools. For the purposes of this study, allthe variables/characteristics of the pupils suggest potentially disadvantagedgroups, such as pupils living in poverty. The reason for this is simple. In mostsocial sciences, segregation has become almost synonymous with stratifica-tion, and the main concern of researchers and policymakers is to producevaluable information in an attempt to reduce social inequalities. It makesno sense to track segregation in the privileged group, because the mainobjective is to make the educational system fairer and more equitable.

Segregation indices are used, therefore, to measure how various socialor ethnic groups of people are distributed across a study region, andwhether there is evidence or not that they are separated. In themselves,the indices are not restricted to any singular view of the process whichled to the separation, or to whether those separations should necessarilybe prevented. (Harris, 2012, p. 671)

One simple example provided by Gorard and Taylor (2002) might helpclarify the concept of segregation. Imagine a school system with two schoolsand 200 pupils divided into equal numbers between them. If school “A” hadonly boys (100 pupils) and school “B” only girls (also 100), it would bepossible to argue that this school system had total segregation by Gender.It is important to note that, if 20 boys from school “A” simply dropped outof school, we would still have total segregation by Gender. However, if anypupil transfers between schools “A” and “B” occurred, then the segregationlevels would decline. Put another way, the index that measures segregationshould be able to take account of pupil transfers, as described in the lastexample.

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Which indices are available, and how are they related? Because theconcept of segregation has been under debate in the social sciences, it isno surprise that many types of indices have been created to measure thesame phenomenon. Thus, it is incorrect to state that a specific index is sim-ply wrong or does not detect segregation. Nevertheless, it is important tohighlight some desirable properties that such an index should have in orderto provide useful information for public policies. This is not an exhaustivereview of all segregation indices, but instead, an attempt to present the gen-eral debate and inform the reader about the options taken by the authors inthis article.

Harris (2012) reinforces that a nonexhaustive typology of indices fallsinto two types. The first measures segregation as a function of the differ-ence between each individual observation and some average or expectedvalue in a region. Here it is possible to include the Dissimilarity Index (D)(Duncan & Duncan, 1955) and the Segregation Index (Gorard et al., 2003;Gorard & Taylor, 2002; Gorard, 2009a), also denominated Gorard Segregation(GS). The second type is a function of the product of the observed andexpected value. The Isolation Index (Bell, 1954; Shevky & Shevky, 1949) isan example. “Whereas the first type of index is comparative, the second isprobabilistic” (Harris, 2012, p. 671).

In this article, the main element of segregation, as previously mentioned,is evenness. Therefore, the index must be a measure of the uneven distri-bution of pupils with shared characteristics across different schools. Becausethere are many indices available in the “market,” it is important that eachresearcher makes a cost-benefit calculation (strengths and weaknesses ofeach indicator) before making his decision. Gorard (2009a) highlights fourdesirable properties that such indices must present, regardless of researchfield:

1) organisationally invariant, such that if a school is broken into two, or iftwo schools merge, with the same proportion of FSM [Free School Meal]pupils in all, then the value of the index remains the same; 2) size orscale invariant, such that if the number of both FSM and non-FSM pupilsis multiplied by a constant in all schools, then the value of the indexremains the same; 3) compositionally invariant, such that if the numberof FSM pupils is multiplied by a constant in all schools, then the valueof the index remains the same (equivalent to the margin-free criterion insex segregation analysis) and; 4) affected by transfers, such that if an FSMpupil moves from a school with more FSM pupils to a school with less,then the value of the index goes down. (Gorard, 2009a, p. 644)

One of the main issues debated by researchers is that the index mustnot change just by a simple shift in the numbers of potentially disadvantaged

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pupils in a specific region. This is a crucial element, especially in situationswhere the researcher is interested in segregation patterns over time. Becauseit is very likely that the number of disadvantaged pupils will fluctuate overthe years, it is important to have an index that does not change just becauseof a simple shift in the total number of pupils in the group of interest.

