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Social Capital in Schools: A Conceptual and Empirical Analysis of the Equity of Its Distribution and Relation to Academic Achievement


by Serena J. Salloum, Roger D. Goddard & Ross Larsen - 2017

Background: Schools face pressure to promote equitable student outcomes as the achievement gap continues to persist. The authors examine different ways in which social capital has been conceptualized as well as prior theory and research on its formation and consequences. While some theoretical and empirical work conceptualizes social capital as a mechanism for prosocial outcomes, other scholars address it as an apparatus of social status.

Purpose: This study was conducted to advance knowledge about (1) the validity of measuring social capital as an organizational construct, (2) the equity of social capital distribution in schools, and (3) the relationship between school social capital and academic achievement.

Research Design: In this paper, the authors examine these possibilities using data collected from 96 Midwestern high schools. Confirmatory factor analysis, hierarchical linear modeling, and structural equation modeling were employed to depict the relationships among social capital, socioeconomic status, and academic achievement in schools.

Findings/Results: The authors found that variance in social capital was significantly related to school membership and that confirmatory factor analysis supported the construction of a school social capital measure. Moreover, more than half of the variance in social capital is unrelated to social class, and social capital is a positive predictor of academic achievement.

Conclusions/Recommendations: Because of its positive relation to achievement, investments in the development of social capital may be worthwhile. Interventions designed to develop social capital in schools should be guided by efforts to strengthen access to school-based resources in poor and low achieving schools.




INTRODUCTION


One of the most pressing issues in American education is the unequal distribution of student outcomes. According to recent National Assessment of Educational Progress (NAEP) data, fourth-graders from low-income communities are three grade levels behind their high-income peers in reading and mathematics. Approximately half of these students will not graduate from high school, while those who manage to graduate will likely have reading and mathematics skills on par with a high-income eighth-grader (National Center for Educational Statistics [NCES], 2012). Typically, the quality of schooling to which students have access is strongly related to their zip code, and thus also their socioeconomic status (SES). Further, the achievement gap is present at “the starting gate” as children enter school (Hart & Risley, 1995; Lee & Burkam, 2002); in the aggregate, schooling often sustains these achievement gaps (Bowles & Gintis, 1976; Duncan & Magnuson, 2005).


Many scholars have investigated the underlying processes of social reproduction present in schooling that drive these relationships. Various explanations are plausible, ranging from school funding (Condron & Roscigno, 2003; Hanushek, 1989; Hedges, Laine, & Greenwald, 1994; Kozol, 1991; Roza, Hill, Sclafani, & Speakman, 2004), to teacher quality (Lankford, Loeb, & Wyckoff, 2002; Rivkin, Hanushek, & Kain, 2005), to school segregation (Massey & Denton, 1993; Orfield, 2001; Orfield & Lee, 2005), to quality of the curriculum (Anyon, 1981; Apple, 1990), to tracking (Lee & Bryk, 1988; Oakes, 2005) among many others. Less understood, but a possible contributing factor to such reproduction is the quality of the social relations to which students have access because of their schools. In this study, we conduct an empirical analysis of organizational social capital in high schools to understand whether teachers’ perceptions of social relationships matter to achievement and the degree to which such perceptions themselves are equitably distributed.


As a construct, social capital derives from an economic analogy, suggesting that people and groups may invest in and prosper from their social connections; in other words, social capital refers to the resources embedded in relationships. Social capital is a well-known construct in social science research, seemingly imbued with the potential to ameliorate many societal problems (Portes, 1998). Because of this potential, social capital has been conceptualized in a variety of ways: as a micro property of individuals (Furstenberg & Hughes, 1995), as a meso property of organizations (Coleman, 1990; Croninger & Lee, 2001; Small, 2009; Stanton-Salazar, 1997), and even as a macro property of neighborhoods and nations (e.g., Coleman, 1990; Garnier & Raudenbush, 1991; Putnam, 2001). While the vast majority of work on social capital conceptualizes it as a personal attribute (Portes, 1998), we agree with Coleman (1990) and others that social capital is also an organizational property, and specifically that it is an attribute of schools. Such parallel conceptual treatments are common in the social sciences (e.g., Bryk & Schneider, 2002; Goddard & LoGerfo, 2007; Hoy & Sabo, 1998) with wealth, for example, existing both as individual and group characteristic (neighborhood, nation, etc.). Similarly, Bandura (1997) has conceptualized efficacy beliefs as both an individual attribute (i.e., self-efficacy) and as a group property (i.e., collective efficacy). A key point in Bandura’s work is that the sum of the individual efficacy beliefs of a team of group members is not necessarily the same as those individuals’ beliefs about collective capability. This argument was supported by Goddard and LoGerfo (2007), who showed empirically that teacher reports of collective responsibility were significant predictors of differences among schools in student achievement, whereas aggregates of individual responsibility perceptions were not related to differences among schools in achievement. Following these findings, and building on the work of Goddard (2003), who conceptualized social capital as a school property, we also conceptualize social capital as a school attribute capable of explaining differences among schools in student achievement. Therefore, the questions driving this paper ask about the causes and consequences of organizational-level social capital, with a particular emphasis on the extent to which social capital 1) can be measured validity at the organizational level, 2) is predicted by socioeconomic status, and 3) predicts student-learning differences among school organizations.


