EQUALIZING, BUT NOT GREATLY: HOW INVERTED …...2 1. Introduction What is the role of schools in...

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EQUALIZING, BUT NOT GREATLY: HOW INVERTED EDUCATIONAL

OPPORTUNITIES IN U.S. HIGH SCHOOLS CONTRIBUTE TO STRATIFICATION IN

COLLEGE DESTINATIONS

Abstract

This study applies the concept of compensatory inversion (Lutfey and Freese 2005) to reconcile

competing views of schools as either stratifying or equalizing institutions. Compensatory

inversion describes resource inequalities benefitting high-SES individuals, even though the

benefits of those resources are strongest for low-SES ones. This study tests this idea by

examining U.S. students’ college destinations. In line with compensatory inversion, marks of

distinction valued by selective colleges (such as enrolling in Advanced Placement courses and

participation in extracurricular activities) increases low-SES students’ chances of enrolling in

selective colleges to a greater extent than those of high-SES students. While marks of distinction

can compensate for low-SES students’ disadvantages, this study suggests that opportunities to

earn them are inverted: attending high schools with more opportunities to earn marks of

distinction (such as school-level Advanced Placement offerings) benefits high-SES students

more than low-SES students.

Keywords: college destinations; high schools; school resources; educational inequalities; class;

Highlights:

Selective colleges base admissions decisions on students' marks of distinction.

I examine U.S. students' chances of enrolling in selective colleges.

Marks of distinction boost the chances of low-SES students more than high-SES ones.

School-level marks of distinction have the opposite effect.

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1. Introduction

What is the role of schools in maintaining class inequalities in educational achievements,

transitions, and attainments? Contrary to Horace Mann’s (1848) view of education as “a great

equalizer of the conditions” of men and women, foundational texts in the sociology of education

argue that schools perform crucial functions of social closure for advantaged groups and

inherently contribute to social reproduction (Bourdieu 1977; Bowles and Gintis 1976; Collins

1979). Researchers in this tradition have put forth compelling evidence on a number of different

fronts, such as disparities in schooling experiences (Condron and Roscigno 2003), the role of

cultural capital in affluent families’ accruing “profits” in educational settings (Calarco 2011;

Lareau 1989; 2003; Lareau and Horvat 1999), and persistent inequalities in educational

outcomes that are robust to egalitarian interventions (e.g. Bar Haim and Shavit 2013; Reimer and

Pollak 2010; but see Breen, Luijkx, Müller, and Pollak 2009). The picture painted by this

research is that educational institutions are, at best, passive bystanders in the face of affluent

families’ active struggles to obtain and hoard educational advantages, and, at worst, actively

complicit in them (Cucchiara 2013; Cucchiara and Horvat 2009).

On the other hand, it is difficult reconciling this view with evidence that inequalities in

student learning are ameliorated during the school year, and maximized when school is not in

session (Alexander, Entwisle, and Olson 2007; Downey, von Hippel, and Broh 2004). Rather

than view schools as stratifiers, this research portrays schools as equalizers, and indicates that

class inequalities in school outcomes occur despite schools, not because of them.

While equalizing and stratifying processes coexist in educational institutions, educational

researchers have yet to explicitly reconcile how this occurs. This paper proposes that the concept

of compensatory inversion clarifies how these diametrically opposite dynamics can occur at the

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same time. Compensatory inversion, borrowed from medical sociology (Lutfey and Freese

2005), refers to situations where resources that are most beneficial to disadvantaged individuals

are more available to advantaged ones.

Analyzing data on high school students in the United States, this study presents estimates

how the benefits of marks of distinction--enrolling in Advanced Placement (AP) and

International Baccalaureate (IB) courses, participating in extracurricular activities and sports, and

having high grades and SAT scores--are contingent on students’ socioeconomic background.

This study also examines if high-SES students are more likely to benefit from school-level AP,

IB, and athletic offerings. The results show that student-level marks of distinction can

compensate and offset low-SES students’ disadvantages. However, this compensation is

inverted because of opportunity hoarding on the part of high-SES students and their families.

Schools with broader opportunities for students to earn marks of distinction also have broader

SES inequalities in students’ chances of enrolling in selective colleges. In other words, SES

inequalities in enrolling in selective colleges are exacerbated in schools offerings more marks of

distinction, but among students who actually possess those marks, SES inequalities in college

destinations are ameliorated.

The compensatory inversion pattern documented in this study is different than predictions

from other theories of educational stratification. These competing theories include cultural

reproduction models that argue that high-SES students will more effectively deploy their marks

of distinction (DiMaggio 1982); institutional arguments that schools will make sure that

opportunities to earn marks of distinction will be distributed equitably; and views that the

benefits of opportunities to earn marks of distinction are more effectively deployed not by high-

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SES students per se but by students attending high-SES schools, because such schools make

more efficient use of their resources.

This study makes two main contributions to the literature. First, it gauges how the effects

of possessing marks of distinction and attending schools with many opportunities to earn marks

of distinction are contingent on SES, something that has not been done in prior research. College

destinations are arguably one of the most important outcomes in high school, since the selectivity

of the college one attends has consequences for labor market outcomes (Liu, Thomas, and Zhang

2010; Long 2008; 2010; Loury and Garman 1995; Rivera 2011; Zhang 2008)1 as well as marital

outcomes (Arum, Roksa, and Budig 2008). Second, it explicitly marries the concept of

compensatory inversion to educational inequalities. While other researchers have acknowledged

compensatory inversion dynamics in educational settings (e.g. Stanton-Salazar 1997; 2001;

Stuber 2012), this paper extends those arguments to show that opportunity hoarding on the part

of high-SES families can exacerbate inversion processes to the point of negating any

compensatory effects of increases in educational opportunities. By doing so, this study adds

nuance and depth to the debate over the relationship between educational institutions and

stratification.

2. Background

2.1. Compensatory Inversion

Researchers have documented compensatory inversion occurring in educational settings.

The economic (Brand and Xie 2010) and health (Schafer, Wilkinson, and Ferraro 2013) benefits

1 This has been disputed by researchers arguing that much of the research showing college selectivity effects on status attainment have not met the challenges posed to causal inference (Black and Smith 2004; Brand and Halaby 2006; Dale and Krueger 2002; 2011). Long (2008) demonstrates that the documented benefits of selective colleges survive these methodological challenges.

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of having a college education accrue mainly to those who have the smallest probability of

obtaining a college degree. There is also evidence that disadvantaged students, when placed in

higher levels of stratified educational placements, benefit more than advantaged students. For

example, lower-SES students benefit more from selective colleges (Bowen, Kurzweil, and Tobin

2005; Dale and Krueger 2011; Stuber 2012), even though they are substantially less likely to

enroll in them. Disadvantaged children also benefit more from higher ability grouping

placements (Tach and Farkas 2006; Condron 2008).

Stanton-Salazar (2001; 1997) comes closest to fully articulating the dynamics of

compensatory inversion in educational settings. He concludes from his interviews with Mexican

American working-class youth that students alienated from school are the ones who stand to

benefit the most from teacher mentors, but in reality it those students most integrated in the

school community—the ones needing institutional mentorship the least—who have the highest

chances of having a teacher mentor. Erickson et al (2009) builds on these insights and shows

that for the general population, access to mentors are stratified by parental education, with

children of less-educated parents having restricted access to teacher mentors. However, the

benefits of having teacher mentors for one’s educational attainment are strongest for the children

of parents without a college education. The interpretation of these effects rests on a functional

substitution argument (Mirowsky and Ross 2003)—individuals with more resources can

substitute one resource for another. Disadvantaged individuals who are less likely to have access

to educational “goods”, like credentials or teacher mentors, do not have the luxury of substituting

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resources, so if they happen to gain access to such goods the benefits are maximized for them.