Gorard and Taylor (2002) make a detailed analysis comparing D and GS,highlighting that the first is “weakly” composition invariant and the second is“strongly” composition invariant. On the other hand, the authors emphasizethat GS is not symmetric, meaning that, if the index is calculated inversely,with the privileged group as the focus group, then the answer given by theindex is different, but not contradictory. It could be argued that the lack ofsymmetry is a smaller problem, if the main/only concern of a segregationindex is the disadvantaged group.

Because this is the first attempt to measure between-school segregationinvolving all the Rio de Janeiro municipal public schools, the article presentsD and GS figures, the two most popular segregation indicators. A full debateabout the properties of both indicators can be seen in Gorard and Taylor(2002). Here we will present the formulas and specify the analytical strategiesfor the article.

Formally, D can be described as the formula above, where: (a) “Fi” isthe number of potentially disadvantaged pupils in school “I,” where “i” variesfrom 1 to the number of schools; (b) “F” is the total number of potentiallydisadvantaged pupils in the Rio de Janeiro public municipal schools; (c)“Ni” is the total number of nondisadvantaged pupils in school “I,” where“i” varies from 1 to the number of schools; (d) “N” is the total number ofnondisadvantaged pupils in the Rio de Janeiro public municipal schools.

D = 0.5∗{∑ ∣∣∣Fi/F − Ni/N

∣∣∣}

Formally, GS can be described as the formula above, where: (a) “Fi” isthe number of potentially disadvantaged pupils in school “I,” where “i” variesfrom 1 to the number of schools; (b) “F” is the total number of potentiallydisadvantaged pupils in the Rio de Janeiro public municipal schools; (c) “Ti”is the total number of pupils in school “I,” where “i” varies from 1 to thenumber of schools; and (d) “T” is the total number of pupils in the Rio deJaneiro public municipal schools.

GS = 0.5∗{∑ ∣∣∣Fi/F − Ti/T

∣∣∣}

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DATABASE AND ITS LIMITATIONS

The article presents data provided by the Rio de Janeiro EducationalDepartment for all the public municipal schools, from 2004 to 2010. Thenetwork is composed of 1,300 schools, of which 900 provide FundamentalEducation. The population of pupils is about 700,000 per year.

The variables selected for assessing segregation are widely known inBrazil, as well as in other countries, to be correlated with educational attain-ment. For pupils’ Ethnic Backgrounds, the indices were calculated for twodistinctive potentially disadvantaged groups: (a) Non-White Pupils, and (b)Black Pupils.

Another variable used to measure between-school segregation wasParents’ Education. Originally, this variable was an ordinal variable, with fivepossible outcomes: (a) illiterate, (b) did not complete fundamental school–first nine years of compulsory school, (c) finished fundamental school, (d)finished high school–first 12 years of schooling, and (e) finished higher edu-cation. In order to construct the index, this variable was summarized, creatingtwo potentially disadvantaged groups: (a) parents who did not finish funda-mental school (EducFS), and (b) parents who did not finish high school(EducHS).

The third variable used to assess segregation is Pupils Living in Poverty(NIS–Número de Inscrição Social [Social Registration No.]). Since 1990, theFederal Government, along with State and Municipal administrations, haveimplemented a number of social policies in an attempt to diminish Poverty.The income transfer policies have made it possible, through a Single NationalRegistry, to identify the families that are receiving this benefit.

The missing data for all three variables were a real challenge. In thelast 4 years (2007–2010), the database has presented better records for vari-ables, such as Ethnic Background and Parents’ Education. The proportion ofmissing data in these two variables declines, as Table 2 indicates:

Missing data in any research is a challenge, mainly because it can inter-fere with the results and lead the researcher to make wrong interpretations.The results presented in Table 1 suggest that the missing data is not randomly

TABLE 2 Proportion of Missing Data and Potentially Disadvantaged Pupil for EthnicBackground and Parents’ Education

2004 2005 2006 2007 2008 2009 2010

Proport Miss Data Ethnic Background 0.24 0.13 0.06 0.05 0.04 0.04 0.04Proport Black Pupils 0.10 0.11 0.12 0.12 0.12 0.12 0.11Proport Non-White Pupils 0.50 0.57 0.60 0.61 0.61 0.61 0.60Proport Miss Data Parents’ Education 0.20 0.18 0.16 0.13 0.12 0.11 0.11Proport Parents EducFS 0.19 0.20 0.21 0.23 0.23 0.24 0.23Proport Parents EducHS 0.57 0.58 0.59 0.60 0.60 0.60 0.59