LITERATURE REVIEW


Schools rely on social relationships among actors to facilitate outcomes. Most prominent are the relationships present between teachers and students, which are critical to student growth, learning, and development. Because schools are one of the most ubiquitous organizational structures found in society, they provide rich context to understand how social capital might translate into outcomes for youth. Consistent with contemporary work on this topic, we consider the concept of organizational embeddedness (Small, 2009) in an educational context or how a child’s access to social capital depends on the institutional practices of the school. Small (2009) describes how individuals form and sustain ties; he argues that no context for relationship building is more important than the organizational context, to which we attend in this study.


Not only do researchers consider social capital at a variety of levels, but the implications of the construct also vary. On the one hand, a line of inquiry has strongly highlighted the potential of social capital, as a consequential form of social organization, to positively impact important educational outcomes for youth (Coleman, 1988, 1990; Croninger & Lee, 2001; Goddard, 2003; Pong, 1998). On the other hand, some scholars consider social capital so deeply embedded in social and economic organization as to heavily influence the probabilities youth face, for better or worse, based on their background and context (Bourdieu, 1986; Granovetter, 1985; Lin, 2000; Loury, 1977; Ream, 2003).


Because these literatures rarely intersect (Dika & Singh, 2002), we designed this study to consider both perspectives in an organizational context. In addition, most other studies investigating social capital fail to account for relationships between teachers and families (students and parents) (Dika & Singh, 2002), which is surprising given the potential for relationship building in light of the considerable time adolescents spend in school. To fill this gap, this paper reports empirical evidence concerning two contrasting views of the impact of organizational social capital on academic success. While most scholars investigate social capital as a positive attribute consistent with Coleman (1988), others theorize that social capital is an outcome of socioeconomic status and that its positive influences are, like wealth, inequitably distributed. This paper offers a unique contribution to the literature because we provide empirical data to test the theoretically possible positive and negative associations among organizational-level social capital, SES, and student outcomes in high schools. The purpose of this analysis is to consider social capital as an organizational property of schools and thus to understand better the degree to which it is a mechanism for advancement, social reproduction, or both. In other words, to what extent is social capital distributed equitably across high schools, and how does the distribution of such social resources facilitate or inhibit educational outcomes? Specifically, we ask both whether social capital predicts academic achievement and the degree to which social capital itself may be explained by contextual factors.


We begin with a consideration of social capital in the promotion of favorable educational outcomes, and then examine how social capital may also inhibit equity. We argue that neither perspective on social capital is complete in an educational context, as access to relational networks, trust, and supportive norms may vary significantly by school. We conclude with a rationale for the hypotheses we test in this work.


SOCIAL CAPITAL IN THE PROMOTION OF DESIRABLE OUTCOMES


Previous research has highlighted the importance of social capital in improving student outcomes (Coleman, 1990; Putnam, 1993). Just as individuals benefit from various forms of physical and human capital, so too can social capital enable the achievement of important outcomes. Consistent with Coleman’s formulation of the construct, Putnam (1993) described social capital as the "features of social organization, such as, trust, norms, and networks that can improve the efficiency of society by facilitating coordinated actions" (p. 167). According to Coleman (1990), social capital has both structural and functional forms. Social structure refers to the array of social relationships that connect individuals within and across social contexts. In addition to structure, functionality is also important. That is, the relationships that connect individuals are more productive when characterized by high levels of social trust and normative expectations that support prosocial goal achievement.


Although this study relies on a comprehensive definition of social capital that emphasizes social trust, norms, and relational networks, it is informative to also consider the results of previous research on the effects of each of these forms of social capital in isolation. Outside of education, for example, Granovetter (1985) showed that a dense array of social networks facilitates occupational mobility for individuals. Within education, several researchers have shown that social trust is important to academic outcomes (Bank, Slavings, & Biddle, 1990; Bryk & Schneider, 2002; Goddard, 2001; Goddard, Salloum, & Berebitsky, 2009; Jones & Maloy, 1988; Lareau, 1987; Lee & Croninger, 1994). Finally, the importance of supportive norms to academic achievement is indicated by research that shows a normative emphasis on academic success is positively and significantly related to differences among schools in student achievement in covariate-adjusted models (Goddard, Sweetland, & Hoy, 2000; Hoy, Smith, & Sweetland, 2002).


Scholars have also found that social capital, conceived of as parental involvement, has a positive relation to student achievement (Pong, 1998; Sui-Chu & Willms, 1996) and high school graduation (Furstenberg & Hughes, 1995; Teachman, Paasch, & Carver, 1996). Not only is social capital related positively to educational outcomes in the K–12 environment, but in higher education, strong parent–child relationships have been related to both college enrollment (Perna & Titus, 2005) and persistence (Bank et al., 1990).


Common across these studies is how factors beyond the quality of classroom instruction influence individual students’ educational outcomes. These examples treat social capital as a kindred property and demonstrate how families foster positive outcomes. However, such literature does little to enhance understanding of how the social capital resources contributed by schools may or may not support children’s academic success. For this reason, we consider the social capital created by schools and how such resources inhibit or enhance educational outcomes.