Stanton-Salazar points out that these individuals are more dependent on schools.2

While these studies have substantially improved knowledge of educational inequalities,

the school’s role in inverting compensatory opportunities remains understudied. Stanton-

Salazar’s (1997; 2001: 214-215) research is a partial exception to this; he argues that schools are

beset with limited resources and that teachers and school officials unthinkingly categorize

students as “deserving” of their help based on arbitrary cultural signals, such as deference to

educational institutions, “help-seeking orientations”, and “mak[ing] demands in an assertive yet

nonthreatening manner”. This paper extends Stanton-Salazar’s argument by showing that the

inversion of access to educational goods persists even when schools have more of those

educational goods, and these inversion processes have stratifying effects for future educational

outcomes.

2.2. Compensatory Inversion and Opportunity Hoarding

Some (e.g. Alexander 1997) have argued that schooling, at least in the early years, is

largely compensatory because of suppressed SES inequalities in learning when school is in

session. However, as children progress through their educational careers, the importance of

marks of distinction grow, since students can use them to signal they are worthy of future

advantages, such as enrolling in a selective college, which in turn signals entitlement to

occupational success (e.g. Rivera 2011). To ensure they can signal such entitlement, high-SES

families and their children strive for educational distinctiveness—to either have relatively higher

2 The “particularistic mobility thesis” (e.g. Wilson and Maume 2013) makes a similar argument about racial inequalities in labor market outcomes—formal job qualifications such as education credentials are more beneficial for racial minorities than whites, because while whites can substitute informal characteristics (such as social ties) for formal qualifications, African Americans and Hispanics cannot afford to do so.

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quantities of education, or higher qualities of it (Lucas 2001; Davies and Guppy 1997). This

dynamic drives increasing competition over admission into selective colleges. In turn, the

chances of assembling portfolios of marks of distinction that selective colleges find attractive, as

well as actually enrolling in those colleges, becomes increasingly stratified based on family SES

(Alon 2009; Bastedo and Jaquette 2011; Hoxby 2009; Bound, Hershbein, and Long 2009;

Domina and Saldana 2012). In sum, while schooling may be largely compensatory in the early

years, growing competition over marks of distinction inverts schools’ compensatory potential.

The most common way to access marks of distinction is through high schools’

programmatic resources—particular forms of curricular or extracurricular content that are direct

opportunities to gain marks of distinction. It is in schools that students can study advanced,

college-level material (in the United States, namely Advanced Placement and International

Baccalaureate subjects), or participate in sports or extra-curricular activities. It is in schools that

students earn high grade point averages (GPAs) and learn enough to score high on SATs.

Students who stand out by earning these marks of distinction increase their chances of enrolling

in selective colleges (Attewell and Domina 2008; Espenshade and Radford 2009; Kaufman and

Gabler 2004).

There is good reason to believe that opportunities to earn these marks of distinction are

inverted. Prior research has shown that high-SES students are more likely than low-SES

students to possess the marks of distinction that are useful for enrolling in selective colleges

(Klugman 2012). Advantaged parents and their children successfully deploy their political,

social, and cultural capital to get schools to steer such opportunities to themselves (Calarco 2011;

Demareth 2009; Horvat, Weininger, and Lareau 2003; Oakes, Wells, Jones, and Datnow 1997;

Wells and Serna 1996; Cucchiara and Horvat 2009; Lucas 2001; Cucchiara 2013). Many

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schools are organized such that students with the most class and academic advantages are

assigned to more experienced teachers and academically rigorous courses (Kalogrides, Loeb, and

Béteille 2012; Oakes 1985), and this dynamic most likely occurs in schools serving advantaged

populations, such as white students or students from high-SES families (Kelly 2009; Kelly and

Price 2011; Kilgore 1991; Attewell 2001). Schools with more programmatic resources tend to

be dominated by advantaged students, and those schools should have greater SES inequalities in

their graduates’ chances of enrolling in selective colleges.3 For example, Conger et al. (2009)

found that the presence of teachers with advanced degrees has significantly more positive effects

on non-poor students’ AP course-taking than that of poor students’.

H1 (inversion of opportunities): The benefits of programmatic resources are stratified based on

students’ family backgrounds, such that high-SES students benefit more from attending schools

with high levels of programmatic resources than low-SES students.

Opportunity hoarding (Tilly 1998) by affluent families and their children produce

inverted educational opportunities in schools. However, opportunity hoarding potentially means

that school-based opportunities to earn marks of distinction will be more beneficial for low-SES

students. Stevens (2007) argues that the most successful applicants to selective schools forge a

qualitatively unique narrative about themselves that sets them apart from others. It is hard to

construct such a narrative solely on the basis of widely-available, easily-quantifiable marks of

distinction obtained in high schools, like taking numerous Advanced Placement courses. High-

SES students have access to non-familial social capital (Lareau 2003) that could facilitate access

3 There is fairly compelling evidence that student test scores, chances of dropping out, grades, advanced-course-taking, and socioemotional outcomes have a higher SES gradient in schools with a greater presence of affluent students, indicating that organizational or social processes in these schools work to the relative detriment of low-SES students (Crosnoe 2009; Rumberger 1995; Rumberger and Palardy 2005).

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to non-school-based opportunities for marks of distinction; an extreme example of this is a

student who volunteers as a lab assistant for a scientist at a local college. In other words,

advantaged students can substitute non-school-based marks of distinction for school-based ones,

and thus will benefit less from the latter. Low-SES students, on the other hand, will be more

dependent on the widely-available, school-based marks of distinction. There is evidence for

this—participation in extracurricular activities results in higher test scores for low-SES than

high-SES students (Dumais 2006; 2008; Covay and Carbonaro 2010), and curricular intensity in

high school results in a higher college selectivity for nonwhite students than for white students

(Stearns, Potochnick, Moller, and Southworth 2010).

H2 (compensatory marks of distinction): The benefits of school-based marks of distinction

compensate for disadvantaged backgrounds, such that low-SES students benefit more from

marks of distinction.

2.3 Alternative Hypotheses

Compensatory inversion is not the only plausible account of how school-based marks of

distinction can affect the stratification of college destinations. In the United States, teachers and

school officials are embedded in an institutional environment where pushes for increasing

equality of opportunities can be powerful (Loveless 1999). This is reflected in concrete school

practices, such as guidance counselors advocating college education for most students

(Rosenbaum, Miller, and Krei 1996). This could produce a situation where stratification in

graduates’ college destinations is not positively associated with high schools’ programmatic

resources. There is some support for this view; certain high school resources, such as small class

sizes and having teachers with graduate degrees, appear to be especially beneficial for the test

scores and behavior of low-SES students or students whose parents are of low-test ability (Parcel

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and Dufur 2001a; 2001b; Krueger 1999). Lee et al. (1998) also found that the availability of

calculus courses is somewhat more beneficial for low-SES students’ math course-taking than for

high-SES students, although this interaction was only marginally significant.

H3 (schools as equalizers): The benefits of programmatic resources are either compensatory and

benefit low-SES students more than high-SES ones, or do not vary by student SES.

Compensatory inversion is also at odds with the “cultural reproduction” model

(DiMaggio 1982) which holds that possessing cultural capital benefits primarily high-SES

students. According to this argument, students who grow up in advantaged families develop a

natural familiarity with the cultural symbols used to signal one’s entitlement to social advantages

(Lamont and Lareau 1988). Research has not unanimously born this view out; some studies have

found evidence inconsistent with the cultural reproduction model (DiMaggio 1982; Jæger 2011;

Evans, Kelley, Sikora, and Treiman 2010; Dumais and Ward 2010) while other studies find

support (Roscigno and Ainsworth-Darnell 1999; Daw 2012).