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distributed, with a higher proportion of disadvantaged pupils among the“missing group.” In other words, as data improve, it becomes more likelythat they are affected by the proportion of disadvantaged pupils. There isempirical evidence that, when indicators of Poverty rise (in economic crises,for example) the segregation levels tend to decline, as a kind of more evendistribution of Poverty. It is also true that, in an economic boom, with adecline in the proportion of poor families, the index tends to rise (Gorard,Taylor, & Fitz, 2003).

In order to try to cope with the missing data, two different strategieswere used to recalculate GS, depending on the variable. For pupils’ EthnicBackground, GS was calculated considering: (a) GS Black Pupil 1/GS Non-White 1–total number of pupils in school “i” equal to the total number ofpupils indicated in the database–including missing data cases/pupils; (b) GSBlack Pupil 2/GS Non-White 2–total number of pupils in school “i” is equalto the sum of all pupils that are not missing from the variable. Example: totalnumber of pupils = sum of all White and all non-White pupils.

For Parents’ Education, two different strategies were used to calculateGS: (a) GS EducFS 1–total number of pupils in School “i” is equal to thetotal number of pupils indicated in the database–including missing datacases/pupils; (b) GS EducFS 2–total number of pupils in school “i” is equalto the sum of all pupils that are not missing from the variable. Example: totalnumber of pupils = sum of all pupils whose parents finished fundamentalschool and all pupils whose parents did not finish fundamental school.

The third variable, pupils living in Poverty, presents a distinct problemwhen compared to the other two. Here the issue is most likely related tosubnotification. As the quality of data improves the proportion of poor fam-ilies increases (2004–2008). In the last 3 years, 2008–2010, the curve haschanged, most probably reflecting economic growth. In this variable, theinformation is recorded in two columns: one indicates the parent’s NIS num-ber and the second, the pupil’s NIS number. If the database had no problemsregarding the records, both parents and pupils should have the numbers,but this is not true. For this reason, GS was calculated in two ways: (a)NIS_SUM–pupil’s family was considered poor only when both the pupil andhis parents had NIS; (b) NIS_MAX–pupil’s family was considered poor whenhis family and/or the pupil had NIS. This second measure was an attempt tocope with the subnotification problem. Table 3 summarizes the proportionof disadvantaged pupils for each Poverty measure.

TABLE 3 Proportion of Pupils Living in Poverty

2004 2005 2006 2007 2008 2009 2010

NIS_Sum 0.19 0.22 0.24 0.26 0.26 0.25 0.23NIS_Max 0.25 0.27 0.31 0.33 0.33 0.33 0.32

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None of the different strategies to present the segregation indices solvesthe problem of missing data. In reality, there is no definitive solution becausethe information is simply not available. Nonetheless, the different GS calcu-lations (see Table 6) and the possibility of comparing the data over the yearsallows the researcher to make useful interpretations of the data. The realdanger is not the missing data itself, but the fact that some studies simplyignore the problem. Virtually all longitudinal studies that use secondary dataface similar problems, and the real question is not if there will be miss-ing data (because most likely there will be), but how researchers approachthe problem and take these issues into consideration in their interpretations(Gorard, 2009b; Yorke, 2011).

BETWEEN-SCHOOL SEGREGATION: SEGREGATION INDEX,AND DISSIMILARITY INDEX RESULTS

Table 4 presents the results of GS and D for three different variables relatedto potentially disadvantaged pupils. As expected, the two indices presentsimilar trends, suggesting that both are capturing the same phenomenon.Measuring segregation in the Rio de Janeiro municipal public schools usingGS or D is a little different from measuring temperature using the Celsius orFahrenheit scales (Gorard & Taylor, 2002). In the end, both indicators willgive similar answers. What changes is the interpretation: GS indicates theexact proportion of disadvantaged pupils who would have to change schoolsfor there to be no segregation; D represents the proportion of one group orother that would have to move, if there were no segregation (Gorard &Cheng, 2011; Gorard & Taylor, 2002).