Scholars contributing to this line of inquiry tend to collect data from teachers and counselors among other educational actors as evidence of social capital in educational organizations. For example, Goddard (2003) found that urban elementary schools with high levels of social capital, conceptualized in terms of norms, social networks, and trust, had higher odds of children passing state-mandated mathematics and writing assessments than schools with lower levels of social capital. Building on this work, Leana and Pil (2006) discovered that both internal and external forms of social capital improved performance at the organizational level in 88 urban public schools—irrespective of grade level. Similarly, Croninger and Lee (2001) analyzed teacher–student relations as well as “student-teacher talks,” as forms of institutional support and linked such support to graduation. The researchers discovered that this particular form of social capital reduced the odds of a high school student dropping out of school by nearly half. Moreover, Croninger and Lee found that the apparent beneficial effects of social capital were greater for students living in poverty and for students who had experienced academic difficulties in the past than for their relatively advantaged counterparts. Such findings are consistent with work by Goddard et al. (2009), who suggested that trust—a key facet of social capital according to Coleman (1990) and Putnam (1993)—moderates the relations between social disadvantage and academic outcomes.


Other scholars considered specific actions of institutional agents other than teachers as a form of social capital and demonstrated the relationship to educational outcomes. For example, Stanton-Salazar (2011) recently defined an institutional agent as “an individual who occupies one or more hierarchical positions of relatively high-status, either within a society or in an institution (or an organization)” (p. 17). Stanton-Salazar (1997) made the case that for Latina/o youth, teachers and counselors are key institutional agents who give students access to social capital by providing students information regarding the opportunities schooling presents. In Stanton-Salazar’s words, “research provides no substantial evidence that academically immigrant youth ‘make it’ without significant institutional support from school-based institutional agents” (1997, p. 33). Therefore, successful socialization among minority youth entails learning to decode the educational system, and for students who lack such resources in the home, school-based assistance is critical.


Stanton-Salazar’s ideas were built upon in a qualitative study by Farmer-Hinton and Adams (2006). The researchers examined the role of the academic counselor in a charter school serving a predominately Black population, with nearly 90% of students qualifying for free and reduced lunch. Much of the social support at this particular school was provided through the counseling office, yet counselors who were hired at this school did not serve in a traditional way. Counselors operated “as advocates for the student population” (p. 107). In this role, counselors not only provided advice about appropriate curricular choices, but connected students to resources beyond the walls of their high school through social service referrals and assistance in college searches and application processes.


Other scholars have also considered how social capital operates in a school setting in ways that help explain its impact on student achievement. For example, Leana and Pil (2006) demonstrated that social capital is related to instructional quality. In particular, when teachers are working on instructional teams with strong group ties, students tend to perform better (Pil & Leana, 2009). In addition, Penuel, Riel, Krause, and Frank (2009) closely examined the social networks of two schools in a mixed-method study to understand the role of social capital in fostering instructional improvement. To this end, the researchers provided indirect evidence that teachers’ social capital was important in facilitating teachers’ instructional change. Together, these studies suggest that social capital may work in part to improve achievement by tightening the connections and collaboration among teachers around instructional improvement.


Not all work on social capital, however, supports the view that it always works to cultivate positive outcomes for disadvantaged students or to facilitate group functioning in ways that lead to positive growth for all members. We turn to these considerations next.


SOCIAL CAPITAL IN THE PERPETUATION OF INEQUITY


As our review demonstrates, a great deal of scholarship in education presents social capital as a critical resource that can facilitate valued outcomes in multiple contexts, and one that may be particularly beneficial to adolescents whose backgrounds are characterized by one or more factors often related negatively to educational success (e.g., Croninger & Lee, 2001; Pong, 1998). However, social capital also has the potential to reinforce dominant and inequitable norms through its symbolic power. Moreover, Bourdieu (1986) asserts that social capital interacts both with economic and cultural capital and that networks are not recreated by organizations but rather are the product of institutions, which, among their many patterns of isomorphism, tend to reproduce inequality. In other words, the social capital to which one has access and the resources this affords derive from the social status of the groups to which one belongs. That is, social capital can serve as a barrier to individuals changing class position. From this perspective, the value of one’s social capital is dependent on one’s social class and, thus, can make it difficult for youth to achieve the social mobility that Labaree (1997) describes as a key goal of public education. This view contends that regardless of the closeness of social networks and the strength of norms of reciprocity, one’s economic capital may limit the potential of social capital to confer prosocial benefits.


Lin (2000) explains two reasons why social capital can further inequality between groups. First, groups have access to differential social standing in a society based on a number of ascribed characteristics. Depending on the particular society, status can be based on race, social class or wealth, caste membership, lineage, religious affiliation, and a number of other socially constructed group distinctions (Van Laar & Sidanius, 2001). Different societies offer unequal opportunities to individuals based on the status of social group membership. Second, the principle of homophily suggests that individuals tend to interact and share sentiments with others of similar characteristics (Homans, 1958; Marsden & Hurlbert, 1988). These two key ideas are rationales for why exploration of social capital in schools is so critical. For example, as the United States becomes increasingly more diverse (culturally, economically, and linguistically), the teaching force remains homogenous. Kober (2010) reports that more than 80% of the teaching force is white and 75% is female; this is in contrast to a student body where 45% are eligible for subsidized lunch, 40% are minority, and 10% are English language learners. The student population is projected to continue to diversify (NCES, 2013). Given that American schools are highly segregated (Massey & Denton, 1993; Orfield, 2001; Orfield & Lee, 2005), the principle of homophily suggests that intentional efforts at the organizational level to facilitate relationships between teachers, families, and students may result in the forms of social capital that can convey benefits to students.