High-SES students may be more likely to translate their marks of distinction into feeling

they are entitled to enroll at a selective college, and that they are better able to navigate the

college admissions process. In other words, they exploit their school-based marks of distinction

more than low-SES students do. This view is also in line with recent concerns that high-ability

working-class students are ignorant of the feasibility enrolling in selective colleges (Hoxby and

Avery 2012; Radford 2013).

H4 (cultural reproduction): The benefits of school-based marks of distinction are stratified based

on students’ SES backgrounds. High-SES students will benefit more from school-based marks of

distinction than low-SES students.

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Finally, marks of distinction could be more advantageous for high-SES students because

of economic segregation among schools. Schools serving predominantly affluent communities

will not be burdened with pervasive student problems, and they will have greater social capital

manifested as trusting relationships among school staff, parents and teachers (Condron 2009;

Wenglinsky 1997; Palardy 2013). Such schools will be better able to deploy their resources than

in low-SES schools. For example, some researchers argue that the expansion of the AP

curriculum to disadvantaged schools has led to lower-quality AP courses (Klopfenstein and

Thomas 2010).

It is also possible that high-SES schools can help their graduates deploy their own marks

of distinction effectively. Research suggests that affluent high schools—and not just elite

boarding schools (Persell and Cookson 1985)—have guidance counselors who help students

marshall their marks of distinction into a portfolio that selective colleges find appealing

(McDonough 1997; Paul 1995; Stevens 2007).

H5 (inequalities in school efficiency): The benefits of programmatic resources and marks of

distinction are stratified not on student SES, but on schools’ socioeconomic mix. Students

attending schools with a more affluent student body will benefit more from their schools’

programmatic resources and from their own school-based marks of distinction than students

attending schools with a more disadvantaged student body.

3. Data/Methods

3.1 The Educational Longitudinal Study of 2002

The data for this study comes from the Educational Longitudinal Study of 2002 (ELS),

which is a nationally-representative probability sample of tenth graders in the United States in

2002, with follow ups conducted in 2004 and 2006. This survey was commissioned by the

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National Center for Education Statistics (NCES). The sample is restricted to students who were

in the 2006 follow-up, who never dropped out of high school, who attended the same high school

in the 10th and 12th grades, who graduated from high school in 2004 or afterwards, and who

participated in the high school transcript study in 2004. This leaves a sample of 10,070 cases in

710 schools.4 Cases with missing values on the dependent variables were dropped, leaving a

sample of 9,880 students in 710 schools.5 The school sample sizes ranged from less than ten to

40. Variables calculated by aggregating values within schools (namely, the average SES of

students in the high school) were based on all sampled students in the school, regardless if they

were included in the final sample. These school-aggregated variables were calculated from

school samples which averaged 20 cases, and 99 percent of students were in schools that

provided samples of at least 10. Multiple imputation routines in Royston, Carlin, and White’s

(2009) ice package for Stata were used to create and analyze ten imputed datasets to address

missing values in predictors.6

4 Restricting the sample this way introduces the possibility for bias. Using sample weights minimizes bias caused by attrition (e.g. students who did not participate in the 2006 wave) and by the omission of students who did not participate in the transcript study. Dropping students because they changed high schools between the 2002 and 2004 waves also introduces the possibility of biased results because the number is fairly large (1,240). In a supplemental analysis (not presented but results available upon request), these students were retained and data on their high school resources were, if possible, based on the averages of the high schools attended (if data on multiple high schools were not available, data from one high school was used). The results are very similar to the main analyses presented here. 5 All sample sizes reported in this study are rounded to 10s, in compliance with NCES requirements for users of restricted-use data. 6 Because this study is using multilevel data, I imputed school-level and student-level variables separately in different datasets (although school-level aggregates were used to impute the school-level variables, and school-level variables were used to impute the student-level variables). In addition, because this study is interested in interactions with school and student SES, I split the school sample into two halves based on school SES (at or below the median, and above it) and imputed each half separately. I split the student-level data file into four quarters based on student and school SES (below-median students attending below-median schools; below-median students attending above-median schools; above-median students attending below-median

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3.2. Variables

3.2.1. Dependent Variables: College Destinations

In the 2006 follow-up, respondents detailed their history of post-secondary enrollments. ELS

lists the first “real” college respondents attended (this excludes colleges attended during summer

before attending a different college). A series of dummy indicators for various college

destinations, based on the 2004 edition of Barron’s Profiles of American Colleges, were created.

This approach is similar to that used by Turley’s (2007; Desmond and Turley 2009)

examinations of college applications. The most selective outcome (highly-most competitive) was

enrolling in a “most competitive” (median SAT score = 1310 – 1600) college or a “highly

competitive” (median SAT score = 1240 – 1309) college. The second most selective outcome

(very-most competitive) was enrolling in a most competitive, highly competitive, or “very

competitive college” (median SAT score = 1146-1239). I also examined enrolling in any four-

year college. As shown in the summary statistics presented in Table 1, 10 percent of respondents

enrolled in a highly or most competitive college, 24 percent enrolled in a very, highly, or most

competitive college, and 55 percent enrolled in a four-year college.

3.2.2. Independent Variables.

Socioeconomic Status. Student SES is a composite measure, provided by NCES, of parents’

education levels, occupations, and family income, measured when students were in the tenth

grade.

Programmatic School Resources. School AP Subjects and School IB Subjects are counts of the

number of unique AP and IB courses offered in the high school. These come from the ELS

schools; and above-median students attending above-median schools) and imputed each quarter separately. The dependent variables were not imputed, nor were they used to impute predictor variables.

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Course Offering File, which contains course-level data on all courses offered in high schools

participating in the transcript study. The Course Offering File made distinctions among 31

different AP courses, and 28 different IB courses. Sports offerings is a count of the number of

different extracurricular sports teams at the school. The ELS administrator questionnaire asked

if a variety of different sports were offered (baseball, softball, basketball, football, soccer, swim,

ice hockey, field hockey, volleyball, lacrosse, tennis, cross-country, track, golf, gymnastics, and

wrestling). Unfortunately, the ELS did not ask administrators about their non-sports

extracurricular offerings. Sports offerings is used as a proxy for extracurricular activities in

general, but the sports offerings themselves can also be an opportunity for students to earn marks

of athletic distinction that make them appealing to colleges, even selective ones (Golden 2006;

Mullen 2010; Stevens 2007; Espenshade, Chung, and Walling 2004). High schools reported

offering between 0 to 16 different kinds of sports.

Marks of Distinction. AP Subject-taking and IB Subject-taking are the number of AP and IB

subjects the student enrolled in, according to the transcript file. Activities is the number of non-

sport extracurricular activities students reported doing in their senior year. Possible activities

that students could indicate are orchestra, play/musical, student government, academic honor

society, newspaper/yearbook, service club, and any kind of academic club. Sports participation

is a dummy indicator for participating in interscholastic sports in both the sophomore and senior

year. Grades is the student’s z-standardized high school grade point average. Finally, SAT

scores is the student’s SAT scores as reported on the student’s transcript. For students who took

the ACT instead of the SAT, ELS converted their scores into the SAT metric. All SAT scores

were imputed in the multiple imputation process. I also control for a dummy indicator for

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students who originally had missing SAT scores and who indicated they never thought about

taking the SAT or were not planning to take it.

Controls For Selection Into High Schools. One problem with studying the effects of high

schools is the possibility that students who are predisposed to enroll in selective colleges attend

resource-rich high schools, and thus any estimated benefits of high school programmatic

resources on college destinations are spurious. Controlling for students’ early achievements and

motivations will attenuate, at least partially, this selection problem. Ideally, coefficients for

family SES will reflect parents’ practices, behaviors, and resources that occur (or were

“invested”) during students’ high school careers, although this rests on the assumption that the

cumulative effect of SES on pre-high school investments can be captured with observed

measures of early achievements and motivations.