Another way of looking at the same figures is to run correlationsbetween GS and D with all the indicators. Table 5 shows high scores forthe correlations in all variables, with the exception of “Non-White Pupil.”

TABLE 4 Segregation Index (%) and Dissimilarity Index (%) for All Indicators of PotentiallyDisadvantaged Pupils

2004 2005 2006 2007 2008 2009 2010

GS Black Pupil 18.5 17.5 17 16 15.5 15.5 15D Black Pupil 18.5 19 18.5 18 17.5 17.5 17,5GS Non-White Pupil 11.5 9 7.5 7 6.5 6.5 6.5D Non-White Pupil 17 17.5 17.5 17 16.5 16.5 16GS Parents’ EducFS 30 28 26 24.5 23 21.5 20.5D Parents’ EducFS 35 34.5 33 32 30.5 29 27.5GS Parents’ EducHS 14.5 13 12 11 10 10 9.5D Parents’ EducHS 27 27 27 26.5 26.5 26 26GS NIS_SUM 27 23 19.5 18 18.5 19 20D NIS_SUM 33 29 26 25 25 26 26

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TABLE 5 Correlation Between GS and D for All Indicators of Potentially Disadvantaged Pupils

Indices GS and D Black Pupil Non-White Pupil EducFS EducHS NIS

Correlation 0,87 0,48 0,98 0,87 1.0

0%

5%

10%

15%

20%

25%

30%

35%

40%

2004 2005 2006 2007 2008 2009 2010

GS NIS

GS Black Pupil

GS Non White

GS Educ FS

GS Educ HS

FIGURE 1 Segregation index trends for all available indicators of potentially disadvantagedpupils (color figure available online).

One possible explanation for this odd result might be changes in the pro-portion of missing data over the years, combined with the overall proportionof disadvantaged groups in the population. Apparently, when the proportionof missing data is higher (2004–2006), GS and D present differences in thetrends for “Non-White Pupil,” although, as data has improved, both indica-tors have shown a small decline in segregation levels (2006–2010). Futureinvestigations will try to explain the difference observed in this particularvariable with complementary empirical tests.

Despite the small difference observed in one variable, the data con-firmed that GS and D give similar answers. The following results will onlyshow figures for GS to enable smaller, more concise tables and figures, in anattempt to make interpretations easier.

So what are the segregation trends? What are the possible interpretationsfor the data presented so far? Figure 1 presents five lines for all indicatorsusing GS. The variables that measure Parents’ Education, suggest a declineof the index, more intense in the variable that measures parents who did notfinish fundamental school (GS EducFS). The variable that measures pupil’sEthnic Background show a small decline over the period. What seems ofinterest is the difference in the overall segregation level comparing Blackand non-White pupils. Black pupils seem to be more segregated than thenon-White. One possible interpretation is that the proportion of Black pupilsis lower (see Table 2) and might influence GS. An alternative explanation is

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TABLE 6 Segregation Index (%) for All Indicators of Potentially Disadvantaged Pupils

2004 2005 2006 2007 2008 2009 2010

GS Non-White 1 11.5 9 7.5 7 6.5 6.5 6.5GS Non-White 2 5.5 5.5 5.5 5.5 5.5 5.5 5.5GS Black Pupil 1 18.5 17.5 17 16 15.5 15.5 15GS Black Pupil 2 16 16.5 16 16 15.5 15.5 15.5GS EducFS 1 30 28 26 24,5 23 21.5 20.5GS EducFS 2 27 26 24,5 23,5 22,5 21 20GS NIS SUM 27 23 19,5 18 18,5 19 20GS NIS MAX 25 21,5 18 16 16 16 16

that members of the educational bureaucracy deliberately deny Black pupilsaccess to specific public schools.

The trend that measures pupils Living in Poverty suggest a distinctivepattern, with a decline in the first three years (2004–2006) and, subsequently,a gradual increase as of 2007. One possible explanation for the decline inthe overall segregation levels in the first three years, observed in all vari-ables, is the change in the proportion of missing data. As Table 2 shows, themissing data have declined over the years, and the proportion of disadvan-taged pupils tends to grow—the only exception is Poverty, which shows aproportional decline in 2009 and 2010.