However, research also illustrates that in some cases the social capital that is exchanged is negative. For example, Ream demonstrated the concept of “counterfeit” social capital in terms of school success; that is, not all relationships with institutional agents are converted into beneficial outcomes for students. Utilizing mixed methods, Ream (2003) elucidated that social network instability accompanying high mobility contributes to Mexican-American underachievement. Ream provided a salient illustration in which a Mexican-American student complained of a headache and the teacher allowed the student to put her head down. Ream explained, “teachers sometimes ameliorate potential classroom conflict by accommodating their expectations and instructional efforts to disengaged students” (p. 252). In other words, simply having a relationship with a teacher is not enough; the interactions between student and teacher as well as the norms, which are communicated through such interactions, are pivotal. At the time of this review, though many have theorized about the negative impact of social capital, we were unable to locate any further examples illustrating the detrimental impact of organizational social capital in schools.


Summary


Our review suggests that while it may be true that those of higher social status have greater access to forms of social capital that support school success, schools may be uniquely positioned to ameliorate this relationship by purposefully working to provide strong social support to the students who need it most. Indeed, positive forms of social capital are not a naturally occurring phenomenon (Bourdieu, 1986; Portes, 1998); instead, social capital must be created and nurtured through personal and group relations. Thus, schools may be intentional in creating opportunities for the development of social capital. The purpose of this research is to examine the conceptualization and measurement of social capital at the organizational level as well as to test the relationships among social capital, sociodemographic features of schools, and academic achievement. Because of the importance of cultural and economic resources, our design includes attention to the relationship between SES and social capital.


RATIONALE FOR HYPOTHESES


Our review of the extant literature reveals several studies suggesting organizational social capital is positively associated with valued outcomes for students. Among these, some authors argue that the benefits of social capital may be most important for our least advantaged students (Croninger & Lee, 2001; Stanton-Salazar, 1997) and that its effects may offset those associated with some forms of disadvantage (Pong, 1998). At the same, time we acknowledge the argument that social class may play a key role in explaining the social capital to which one has access (Bourdieu, 1986), and that mobility in some poor communities may regularly erode forms of social capital that support academic achievement (Ream, 2003). Thus, if those of higher social class use their relationships to preserve social advantage, social capital may play a role in perpetuating inequity for the very adolescents contemporary accountability policy is intended to benefit the most.


In sum, social capital matters to students’ educational experiences. When relationships between teachers and students are characterized by mutual respect and trust, the educational process may become more efficient. In such cases, strong social capital likely facilitates student engagement and develops a normative environment that supports learning. When teachers in a school have open communication and are in frequent contact with parents, the values between home and school could become more consistent and supportive in fostering outcomes for students. At the same time, some schools may put forth barriers to involvement that restrict access and communication for those not in socially advantaged groups. Given these complexities, we designed our study to examine the validity of measuring social capital as an organizational construct. In addition, we ask about the degree to which social capital is inequitably distributed, and whether its presence makes a difference above and beyond that of social class in explaining adolescents’ academic success. Specifically, we ask the following three research questions: 1) Does evidence exist to measure social capital with validity at the organizational level? 2) To what extent are levels of social capital explained by school-level socioeconomic status? and 3) Does social capital have a significant relationship with academic achievement after accounting for the influence of prior achievement and school sociodemographic background including socioeconomic status? These questions are represented by the following hypotheses:


H1: Validity evidence supports the measure of social capital at the organizational level.

H1A: The between-school variance component (τ) for social capital is statistically significant.

H1B: The fit statistics are adequate to measure social capital as a latent construct at the organizational level.

H2: There is a statistically significant and negative relationship between school socioeconomic status and the level of social capital characterizing schools.

H3: There is a statistically significant and positive relationship between school-level social capital and academic achievement after accounting for school sociodemographic background characteristics.

We turn next to the method we employed to test these hypotheses.


METHOD


This section describes the sample, measures, and analytic method employed to test the hypotheses described above.


SAMPLE


The population of schools eligible for sampling in our study included the noncharter public high schools in one large Midwestern state. One hundred forty-nine high schools (both 9–12 and 10–12) were originally selected for inclusion in the study and 96 ultimately agreed to participate (64%). Although we did not draw our sample randomly, we made concerted efforts to select schools for inclusion in the sample from across the range of urban, rural, suburban and socioeconomic contexts found in the state. In fact, data from the state department of education support the representativeness of the sample in terms of SES and urban–rural balance.1


Data were collected from school faculties during regularly scheduled staff meetings. Only schools with 15 or more faculty members were considered for the sample. A trained researcher administered surveys that contained the social capital scale described below.


Measures


The 11-item scale utilized to measure social capital in this study was the same one employed in a study of social capital by Goddard (2003). Teachers responded to each survey item with Likert-type responses scaled from 1 (strongly disagree) to 6 (strongly agree). All three elements of social capital theory (norms, networks, and trust1), consistent with Coleman’s framework, are tapped by this measure (see Table 1 for items). Questions were designed to measure the organizational construct of social capital as opposed to individual measures of social capital aggregated to the school level. For example, a sample item from the scale is “Teachers in this school have frequent contact with parents.” This item requires teachers to make judgments about the behaviors of colleagues rather than referencing themselves (e.g., I have frequent contact with parents). As demonstrated by Goddard and LoGerfo (2007), framing items with the organizational referent is more predictive of organizational effectiveness. The social capital scale was administered to a random set of half2 of the teachers in each school (the other half received a different survey). The number of responses in each school ranged from 5 to 33 (mean = 12.06; SD = 6.53). Based on average school size and class size, the average number of faculty sampled per school schools was approximately 15. Thus, the survey was completed by approximately 80% of the random sample of teachers who received it. Further checks verified that the schools with lower numbers of respondents also had smaller sizes and in all cases teacher response rates were above 50%. Notably, other large-scale research projects have succeeded in identifying important school-level factors with even lower overall sampling rates including, for example, the study by the Consortium on Chicago School Research, which administered a different survey to each third of school faculties (Bryk, Sebring, Allensworth, Luppescu, & Easton, 2010).