Unfortunately, since the ELS data traces a cohort of tenth graders, it is impossible to

obtain good measures of the students’ abilities and predispositions prior to entering high school.

Instead, measures collected in the tenth grade are used. Students’ 10th grade test scores is the

student’s composite IRT-scaled score on the math and reading tests administered in the 10th

grade. Pre-high school track placement is measured with an indicator for students who did not

take Algebra I during high school but did take a math course that follows Algebra I (e.g.

geometry, trigonometry, Algebra II, calculus); such students in all likelihood took 8th grade

algebra. Students’ 10th grade educational expectations, are measured with dummy indicators for

less than a BA degree, BA degree, and post-BA degree; the same measures are used for parents’

educational expectations for the student (reported in the 10th grade).

Other Controls. Student race is measured using dummy indicators for Asians, Blacks, Hispanics,

Whites, and Other; sex is controlled for as an indicator variable for males. At the school level, I

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control for logged school enrollment, which are the reports from the Common Core of Data

(CCD) and Private School Survey (PSS) databases averaged from 2000-01 to 2003-04, location

(urban, suburban, rural), and for region, measured as dummy variables for Northeast, Midwest,

South, and West.

3.3. Plan of Analysis

Because each outcome is dichotomous, and since the ELS data has students clustered in

their high schools, multilevel logistic regressions (in HLM v. 6) are used, which provides more

efficient coefficient estimates and less biased estimates of standard errors than would be obtained

in a regular logistic regression. Per the recommendations of Goldstein and Rasbash (1996), unit-

specific coefficients (as opposed to population-averaged coefficients) are presented in the tables.

First, Hypotheses 1-4 were tested by presenting analyses with interactions between

student SES, on the one hand, and programmatic resources and marks of distinction on the other,

to see if the benefits of the latter depend on the former. Second, Hypothesis 5 was tested by

simultaneously interacting programmatic resources and marks of distinction (on the one hand)

with student SES and school SES (on the other). This will get at if economic segregation

produces a situation where programmatic resources and marks of distinction are more efficacious

in high-SES schools. Interactions were tested individually in separate models.

Per the advice given in Brambor et al. (2006), all interaction effects, including

insignificant ones,7 were probed by estimating the conditional effects (or “simple slopes”) of

programmatic resources and marks of distinction when student SES is one standard deviation

above and below the mean. These were estimated by rerunning models where student SES is

7 As Brambor et al.(2006: 74) put it, “Numerous articles…drop interaction terms if [the interaction] coefficient is insignificant. In doing so, they potentially miss important conditional relationships between their variables.”

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recentered on these low and high values. When testing Hypothesis 5 (inequalities in school

efficiency), four simple slopes were estimated: when both student and school SES are one

standard deviation below the mean, when both are one standard deviation above the mean, and

when one is a standard deviation above the mean while the other is a standard deviation below

the mean (and vice-versa).

When testing the effects of programmatic resources, all programmatic resources are

controlled for, and when testing the effects of marks of distinction, all programmatic resources

and marks of distinction are controlled for. This raises the possibility of multicollinearity,

although diagnostics suggest it is not a problem. When a linear regression is run with the main

effects of all predictors used in this study, the average VIF is 1.8 and the highest variance

inflation factor (VIF) is 4.6 (for SAT scores), well below the threshold of 10 proposed by

Hocking (2003).

Because this study is primarily focused on enrollment in selective colleges, predicted

probabilities are calculated for “successful” students—students who expect to earn a BA degree

and whose parents expect the same, who enrolled in algebra in the 8th grade, and who scored at

the 90th percentile on the 10th grade ELS test. When showing the effects of marks of distinction,

“successful” students also means scoring at the 90th percentile on the SAT/ACT test as well as

getting grades in the 90th percentile. All other predictors are held at their means.

While this study has attempted to account for selection into schools by using measures of

tested ability and educational expectations observed in the 10th grade, the possibility of selection

bias remains. Sampson (2011; Sampson and Sharkey 2008) argues that researchers often

overstate the problem of selection bias in estimating the causal effects of neighborhood context.

He based this conclusion on a longitudinal analysis of Chicago residents, finding that among

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movers, the main determinants of the characteristics of the neighborhood they ended up in were

the characteristics of the neighborhood from which they originated. As Sampson (2011: p. 327)

puts it, “neighborhoods choose people rather than…people choose neighborhoods.” While

Sampson’s argument does not speak directly to the issue of selection into schools, it does imply

that selection bias should be less of a problem for neighborhood public schools (Palardy 2013

also argues that samples limited to public school students are less vulnerable to selection bias

than samples including private school students). Utilizing this insight, I replicate my analyses

for a sample of 2,680 students attending 240 neighborhood public schools. These are public

schools excluding vocational schools and charter schools; students attending magnet schools and

“public schools of choice” are also excluded unless their school shares the same zip code as their

residence. These analyses, which are largely consistent with the main ones, are presented in

Table A1.

4. Results

4.1. Are Opportunities Associated With Programmatic Resources Inverted By SES?

Table 2 presents the results for how the associations between school programmatic

resources and college destinations vary by student SES. As laid out in Hypothesis 1,

compensatory inversion predicts that the benefits of programmatic resources should be

heightened for high-SES students. Table 2 gives evidence for this, as far as Advanced

Placement subject offerings and sports offerings are concerned. For all three outcomes, the effect

of Advanced Placement subject offerings are significant and positive for high SES students; the

effects are substantially lower and non-significant for low-SES students (however, the interaction

with SES is only significant at the .10 level for enrolling in very, highly, or most competitive

colleges and not significant for the other outcomes). Figure 1 graphs the effects of going from

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the 10th percentile of AP subjects to the 90th percentile for successful students; it shows how the

presence of the AP subject offerings is associated with a greater SES gradient in college

destinations. The results for enrolling in a highly or most competitive college show the starkest

pattern; if a school has zero AP subjects, a high-SES student (one standard deviation above the

mean) has around a 17 percent chance of enrolling in a highly-most competitive college, while a

low-SES student has only a 10 percent chance. If the school’s AP subject offerings increases to

16, the high-SES student’s chances of enrolling in a highly-most competitive college grows to

around 35 percent, while those of a low-SES student only grow to around 15 percent.

The inversion of opportunities associated with greater AP subjects does not occur with

regards to the IB program. If anything, the IB program promotes compensatory targeting of

educational opportunities, so there is some support for Hypothesis 3 (schools as equalizers). For

enrolling in a highly-most competitive college, there is a marginally significant negative

interaction between IB subject offerings and student SES. The simple slopes show positive and

significant effects of the IB program for low-SES students but not high-SES students. Figure 2

graphs these effects across the 10-90th percentile range for IB subject offerings; it shows that

low-SES students never close the gap with high-SES students, but they manager to reduce it.

Like AP subjects, sports offerings reflect an inversion of opportunities. However, there

are no significant benefits of attending a high school with more sports offerings; rather, there is a

marginally significant cost to attending such a high school for low-SES students, as far as

enrolling in a very-most competitive college is concerned. The interaction terms indicate the

effect of sports offerings significantly varies by student SES (there is also a significant

interaction between sports offerings and student SES for enrolling in any four-year college,

although none of the simple slopes are significant). Figure 3 shows that going from the 10th to

20

the 90th percentile in sports offerings (7 to 14 sports) decreases a low-SES student’s chances of

enrolling in a very-most competitive college from around 43 to 30 percent, while a high-SES

student’s chances grow from around 50 to 60 percent. A straight-forward interpretation of the

stratifying effects of sports offerings is that low-SES students’ investments in athletics are

detrimental to their college destinations. However, the results for being an athlete (presented in

the next section) indicate that low-SES students do not harm their college destinations by being

athletes (although their college destinations are not helped either). Schools with more sports

offerings may also have exclusionary organizational and social practices that hurt low-SES

students’ chances of academically succeeding or getting help in the college application process.