In order to test the influence of missing data in the GS results, allvariables were calculated in different ways, in an attempt to cope withthe problem–Table 6. The characteristics of each summary variable forall indicators were described in the previous section, “Database and itslimitations.”

What we can infer from the data is: (a) missing data is most proba-bly not randomly distributed, with a higher concentration in the potentiallydisadvantaged pupils; (b) missing data seems to artificially inflate the seg-regation index, giving the wrong impression that the segregation levels aredeclining for all indicators in the first 4 years (2004–2007).

Another way of looking at the data presented in Table 6 is to present justthe percentage difference when comparing different time periods. Table 7shows if the GS, after a specific period of time, has declined or increased.Because of the apparent influence of the missing data on the trends, twodifferent periods were calculated: (a) 2004–2010, and (b) 2007–2010. Thetwo periods were chosen based on the proportion of missing data presentedpreviously in Table 2.

When comparing the columns in Table 7, it is possible to observe dif-ferences in the interpretation of the data. Segregation by Parents’ Educationsuggests, in both analyses, a decline over the period. However, segregationby pupils living in Poverty, do not allow the same interpretation. The vari-able “GS NIS SUM,” the more conservative measure, suggests a small, butgradual, increase (total of 11%) for the last 4 years–2007–2010. The other

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TABLE 7 Segregation Index–Percentage Difference (2004–2010 and2007–2010) for All Indicators of Potentially Disadvantaged Pupils

2004–2010 % Difference 2007–2010 % Difference

GS Non-White 1 −43 −7GS Non-White 2 — —GS Black Pupil 1 −19 −6GS Black Pupil 2 −3 −3GS EducFS 1 −32 −16GS EducFS 2 −24 −15GS NIS SUM −24 +11GS NIS MAX −36 —

measure of Poverty, “GS NIS MAX,” indicates stability over the same periodof time. The last variable, Ethnic Background, suggests more stability, espe-cially in the variable “GS non-White 2,” which tries to cope with the problemof missing data. The other measure of Ethnic Background, GS Black Pupil,shows a very small decline, which hardly convinces a real change occurredin the period.

Gorard and Cheng (2011), analyzing public secondary schools inEngland, conclude that there are at least two distinctive kinds of pupilsegregation.

[. . .] the clustering of pupils with special needs but no statement is a sep-arate phenomenon from everything else. Whatever causes it, and causesit to change over time or vary between places, appears to be largelyunrelated to what causes segregation by poverty, language, and ethnic-ity. In fact, the trend over time seems to be a simple reflection of thegrowth in the number of pupils deemed to have such special needs [. . .].(Gorard & Cheng, 2011, p. 338)

Jacobs (2011), addressed the same question analyzing the District ofColumbia, and found a similar answer measuring racial, economic, and lin-guistic segregation for Charter public schools. Despite the limitations of thecomparison between the initial findings of this article and the analyses madein public schools in England and the United States, the results so far corrobo-rate the argument that pupil segregation might not be one process (Gorard &Cheng, 2011; Jacobs, 2011). Identifying different causes of segregation canbe important for future policy, aiming to reach more equitable educationalsystems.

Currently in Brazil, the challenge is how to increase the overall level ofattainment and, at the same time, close the gap between the different groupsthat are at school. It is to be recalled that the universal attendance has onlyrecently been achieved and the “new group” that has entered schools arethe most disadvantaged. School segregation must be taken seriously because

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there is an increasing amount of evidence suggesting that clustering pupilswith similar characteristics can have an impact on how they are treatedat school, the quality of teaching, the overall levels of attainment, post-compulsory education and also an increasing association between academicachievement and socioeconomic status (EGGRES, 2005; Haarh et al., 2005).

Further investigations will run correlations and factor GS analyses withother variables, such as: proportion of disadvantaged pupils, economicgrowth, unemployment rates, demand and supply indices of schools, anda social development index for the region in which each school is situ-ated. These complementary analyses might give important insights into whatimpacts segregation in the Rio de Janeiro public municipal schools.