Table 1. Social Capital Scale Items



Strongly Disagree



Strongly Agree

 

1    2    3    4    5    6

Teachers in this school have frequent contact with parents

  

Parental involvement supports learning here

  

Community involvement facilitates learning here

  

Parents in this school are reliable in their commitments

  

Teachers in this school trust their students

  

Students in this school can be counted on to do their work

  

Students are caring toward one another

  

Parents of students in this school encourage good habits of schooling

  

Students respect others who get good grades

  

The learning environment here is orderly and serious

  



Data on SES, urbanicity, school size, and achievement for each high school were collected from the state department of education. School-level student achievement is measured as the proportion of students who passed the state-mandated 12th-grade mathematics and reading assessments. These assessments were mandated by the state department of education as part of an accountability framework designed to comply with No Child Left Behind (NCLB). Importantly, the state documented adequate internal consistency for scores on the dependent measures of mathematics and reading employed here. Finally, 12th-grade students took these assessments approximately one to two months after school faculties completed the social capital surveys. These data were collected and publicly reported by the state as part of its school accountability framework. The proportion of students passing the 10th-grade mathematics and reading assessments 2 years earlier served as prior achievement controls. Less than 3% of the reading and mathematics data were missing.


ANALYTIC METHOD


To begin these analyses, we calculated Cronbach’s alpha for the aggregated social capital items to ensure reliability. We also performed a confirmatory factor analysis (CFA) to ensure that the items captured social capital as a latent school property.


CFA


To assess whether the items we used to measure social capital (taken from Goddard, 2003) had empirical support for representing a single latent construct at the organizational level, we employed CFA. An advantage of CFA as compared to exploratory factor analysis (EFA) is that statistics indicating model fit are generated. These fit statistics (as discussed below) provide analytical evidence regarding the degree to which items within the CFA capture a latent construct, whereas in EFA such fit statistics are unavailable. Finally, when a strong theoretical rationale for the combination of the observed variables to produce one latent measure is warranted as in the case of social capital, CFA is the preferred analytic technique.


Descriptive statistics. After creating the latent variable of social capital, we calculated descriptive statistics for each of the observed variables used in our study and the correlations among all of these variables.


Intraclass correlation. Because our school-level measure of social capital is based on responses obtained from teachers, we were able to capitalize on the nested nature of these data by employing multilevel modeling to decompose the variance in social capital into its within- and between-school components. Such an analysis was possible because our measure of social capital was based on teacher-level survey responses; thus, the level 1 outcome was individual teacher’s perceptions of social capital in their respective school. This portion of the analysis allowed us to assess the appropriateness of treating social capital as an organizational characteristic, in further analysis. We assessed this by examining the magnitude of the between-school variance component (τ) for social capital and whether it was statistically nonzero.


Structural Equation Modeling (SEM). Because our hypothesized conceptual model involves several structural relationships as well as a latent variable, we employed structural equation modeling (SEM) as the primary analytic method (see Appendix A for an explanation). The hypothesized structural relationships implied by our hypotheses are presented in Figure 1.


Figure 1. SEM of Social Capital and School Achievement

[39_21811.htm_g/00002.jpg]


RESULTS


SOCIAL CAPITAL AS A LATENT ORGANIZATIONAL CHARACTERISTIC


Coleman (1990) parsed out three components of social capital: norms, networks, and trust. For our CFA, we created four parcels from the three theoretical categories of social capital. The first two parcels were: 1) normative behavior, 2) relational networks, and we divided trust into two separate parcels: 3) trust in parents, and 4) trust in students. Although other referents of trust are potentially relevant to the study of social capital (e.g., trust in teacher colleagues, trust in the principal, students’ trust in their teachers), we were limited to these variables to draw from based on the availability of measures in our survey.


Because Cronbach’s alpha was strong (.95), we proceded with a CFA. The fit of the CFA was excellent (χ2, df=3.13, CFI=.988, TLI=.964), which exceeds or is lower than the standard cutoff values of <8 for the chi-square statistic (Marsh & Hocevar, 1985), >.9 for CFI (Bentler, 1990) and >.9 for TLI (Bentler & Bonett, 1980) respectively. The root mean square of approximation (RMSEA) was a little high (.15) but a 90% confidence interval (.022, .289) overlapped the standard cutoff value of .08 (Browne & Cudeck, 1993). The standardized factor loadings are located in Table 3. Because the CFA fit well, we concluded that a single factor model for social capital was appropriate. Additionally, because the factor loadings were similar in magnitude, each of the parcels contributes more or less equally to teachers’ perceptions of school-level social capital.


Descriptive Results


After the CFA, we conducted a descriptive analysis to understand the basic relationships present in our data. To facilitate interpretation of the results, all variables employed in the analyses were standardized (mean = 0, sd = 1). Descriptive statistics and correlations among the variables are reported in Tables 2 and 3. Data indicate that mean scores for urbanicity and SES closely match means and standard deviations for the state’s population of secondary schools on these variables.