4.2. Do Marks of Distinction Have Compensatory Effects?

As stated in Hypothesis 2, compensatory inversion argues that actually earning school-

based marks of distinction should be more beneficial for low-SES students, and the results for

marks of distinction, presented in Table 3, bear this out for the most part. Enrolling in AP and IB

subjects, as well as participating in extracurricular activities, all produce significantly greater

benefits for low-SES students’ chances of enrolling in very-most competitive colleges, compared

to those of high-SES students. In addition, the effect of taking AP subjects has larger benefits

for low-SES students’ chances of enrolling in highly-most competitive colleges than for high-

SES students. Figures 4 and 5 graph these effects; the effect of IB subject-taking on enrolling in

very-most competitive colleges is particularly stark; among students who have taken zero IB

subjects, a high SES student has a 62 percent chance of enrolling in a very-most competitive

college, while a low SES student has a 50 percent chance. Among students at the 90th percentile

of IB subject-taking (two IB subjects), SES inequalities are nonexistent; both high- and low-SES

students have a 76 percent chance of enrolling in a very-most competitive college.

21

However, there is some evidence for the cultural reproduction argument that high-SES

students are better able to deploy their marks of distinction for educational “profits” (Hypothesis

4). In particular, being an athlete is more advantageous for high-SES than for low-SES students.

For enrolling in a highly-most competitive college, and enrolling in a very-most competitive

college, athletic participation has a significant benefit for high-SES students but not for low-SES

students, although the interaction terms are not significant at the .05 level. For enrolling in any

four-year college, there is a significant interaction between student SES and athletics

participation, and the simple slopes show that a the benefit for a high-SES student is twice that of

a low-SES one. Figure 6 shows predicted probabilities for high- and low-SES athletes and non-

athletes for all three outcomes; the SES differential in the benefit of being an athlete is

pronounced for enrolling in a very-most competitive college. High-SES athletes have a 69

percent chance of enrolling in a very-most competitive college compared to the 58 percent

chance of high-SES non-athletes. On the other hand, low-SES students have around a 50 percent

chance of enrolling in such a college regardless if they are an athlete or not.

In addition, high-SES students appear to benefit from having high SAT scores more than

low-SES students in terms of enrolling in any four-year college. The SES-SAT interaction

however does not occur for the other outcomes of enrolling in highly-most competitive colleges

or very-most competitive colleges. Moreover, as will be seen in the next section, this effect is

misleading: the benefits of a higher SAT score are not stratified by student SES but rather by

school SES.

4.3. Is There School Inequality in Deploying Programmatic Resources and Marks of Distinction?

Hypothesis 5 (inequalities in school efficiency) states that the benefits of high school’s

programmatic resources and students’ marks of distinction are stratified by school SES, not

22

student SES—that high-SES high schools are better able to deploy their resources, or help their

students deploy their marks of distinction. This hypothesis is tested by adding interactions with

school SES. Hypothesis 5 is supported by significant interactions with school SES, by simple

slopes showing that the benefits of programmatic resources or marks of distinction are confined

to high-SES schools (not high-SES students), and decreases in the interactions involving student

SES.

The evidence for Hypothesis 5 is sporadic. In Table 4, the simple slopes and the

interaction coefficients give very little evidence that the benefits of programmatic resources are

confined to high-SES schools. Table 5 suggests some marks of distinction are better deployed

by students who attend high-SES schools. Athletes are more likely to enroll in highly-most

competitive colleges, but the simple slopes show being an athlete is only beneficial for high-SES

students attending high-SES schools (however, the benefits of being an athlete for enrolling in

very-most competitive colleges is confined to high-SES students, regardless of their schools’

socioeconomic mix). Examination of the effects of AP and IB subject-taking or extracurricular

participation show little support for Hypothesis 5; in fact, the benefits of IB subject-taking for

enrolling in highly-most competitive colleges appear to be strongest for students in low-SES

schools.

There is some evidence for Hypothesis 5 with regards to enrolling in any four-year

college. The benefits of increasing levels of grades and ACT / SAT scores appear to be strongest

for students in high-SES schools (although this benefit does not occur for enrolling in highly-

most competitive colleges or very-most competitive colleges). Since having high grades and test

scores is not a requirement for enrolling in any four-year college, it is probable that affluent

schools help students who are academically mediocre (but not students who are in the very

23

bottom of the distribution) apply to and secure financial aid at less competitive four-year

colleges.

4.4. Effects of School Resources for Students in Neighborhood Public Schools

Table A1 presents a sensitivity analysis where the sample is limited to students enrolled

in neighborhood public schools. Among these students, selection into schools based on

unobserved individual characteristics should be minimal, relative to students in private schools

or public schools of choice. By and large, the results are consistent with the main analyses

discussed in the previous section. The benefits of schools’ AP subject-offerings for high-SES

students are somewhat weaker, but there is still a significant positive effect for enrolling in very-

most competitive colleges. Low-SES students benefit from schools’ IB subject-offerings and are

hurt by schools’ sports offerings.

5. Discussion

Sociologists of education focus on stratifying processes that occur in educational settings,

but the general thrust of their research conflicts with the finding that inequalities in learning are

reduced when schools are in session. This study suggests compensatory inversion as a way to

reconcile this tension. Educational opportunities are hoarded by high-SES students and their

families, and thus inverted. Because low-SES students lack the resources to pursue non-school-

based opportunities, they are especially reliant on school-based ones. Consequently, if low-SES

students manage to access school-based opportunities, they draw especially large benefits from

them.

This study illustrated this dynamic by examining U.S. high school students’ chances of

enrolling in selective colleges. High schools are major source of the marks of distinction that

students use to signal their worthiness of admission to selective colleges. The inversion of

24

opportunities is evident by the results showing that schools with more programmatic resources—

that is, curricular and extracurricular offerings that students can use to earn marks of

distinction—show greater SES inequalities in college destinations. The compensatory nature is

demonstrated by the fact that once low-SES students are able to access marks of distinction, they

draw larger benefits from them than high-SES students.

The main contribution this study makes is demonstrating that while secondary schools in

the United States have important compensatory potential, there are substantial barriers

preventing them from realizing it. These barriers are in all likelihood rooted in the interaction

between high-SES families and their children and school organizations, which result in the

former hoarding educational opportunities. If policy-makers wanted to facilitate low-SES

students’ access to marks of distinction, such as expanding access to Advanced Placement

subjects, this study suggests the equalizing goals could not be achieved unless school practices

were modified.

This study also assessed various alternative hypotheses. While the findings provided

some support for each hypothesis, the overall pattern is consistent with compensatory inversion.

The schools-as-equalizers hypothesis predicted that school programmatic resources would be

deployed in an equitable or compensatory way, so that class stratification would be either

independent of school resources, or inversely associated with them. The IB program is in line

with this hypothesis. This raises the possibility that IB schools have egalitarian organizational

practices that could be used to equitably distribute opportunities for AP subject-taking and sports

participation, a subject that future research should consider. However, the schools-as-equalizers

hypothesis was decidedly not the pattern found with regards to schools’ sports offerings and AP

programs.

25

The cultural reproduction hypothesis predicted that marks of distinction would be most

advantageous for high-SES students because they have a natural familiarity with deploying

cultural signals of their entitlement to admission to selective colleges. This appears to be the

case for athletics; among high-SES students the athletic advantage in enrolling in very-most

selective colleges is greater than among low-SES students. However, contrary to the cultural

reproduction hypothesis, other marks of distinction, namely AP and IB subjects and extra-

curricular activities, are more advantageous for low-SES students. High- and low-SES students

are equally effective in deploying grades and SAT scores to enroll in selective colleges.