CONCLUSION

The article presents the first attempt to measure between-school segregationutilizing two indices of segregation (D and GS) considering the entire publicnetwork of a major Brazilian city. Future analyses will present complemen-tary data regarding the segregation levels for each educational authority (totalof 10) in Rio de Janeiro city. Clustering pupils with similar characteristics is awider phenomenon, and the segregation levels must be considered as a con-sequence not only of admission policies, but also of residential segregationand parental choice. One of the methodological challenges of this researchproject is to separate the effect of each of these factors in an attempt toprovide useful information for future policy.

The use of concepts such as School Choice, Quasi-Markets, or Hidden-Quasi-Markets should be treated with great caution by researchers analyzingthe public educational systems in Brazil. Lack of rigor and misconceptionmight lead to more confusion and unfruitful analysis (Merrifield, 2008) of thedistribution of educational opportunities. It could be argued that is the lackof a school market, and not the existence of one, that characterizes a schoolsystem, such as that in Rio de Janeiro or São Paulo. Evidence suggests that,in the case of Rio de Janeiro, families compete for schools with good repu-tations, but schools do not seem to compete for pupils (Costa & Koslinski,2012). The concept of “Market Ecology” could be more appropriate to under-stand what seems to be collaboration among schools, exchanging pupils ina nonrandom away (Yair, 1996).

Tables 2 and 3 present a descriptive analysis about the quality of thedata, with possible implications for future analyses. The proportion of poten-tially disadvantaged pupils and the proportion of missing data have differenttrends and are inversely proportional. It is most likely that the missing datais not randomly distributed, with a higher concentration in the potentiallydisadvantaged groups. One possible interpretation is that the missing data,more concentrated in the first three years (2004–2006), artificially inflate the

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GS, leading to the wrong impression that the segregation levels are declin-ing over the period (2004–2010). The different attempts to measure GS (seeTable 6) reinforce this concern and suggest that the segregation levels forEthnic Background and Poverty are not declining over the period underanalysis.

Both indicators, D and GS, essentially give a similar answer. The correla-tions in Table 4 indicate that future analyses can use one of the two and willcome to similar conclusions. The indices corroborate the findings of Gorardand Cheng (2011) and Gorard (2009a), the only exception being the vari-able “Non-White Pupil,” which shows a smaller coefficient. It is most likelythat this odd result is related to the quality of the data. As the proportion ofmissing data has declined over the years, the proportion of disadvantagedpupils has increased. These abrupt changes in the proportions of the disad-vantaged group might explain the small differences observed between D andGS. Further investigation, applying the concepts of “weak” and “strong” com-position invariant (Gorard & Taylor, 2002), will try to clarify the differencesobserved in complementary empirical tests.

The figures in Table 7 (patterns over time for GS) suggest at leasttwo different segregation processes happening at the same time. The GScalculations for EducFS1 and EducFS2 indicate a decline over the periods(2004–2010 and 2007–2010). All four calculations present negative values(see Table 7). However, GS for Poverty (NIS) tells a different story, espe-cially when analyzing the calculations considering only the last four years ofdata, 2007–2010 (the most reliable). In this case, GS NIS SUM presents a rela-tive percentage increase of 11%, suggesting that whatever causes segregationby Parents’ Education might not be related to segregation by Poverty.

These are preliminary analyses that raise an important question: Isbetween-school segregation one single process or should we consider amodel with more than one cause? Gorard and Cheng (2011) indicate that theclustering of pupils with the same characteristics in public schools in Englandis not one process, but instead, three distinct segregation processes occurringsimultaneously. Jacobs (2011) came to a similar conclusion after analyzingracial, economic, and linguistic segregation in Charter public schools in theUnited States.

These initial findings are important for future analysis regarding admis-sion policies and school segregation, and reinforce the need to tracksegregation by multiple pupil characteristics. If in fact between-school seg-regation is not only one process, as stated by Jacobs (2011) and Gorard andCheng (2011), then it could also be true for educational systems in develop-ing countries. The key point is that this multiple segregation process couldhave some type of interaction, and policy makers must be alert to the risks.If future evidence confirms the initial claim that there are two or more seg-regation processes taking place concomitantly, then it would be reasonableto think of different solutions to deal with between-school segregation.

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