Table 2. Descriptive Statistics (n=96 schools)

Variable

 

Min

Max

Mean

SD

10th-Grade Mathematics Achievement

 

38.3

100.0

81.49

11.45

12th-Grade Mathematics Achievement

 

13.3

83.4

52.62

14.57

10th-Grade Reading Achievement

 

74.0

100.0

94.70

4.64

12th-Grade Reading Achievement

 

41.7

94.6

68.24

10.76

Social Capital

 

-2.54

2.49

0.00

0.98

SES

 

-1.21

3.59

-0.01

0.91

Urbanicity

 

-2.07

2.09

-0.02

0.96

School Size

 

150.00

2,156.00

730.33

456.04


Table 3. Correlations (n=96 schools)

Variable

Social Capital

 

School Size

-.10

 

SES

.27

**

Urbanicity

-.17

 

10th Math

.55

***

12th Math

.66

****

10th Read

.34

****

12th Read

.62

****

~ p<.1, * p<.05, ** p<.01, *** p<.001


INTRACLASS CORRELATION ANALYSIS OF SOCIAL CAPITAL


We conducted a fully unconditional model multilevel model with only the teacher-level social capital variable as an outcome whereby we learned that 29% of the variance (or ICC) in social capital lies between schools, which is a considerable amount given many analysts identify less between-school variance in even student achievement (Goldstein, 1986; Morgan & Sørensen, 1999). Given the ways in which accountability policies hold schools responsible for student learning, we argue that it is important to study a school characteristic that varies greatly among schools and that is also theoretically important to student achievement. In addition, the chi-square statistic for the between-school variance component was statistically significant (nonzero). Thus, with such a high and statistically significant ICC, we aggregated the data to the school level and consider social capital as a latent school characteristic.3


SEM


There are several assumptions that are needed in order to have a valid SEM: normality of the endogenous variables, linear relationships between the variables, independence, absence of outliers, and very low missing data or multiple imputation to deal with the missing data . This dataset had no missing data at the school level; histograms and scatterplots of the endogenous variables and their relationships with the covariates were examined and no large departures from normality, outliers, or nonlinear relationships were detected.


To begin our SEM analysis, we added the covariates (SES, size, urbanicity, and prior achievement) to the model with paths from the covariates to both the 12th-grade achievement and social capital. This allowed us to model the extent to which social capital was predicted by SES and other measures of school context, as well as whether social capital made a unique positive contribution to the explanation of school achievement after accounting for the influence school SES, size, urbanicity, and prior achievement. Results of the SEM provide support for both of our hypothesized relationships.


The results from the SEM showed that the model fit well (χ2, df= 1.923, CFI=.963, TLI=.937). The RMSEA was a little high (.100) but a 90% confidence interval overlapped the standard cutoff of .08. Our discussion of these results is divided into two sections that address the prediction of social capital and student achievement, respectively.

 


Table 4. Social Capital Standardized Factor Loadings (n=96 schools)



Parcel

Standardized Factor Loading

Normative behavior

.93

Relational networks

.89

Trust in parents

.91

Trust in students

.86


PREDICTING SOCIAL CAPITAL


The first stage of our model examined the degree to which social capital was predicted by school demographic characteristics and prior achievement. Only prior achievement and SES emerged as statistically significant predictors of the latent social capital variable across both the mathematics and reading models. Specifically, a 1-SD increase in SES predicted increases of .41 SD and .53 SD in social capital in the mathematics and reading models, respectively. Urbanicity was a statistically significant negative predictor of social capital in the reading model (ES = -.36) while the effect of school size was not significant in either model. These results are reported in Table 5.


Table 5. School Context as a Predictor of Social Capital (n=96 schools)

 

Math Model

 

Reading Model

 

Standardized β

S.E.

 

Standardized β

 

S.E.

School Size

-.11

 

.12

 

-.08

 

.13

SES

.41

***

.10

 

.53

***

.12

Urbanicity

-.20

 

.12

 

-.36

***

.13

Past Math Achievement

.46

***

.08

 

NA

 

NA

Past Reading Achievement

NA

 

NA

 

.26

**

.10

R2

.42

***

  

.30

***

 

~ p<.1, * p<.05, ** p<.01, *** p<.001


PREDICTING 12TH-GRADE ACHIEVEMENT


The second stage of our model examined the degree to which social capital was predictive of student achievement after controlling for demographic context and prior achievement. Consistent with our main hypothesis, social capital was a positive and statistically significant predictor of both the 12th-grade mathematics and 12th-grade reading pass rates. Specifically, a 1-SD increase in social capital was associated with an increase of .33 SD in 12th-grade mathematics pass rates and an increase of .51 SD in 12th-grade reading achievement. In addition to social capital, prior 10th-grade achievement and SES were also statistically significant predictors of both mathematics and reading achievement. Finally, neither school size nor urbanicity were significantly related to mathematics or reading achievement in 12th grade. In sum, the model explained 72% and 46% of the variance for 12th-grade mathematics and reading, respectively. These results are reported in Table 6.