Finally, the inequality-in-school-efficiency hypothesis argued that marks of distinction

and programmatic resources are more effectively deployed, not by high-SES students, but by

students attending high-SES schools. This study found modest evidence for this hypothesis. The

benefit of being an athlete for enrolling in highly-most competitive colleges is limited to high-

SES students in high-SES high schools (but the benefit for enrolling in very-most competitive

colleges occurs for high-SES students regardless of their schools’ SES mix). Students in high-

SES schools are better able to deploy their grades and SAT scores to enroll in four-year colleges

(but not selective colleges). For the most part, the bulk of the results contradict this hypothesis.

Most notably, the benefits of schools’ AP subject-offerings is limited to high-SES students

(regardless of school SES) and the benefits of student AP subject-taking occur for all students,

but are stronger for low-SES students than high-SES students (regardless of school SES).

Concerns that AP subjects are of lower quality in low-SES schools are not born out in these

results. The same is true with regards to the IB program (which, if anything, is more effective in

low-SES schools) and with regards to participation in extra-curricular activities.

26

One limitation of this study is that it does not eliminate the possibility of selection bias,

which is a concern researchers have especially regarding to school effects (e.g. Crosnoe 2009).

This study’s solution was controlling for a wide array of measures of academic achievement and

aspirations in the early high school career. In addition, this study replicated the analyses of the

effects of school resources for a sample limited to students in non-choice public schools.

Selection on unobserved factors should be less of a problem for this sample, and this study’s

main story is by and large upheld in those analyses. While these measures increase our

confidence that there are true causal effects occurring, the possibility that the effects of school

resources reflect an unmeasured characteristic of individual families can never be completely

eliminated.

This article opened with a discussion of the durability and persistence of inequalities in

educational achievement. While acknowledging and documenting the compensatory potential of

schools, this study’s findings are consistent with the view that that this potential is substantially

unrealized, and that school processes play an important role in maintaining inequalities in college

destinations. Identifying how families and schools can overcome these effects is a subject

worthy of much future research.

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33

Table 1 • Summary Statistics

Variable Mean SD Range Source

Outcomes Destinations Any Four-Year College 0.55 — — ELS Follow-Up 2 (2006) Very, Highly, Most Competitive College

0.24 — —

Highly, Most Competitive College 0.10 — — Predictors Mean SD Student Characteristics SES (z) 0.00 1.00 -3.0 - 2.4 ELS Base Year AP Subject-Taking 0.81 1.57 0.0 - 12.0 ELS Follow-Up 1

Transcript Study

IB Subject-Taking 0.05 0.48 0.0 – 10.0 ELS Follow-Up 1 Transcript Study

Activities 1.45 1.45 0.0 - 7.0 ELS Follow-Up 1 Sports Participation 0.37 0.48 0,1 ELS Base-Year and

Follow-Up 1 SAT score (100s) 9.64 2.22 4-16 ELS Follow-Up 1

Transcript Study No SAT Score 0.12 — 0,1 ELS Follow-Up 1

Transcript Study

Race Other 0.05 — 0,1 ELS Base Year Asian 0.10 — 0,1 Black 0.11 — 0,1 Hispanic 0.12 — 0,1 White 0.62 — 0,1 Male 0.48 — 0,1 10th Grade Tested Ability (z) 0.00 1.00 -3.3 – 3.0 ELS Base Year GPA (z) 0 1.00 -3.6 – 2.2 ELS Follow 1

Transcript Study Educational Expectations Less Than BA 0.15 — 0,1 ELS Base Year BA 0..40 — 0,1 Post-BA Degree 0.45 — 0,1

34

Table 1 (con’t) • Summary Statistics

Variable Mean SD Range Source

Parents’ Educational Expectations Less Than BA 0.12 — 0,1 ELS Base Year BA 0.41 — 0,1 ELS Base Year Post-BA Degree 0.47 — 0,1 ELS Base Year Algebra 0.23 — 0,1 ELS Follow-Up 1

Transcript Study School Characteristics School SES -.10 .99 -2.5 – 2.9 ELS Base Year

School AP Subjects 7.72 6.10 0.0 - 28.0 ELS Follow-Up 1 Transcript Study

School IB Subjects 0.45 2.14 0.0 – 16.0 ELS Follow-Up 1 Transcript Study

School Sports Offerings 10.68 2.87 0.0 - 16.0 ELS Base Year Public School 0.79 — 0,1 ELS Base Year Catholic School 0.13 — 0,1 ELS Base Year Other Private School 0.08 — 0,1 ELS Base Year Log Enrollment 6.86 0.83 3.5 - 8.4 CCD/PSS 2001-2004 Location Rural 0.19 — 0,1 ELS Base Year Suburb 0.50 — 0,1 ELS Base Year Urban 0.31 — 0,1 ELS Base Year Region Northeast 0.16 — 0,1 ELS Base Year Midwest 0.27 — 0,1 ELS Base Year South 0.36 — 0,1 ELS Base Year West 0.20 — 0,1 ELS Base Year

35

Table 2 • HGLM estimates of effects of programmatic resources on college destinations, conditioned on student SES (ELS 2006; 9,880 students in 710 schools)

Highly, Most Competitive

Colleges

Very, Highly, Most

Competitive Colleges

Any 4-Year College

Model A Model A Model A Model 1 • Baseline Model Student SES 0.457 ** 0.415 ** 0.425 ** School SES 0.142 0.238 ** 0.214 ** School AP Subjects 0.053 ** 0.035 ** 0.012 School IB Subjects 0.027 0.037 * 0.000 Sports Offerings -0.033 -0.005 -0.013 Model 2 • School AP Subjects

Main Effect1 0.046 ** 0.030 * 0.013 Interaction With Student SES 0.013 0.015 † 0.008 Simple Slopes Conditioned on Student SES -1 SD 0.032 0.015 0.005 Conditioned on Student SES +1SD 0.059 ** 0.045 ** 0.021 † Model 3 • School IB Subjects

Main Effect1 0.044 † 0.044 * 0.000 Interaction With Student SES -0.038 † -0.025 -0.022 Simple Slopes Conditioned on Student SES -1 SD 0.082 * 0.069 ** 0.022 Conditioned on Student SES +1SD 0.006 0.020 -0.021 Model 4 • Sports Offerings

Main Effect1 -0.049 -0.017 -0.008 Interaction With Student SES 0.031 0.053 ** 0.033 * Simple Slopes Conditioned on Student SES -1 SD -0.080 -0.071 † -0.041 Conditioned on Student SES +1SD -0.017 0.036 0.025 NOTE: Coefficients from unit-specific, multi-level logistic regressions are presented. Simple slopes are calculated by rerunning the model with SES centered on different values. All models include controls for school AP and IB subjects, sports offerings, school SES, school sector, school location, log school enrollment, region, 10th grade standardized test scores, race, sex, student 10th grade educational expectations, parental educational expectations, and 8th grade algebra course-taking. 1. Main effect is conditional on student SES being at its mean level † p < .10; * p < .05; ** p < .001

36

Table 3 • HGLM estimates of effects of marks of distinction on college destinations, conditioned on student SES (ELS 2006; 9,880 students in 710 schools)