Table 6. School Context and Social Capital as Predictors of Student Achievement (n=96 schools)

 

Mathematics

 

Reading

 

Standardized β

Standard Error

 

Standardized β

Standard Error

School Size

.11

!~

.06

 

.08

 

.07

SES

.27

 **

.08

 

.21

 *

.08

Urbanicity

-.04

 

.08

 

-.09

 

.13

Past Math Achievement

.52

 ***

.08

 

NA

 

NA

Past Reading Achievement

NA

 

NA

 

.21

 ***

.06

Social Capital

.33

 ***

.08

 

.51

 ***

.10

.72

 ***

  

.46

 ***

 

~ p<.1, * p<.05, ** p<.01, *** p<.001


Finally, Table 7 reports tests of the statistical significance of the indirect paths implied by our model. Notably, both SES and prior achievement are statistically and significantly related to current achievement through their relationships with social capital whereas urbanicity is significantly and negatively related only to reading achievement indirectly through its relationship with social capital. Thus, while urbanicity was not a significant direct predictor of reading achievement, it was related to reading achievement through its negative relationship to social capital.


Table 7. Indirect Effects of School Context Through Social Capital on Student Achievement (n=96 schools)

 

Mathematics

 

Reading

 

Standardized β

Standard Error

 

Standardized β

Standard Error

School Size

-.04

!

.04

 

-.04

 

.07

SES

.14

 **

.05

 

.27

 **

.09

Urbanicity

-.07

 

.04

 

-.18

 **

.07

Past Math Achievement

.15

 **

.05

 

NA

 

NA

Past Reading Achievement

NA

 

NA

 

.13

 **

.05

~ p<.1, * p<.05, ** p<.01, *** p<.001


OVERALL RESULTS


Thus, through our results, we were able to confirm our hypotheses. Social capital is important at the school level for predicting student reading and mathematics scores above and beyond other important demographic characteristics of schools.


We turn next to a discussion of the significance of our findings for theory, practice, and future research.


DISCUSSION


Our study examined the conceptualization and operationalization of social capital at the organizational level and two very different perspectives on its role in the promotion of desirable outcomes. We found that social capital varies significantly with school membership and its measure at the school level was supported strongly by a CFA. Further, on the one hand, a great number of scholars have shown that social capital is positively related to the achievement of important academic outcomes for students and schools even after accounting for the effects of sociodemographic background and prior achievement. Our findings are consistent with such prior research, supporting Coleman’s (1988, 1990) social theory and description of social capital as a resource that can support academic achievement. On the other hand, while social capital may promote valued outcomes, our results also showed that social capital itself is not equitably distributed. To the extent that social capital is partly a function of social class, then it may serve in part to reinforce dominant and inequitable norms (Bourdieu, 1986; Granovetter, 1985; Lin, 2000; Loury, 1977; Ream, 2003).


Thus, even though social capital was a positive predictor of student achievement, low achieving and poor schools, on average, had lower levels of social capital to draw upon as compared to their higher achieving nonpoor peers. Given these results, neither the position that social capital is a proxy for social class nor that it can ameliorate the negative relation between social class and academic achievement provides a wholly accurate understanding of the distribution and effects of social capital across schools. Rather, each perspective finds partial merit in the results. This suggests that interventions designed to develop social capital in schools should be guided by deliberate efforts to strengthen access to school-based resources, particularly in poor and low achieving schools.


It is also critical to recognize that our results indicate that approximately 60–70% of the variation across schools in social capital is unrelated to SES and prior achievement. That is, social class did not explain the majority of variation among schools in social capital. Although we acknowledge that our measure of SES may not fully capture the social class of the schools we studied, there is no evidence here to support the expectation that the inclusion of some ideal measure of social class would allow us to predict all of the variation in social capital and thus render the strength of social relations characterizing a school community unimportant to the outcomes adolescents experience once we account for their social class. Indeed, to adopt such a perspective would be to choose a deterministic interpretation grounded in a deficit model that suggests schools are incapable of operating in ways that provide high levels of social capital to youth living in poverty.


The results seem to provide a specific challenge for those interested in increasing equity in schools. Our finding that the level of social capital characterizing schools is partly independent of school context and prior achievement provides hope that schools can organize in ways that provide social resources that benefit all students regardless of social class. The key issue is that although social capital appears to make an independent contribution to academic achievement, the relation we detected between SES and social capital is still not desirable. The challenge for researchers and school reformers interested in promoting equity is to understand better how social capital might be developed and more importantly, how it can be promoted in schools serving large proportions of students living in poverty.


According to Small (2009) and Stanton-Salazar (1997), by connecting students, families, and resources, school agents can broker a form of social capital that provides students and their families with access to the myriad advantages schools confer. In our study, schools with stronger reports of connecting teachers, parents, and students had higher average levels of achievement in our study. Based on this, researchers might wish to investigate the efficacy of programs that connect parents and community members with schools for developing social capital. For example, the Harlem Children’s Zone provides services from early childhood through college to children and families; however, most of the studies of this intervention focus on student achievement as opposed to the impact of the program on social capital (see, for example, Dobbie & Fryer, 2009). Researchers may be interested in examining the social capital outcomes of such integrated systems apart from achievement.


Not only might we consider how to connect adolescents and families to outside organizations, intentional efforts inside schools to connect institutional agents to students and parents may also have the power to enhance students’ access to social capital. Such efforts should be carefully designed to facilitate strong relational ties with attention to how actors interact, including, as suggested by Small (2009), the duration, frequency, and intensity of such relationships. That is, such work might attend to how efforts to support teacher–parent and teacher–student relationships can be authentic and sustained as opposed to superficial and temporary. Although we did not investigate such development efforts, future researchers may wish to do so.