Colleges

Very, Highly, Most


Any 4-Year College

Model A Model A Model A Model 5 • Baseline Model Student SES 0.231 ** 0.225 ** 0.272 ** School SES 0.173 0.323 ** 0.276 ** Student AP Subject-Taking 0.245 ** 0.162 ** 0.191 ** Student IB Subject-Taking 0.134 * 0.381 * 0.153 † Sports Participation 0.291 * 0.364 ** 0.572 ** Extracurricular Activities 0.118 ** 0.096 ** 0.162 ** Grades (z) 0.840 ** 0.931 ** 0.756 ** ACT / SAT Score (z) 0.963 ** 0.946 ** 0.698 ** Model 6 • Student AP Subject-Taking Main Effect1 0.300 ** 0.189 ** 0.191 ** Interaction With Student SES -0.082 * -0.056 * -0.002 Simple Slopes Conditioned on Student SES -1 SD 0.382 ** 0.245 ** 0.193 ** Conditioned on Student SES +1SD 0.219 ** 0.133 ** 0.189 ** Model 7 • Student IB Subject-Taking Main Effect1 0.152 * 0.459 ** 0.160 † Interaction With Student SES -0.027 -0.123 * -0.021 Simple Slopes Conditioned on Student SES -1 SD 0.180 † 0.582 ** 0.180 Conditioned on Student SES +1SD 0.125 0.337 * 0.139 Model 8 • Sports Participation Main Effect1 0.230 † 0.299 ** 0.582 ** Interaction With Student SES 0.099 0.175 † 0.195 * Simple Slopes Conditioned on Student SES -1 SD 0.131 0.124 0.387 ** Conditioned on Student SES +1SD 0.330 ** 0.474 ** 0.776 ** Model 9 • Extracurricular Activities Main Effect1 0.149 ** 0.117 ** 0.160 ** Interaction With Student SES -0.055 -0.060 † -0.012 Simple Slopes Conditioned on Student SES -1 SD 0.203 ** 0.177 ** 0.172 ** Conditioned on Student SES +1SD 0.094 * 0.056 0.149 **

37

Table 3 (con’t) • HGLM estimates of effects of marks of distinction on college destinations, conditioned on student SES (ELS 2006; 9,880 students in 710 schools) Model 10 • Grades Main Effect1 0.902 ** 0.950 ** 0.756 ** Interaction With Student SES -0.128 -0.071 0.001 Simple Slopes Conditioned on Student SES -1 SD 1.030 ** 1.020 ** 0.755 ** Conditioned on Student SES +1SD 0.775 ** 0.879 ** 0.757 ** Model 11 • ACT / SAT Scores Main Effect1 0.962 ** 0.968 ** 0.710 ** Interaction With Student SES 0.002 -0.062 0.118 * Simple Slopes Conditioned on Student SES -1 SD 0.960 ** 1.030 ** 0.592 ** Conditioned on Student SES +1SD 0.964 ** 0.906 ** 0.827 **

NOTE: Coefficients from unit-specific, multi-level logistic regressions are presented. Simple slopes are calculated by rerunning the model with SES centered on different values. All models include controls for student AP and IB subject-taking, sports participation, extra-curricular activities, grades, ACT / SAT scores, an indicator for not taking ACT / SAY scores, school AP and IB subjects, sports offerings, school SES, school sector, school location, log school enrollment, region, 10th grade standardized test scores, race, sex, student 10th grade educational expectations, parental educational expectations, and 8th grade algebra course-taking.

1. Main effect is conditional on student SES being at its mean level.

† p <= .10; * p < .05; ** p < .001; *** p < .0001

38

Table 4 • HGLM estimates of effects of programmatic resources on college destinations, conditioned on student and school SES (ELS 2006; 9,880 students in 710 schools)


Colleges

Very, Highly, Most Competitive

Colleges Any 4-Year

College

Model B Model B Model B Model 2 • School AP Subjects

Main Effect1 0.046 ** 0.030 * 0.012 Interaction With Student SES 0.015 0.012 0.009 Interaction With School SES -0.003 0.010 -0.003 Simple Slopes Conditioned on Student & School SES -1 SD 0.035 0.008 0.007 Conditioned on Student SES -1 SD School SES +1 SD 0.027 0.028 0.000 Conditioned on Student SES +1SD & School SES -1 SD 0.064 ** 0.032 † 0.024 Conditioned on Student & School SES +1 SD 0.057 ** 0.052 ** 0.018 Model 3 • School IB Subjects

Main Effect1 0.044 † 0.046 ** 0.004 Interaction With Student SES -0.038 † -0.024 -0.018 Interaction With School SES 0.001 -0.008 -0.029 Simple Slopes Conditioned on Student & School SES -1 SD 0.081 0.078 * 0.051 Conditioned on Student SES -1 SD School SES +1 SD 0.082 * 0.061 * -0.007

Conditioned on Student SES +1SD & School SES -1 SD 0.005 0.030 0.016 Conditioned on Student & School SES +1 SD 0.006 0.014 -0.043 † Model 4 • Sports Offerings

Main Effect1 -0.045 -0.017 -0.005 Interaction With Student SES 0.038 0.055 ** 0.027 * Interaction With School SES -0.019 -0.007 0.020 Simple Slopes Conditioned on Student & School SES -1 SD -0.065 -0.066 -0.053 Conditioned on Student SES -1 SD School SES +1 SD -0.103 † -0.079 † -0.012 Conditioned on Student SES +1SD & School SES -1 SD 0.012 0.045 0.002 Conditioned on Student & School SES +1 SD -0.026 0.031 0.043 NOTE: Coefficients from unit-specific, multi-level logistic regressions are presented. Simple slopes are calculated by rerunning the model with SES and school SES centered on different values. All models include controls for school AP and IB subjects, sports offerings, school SES, school sector, school location, log school enrollment, region, 10th grade standardized test scores, race, sex, student 10th grade educational expectations, parental educational expectations, and 8th grade algebra course-taking. 1. Main effect is conditional on both student and school SES being held at their respective grand means. † p <= .10; * p < .05; ** p < .001; *** p < .0001

39

Table 5 • HGLM estimates of effects of marks of distinction on college destinations, conditioned on student and school SES (ELS 2006; 9,880 students in 710 schools)


Colleges

Very, Highly, Most Competitive

Colleges Any 4-Year

College

Model B Model B Model B Model 6 • Student AP Subject-Taking

Main Effect1 0.300 ** 0.189 ** 0.203 **

Interaction With Student SES -0.082 * -0.045 -0.029

Interaction With School SES 0.000 -0.024 0.056 Simple Slopes Conditioned on Student & School SES -1 SD 0.382 ** 0.259 ** 0.176 ** Conditioned on Student SES -1 SD School SES +1 SD 0.382 ** 0.211 ** 0.288 ** Conditioned on Student SES +1SD & School SES -1 SD 0.219 ** 0.168 ** 0.119 Conditioned on Student & School SES +1 SD 0.219 ** 0.120 ** 0.231 ** Model 7 • Student IB Subject-Taking

Main Effect1 0.182 ** 0.457 ** 0.167 † Interaction With Student SES -0.030 -0.124 * -0.022 Interaction With School SES -0.101 * -0.079 0.068 Simple Slopes Conditioned on Student & School SES -1 SD 0.314 ** 0.661 * 0.122 Conditioned on Student SES -1 SD School SES +1 SD 0.111 0.503 ** 0.257 Conditioned on Student SES +1SD & School SES -1 SD 0.253 ** 0.412 † 0.077 Conditioned on Student & School SES +1 SD 0.051 0.254 † 0.213 Model 8 • Sports Participation

Main Effect1 0.212 0.308 ** 0.588 ** Interaction With Student SES 0.061 0.204 † 0.146 Interaction With School SES 0.081 -0.066 0.115 Simple Slopes Conditioned on Student & School SES -1 SD 0.071 0.169 0.327 * Conditioned on Student SES -1 SD School SES +1 SD 0.232 0.038 0.558 ** Conditioned on Student SES +1SD & School SES -1 SD 0.192 0.577 ** 0.619 ** Conditioned on Student & School SES +1 SD 0.353 * 0.446 ** 0.850 ** Model 9 • Extracurricular Activities

Main Effect1 0.147 ** 0.114 ** 0.160 ** Interaction With Student SES -0.058 -0.071 * -0.012 Interaction With School SES 0.008 0.026 0.000 Simple Slopes Conditioned on Student & School SES -1 SD 0.197 * 0.159 ** 0.172 ** Conditioned on Student SES -1 SD School SES +1 SD 0.213 * 0.211 ** 0.172 ** Conditioned on Student SES +1SD & School SES -1 SD 0.081 0.016 0.149 * Conditioned on Student & School SES +1 SD 0.097 * 0.069 † 0.148 **

40

Table 5 (con’t) • HGLM estimates of effects of marks of distinction on college destinations, conditioned on student and school SES (ELS 2006; 9,880 students in 710 schools)Model 10 • Grades

Main Effect1 0.896 ** 0.942 ** 0.780 ** Interaction With Student SES -0.147 -0.101 -0.072 Interaction With School SES 0.039 0.075 0.205 ** Simple Slopes Conditioned on Student & School SES -1 SD 1.004 ** 0.968 ** 0.647 ** Conditioned on Student SES -1 SD School SES +1 SD 1.082 ** 1.118 ** 1.057 ** Conditioned on Student SES +1SD & School SES -1 SD 0.711 ** 0.765 ** 0.504 ** Conditioned on Student & School SES +1 SD 0.789 ** 0.915 ** 0.914 ** Model 11 • ACT / SAT Scores

Main Effect1 0.960 ** 0.967 ** 0.726 ** Interaction With Student SES -0.004 -0.066 0.044 Interaction With School SES 0.012 0.008 0.185 ** Simple Slopes Conditioned on Student & School SES -1 SD 0.952 ** 1.026 ** 0.497 ** Conditioned on Student SES -1 SD School SES +1 SD 0.976 ** 1.041 ** 0.867 ** Conditioned on Student SES +1SD & School SES -1 SD 0.944 ** 0.894 ** 0.586 ** Conditioned on Student & School SES +1 SD 0.968 ** 0.909 ** 0.955 ** NOTE: Coefficients from unit-specific, multi-level logistic regressions are presented. Simple slopes are calculated by rerunning the model with SES and school SES centered on different values. All models include controls for student AP and IB subject-taking, sports participation, extra-curricular activities, grades, ACT / SAT scores, an indicator for not taking ACT / SAY scores, school AP and IB subjects, sports offerings, school SES, school sector, school location, log school enrollment, region, 10th grade standardized test scores, race, sex, student 10th grade educational expectations, parental educational expectations, and 8th grade algebra course-taking.

1. Main effect is conditional on student SES being at its mean level. † p <= .10; * p < .05; ** p < .001; *** p < .0001

41

Table A1 • HGLM estimates of effects of programmatic resources on college destinations, conditioned on student SES, for students in neighborhood public schools (ELS 2006; 2,680 students in 240 schools)


Colleges

Very, Highly, Most


Any 4-Year College

Model A Model A Model A

Model 1 • Baseline Model Student SES 0.593 ** 0.365 ** 0.415 ** School SES 0.145 0.349 * 0.219 * School AP Subjects 0.039 0.057 * 0.017 School IB Subjects 0.074 0.043 0.008 Sports Offerings -0.147 -0.092 -0.050 Model 2 • School AP Subjects

Main Effect1 0.033 0.055 * 0.021 Interaction With Student SES 0.012 0.009 0.015 Simple Slopes Conditioned on Student SES -1 SD 0.021 0.047 0.006 Conditioned on Student SES +1SD 0.045 0.064 * 0.036 Model 3 • School IB Subjects

Main Effect1 0.097 * 0.054 * 0.008 Interaction With Student SES -0.037 -0.028 -0.005 Simple Slopes Conditioned on Student SES -1 SD 0.134 * 0.082 † 0.013 Conditioned on Student SES +1SD 0.060 0.027 0.003 Model 4 • Sports Offerings

Main Effect1 -0.160 † -0.097 -0.029 Interaction With Student SES 0.033 0.038 0.072 ** Simple Slopes Conditioned on Student SES -1 SD -0.193 † -0.135 † -0.102 * Conditioned on Student SES +1SD -0.127 -0.059 0.043 NOTE: Coefficients from unit-specific, multi-level logistic regressions are presented. Simple slopes are calculated by rerunning the model with SES centered on different values. All models include controls for school AP and IB subjects, sports offerings, school SES, school location, log school enrollment, region, 10th grade standardized test scores, race, sex, student 10th grade educational expectations, parental educational expectations, and 8th grade algebra course-taking. 1. Main effect is conditional on student SES being at its mean level † p <= .10; * p < .05; ** p < .001

42

0.1

.2.3

.4.5

.6.7

.8.9

1

Pro

babi

lity

0 5 10 15AP Subject Offerings

Low SES, 4-Year High SES, 4-Year

Low SES, Very-Most High SES, Very-Most

Low SES, Highly-Most High SES, Highly-Most

NOTE: High SES is a student whose family SES is 1 SD above the mean, and Low SES is a student whose family SESis 1 SD below the mean. Predicted probabilities calculated from Models 2A in Table 2. Probabilities calculated for a student whose 10th grade test scores are at the 90th percentile; who expects to obtain a BA degree, whose parents expect him/her to obtain a BA degree; who was enrolled in algebra in the 8th grade, and is at the mean for all other predictors.

Figure 1 - Effect of High School's AP Subject Offerings onCollege Destinations for Successful Students (ELS 2006)

0.1

.2.3

.4.5

.6.7

.8.9

1

Pro

babi

lity

0 2 4 6 8IB Subject Offerings


Low SES, Highly-Most High SES, Highly-Most


Figure 2 - Effect of High School's IB Subject Offerings onCollege Destinations for Successful Students (ELS 2006)

43

0.1

.2.3

.4.5

.6.7

.8.9

1

Pro

babi

lity

6 8 10 12 14Sports Offerings

Low SES, Four-Year High SES, Four-Year



Figure 3 - Effect of High School's Sports Offerings onCollege Destinations for Successful Students (ELS 2006)

0.1

.2.3

.4.5

.6.7

.8.9

1P

roba

bilit

y

0 1 2 3Subjects Taken

AP, Low SES, Very-Most

AP, High SES, Very-Most

IB, Low SES, Very-Most

IB, High SES, Very-Most

AP, Low SES, Highly-Most

AP, High SES, Highly-Most

NOTE: High SES is a student whose family SES is 1 SD above the mean, and Low SES is a student whose family SES is 1 SD below the mean.Predicted probabilities calculated from Models 6A & 7A in Table 3. Probabilities calculated for a student whose 10th grade test scores, SAT scores, and grades are at the 90th percentile; who expects to obtain a BA degree, whose parents expect him/her to obtaina BA degree; who was enrolled in algebra in the 8th grade, and is at the mean for all other predictors.

Figure 4 - Effect of AP & IB Subject-Taking onCollege Destinations for Successful Students (ELS 2006)

44

0.1

.2.3

.4.5

.6.7

.8.9

1

Pro

babi

lity

0 1 2 3 4Extracurricular Activities Participated In

Low SES High SES


Figure 5 - Effect of Extracurricular Participation on Enrolling in aVery-Most Competitive College for Successful Students (ELS 2006)

0.2

.4.6

.81

Pro

babi

lity

4-Year Very-Most Highly-Most

Low SES High SES Low SES High SES Low SES High SES


Figure 6 - Effect of Athletic Participationon College Destinations for Successful Students (ELS 2006)

Athlete Non-Athlete

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