Importantly, we are heartened by the evidence found here that the majority of variance in social capital across schools is not a function of school sociodemographic background. This finding supports the conclusion that the level of social capital in schools is partly independent of social class; thus, schools may in fact already play a role in equalizing access to social capital. This perspective is strengthened when coupled with our finding that social capital makes a unique positive contribution to academic achievement after adjusting for the direct relationship between school background factors and academic achievement. Nevertheless, a key challenge for reformers is to further reduce the link between social class and social capital while simultaneously strengthening social relations for the benefit of all students. For example, although our research did not focus on leadership, future researchers may wish to consider whether what we know about the importance of leadership to school organization and instructional improvement (see Marzano, Waters, & McNulty, 2005) can be extended to understand how leaders can support the development of social capital, particularly as a means of improving achievement and the equity of its distribution.


Social capital theory offers a way to think about the potential of social relationships for conferring benefits as we have demonstrated here. However, a limitation of this work is that it does not describe the actual structure or social patterns responsible for the varying levels of social capital present in the schools we studied. Thus, the potential of social network analysis coupled with social capital theory also provides an opportunity for deeper understanding of such resource development in future research (Moolenaar, 2012). At a minimum, our results suggest that while social capital does vary somewhat with the SES of school organizations, social capital also explains variation among schools in student achievement above and beyond that explained by SES. Future researchers may therefore wish to understand how factors such as leadership and relational network structure can reduce the ability of social capital to perpetuate disadvantage by providing access to school-based success to all children, particularly those least likely to receive such support without schools.


Notes


1. The measures of trust employed here are limited to teachers’ perceptions of trust in students and parents. Although teachers’ perceptions of other forms of trust (in colleagues or the principal) as well as student and parent perceptions are potential indicators of social capital, these questions were not asked and only teachers were surveyed. Even with this potential limitation, the measure of social capital employed here is consistent with Coleman and Putnam’s formulation of the construct as the trust, norms, and relational networks characterizing an individual or group.

2. We did not attempt to follow up with teachers who may have been absent the day the survey was administered.

3. Note that the multilevel modeling was employed only to test the ICC of the social capital variable.


References


Anyon, J. (1981). Social class and school knowledge. Curriculum Inquiry, 11(1), 3–42.


Apple, M. W. (1990). Is there a curriculum voice to reclaim? Phi Delta Kappan, 71(7), 526–530.


Bank, B. J., Slavings, R. L., & Biddle, B. J. (1990). Effects of peer, faculty, and parental influence on students’ persistence. Sociology of Education, 63, 208–225.


Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107(2), 238–46.


Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin, 88(3), 588–606.


Bourdieu, P. (1986). The forms of capital. In J. G. Richardson (Ed.), Handbook of theory and research for the sociology of education. New York, NY: Greenwood Press.


Bowles, S., & Gintis, H. (1976). Schooling in capitalist America: Education and the contradictions of economic life. New York, NY: Basic.


Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 136–162). Newbury Park, CA: Sage Publishing.


Bryk, A. S., & Schneider, B. (2002). Trust in schools: A core resource for improvement. New York, NY: Russell Sage Foundation.


Bryk, A. S., Sebring, P. B., Allensworth, E., Luppescu, S., & Easton, J. Q. (2010). Organizing schools for improvement: Lessons from Chicago. Chicago, IL: University of Chicago Press.


Coleman, J. S. (1988). Social capital in the creation of human capital. American Journal of Sociology, 94, S95–S120.


Coleman, J. S. (1990). Foundations of social theory. Cambridge, MA: Harvard University Press.


Condron, D. J., & Roscigno, V. J. (2003). Disparities within: Unequal spending and achievement in an urban school district. Sociology of Education, 76, 18–36. doi:http://dx.doi.org/10.2307/3090259


Croninger, R. G., & Lee, V. E. (2001). Social capital and dropping out of high school: Benefits to at-risk students of teachers’ support and guidance. Teachers College Record, 103(4), 548–581.


Dika, S. L., & Singh, K. (2002). Applications of social capital in educational literature: A critical synthesis. Review of Educational Research, 72(1), 31–60.


Dobbie, W., & Fryer Jr, R. G. (2009, November). Are high quality schools enough to close the achievement gap? Evidence from a social experiment in Harlem (NBER Working Paper No. 15473). Cambridge, MA: National Bureau of Economic Research.


Duncan, G. J., & Magnuson, K. A. (2005). Can family socioeconomic resources account for racial and ethnic test score gaps? Future of Children, 15(1), 35–54.


Farmer-Hinton, R. L., & Adams, T. L. (2006). Social capital and college preparation: Exploring the role of counselors in a college prep school for black students. Negro Educational Review, 57(1–2), 101–116.


Furstenberg, F. F., & Hughes, M. E. (1995). Social capital and successful development among at-risk youth. Journal of Marriage and the Family, 57(3), 580–592.


Garnier, C. L., & Raudenbush, S. W. (1991). Neighborhood effects on educational attainment: A multilevel analysis. Sociology of Education, 64, 251–262.


Goddard, R. D. (2001). Teacher trust in students and parents: A multilevel examination of the distribution and effects of teacher trust in urban elementary schools. Elementary School Journal, 102(1), 3–17.


Goddard, R. D. (2003). Relational networks, social trust, and norms: A social capital perspective on students' chances of academic success. Educational Evaluation and Policy Analysis, 25(1), 59–74.


Goddard, R. D., & LoGerfo, L. F. (2007). Measuring emergent organizational properties: A structural equation modeling test of self- versus group-referent perceptions. Educational and Psychological Measurement, 67(5), 845–858.


Goddard, R. D., Salloum, S. J., & Berebitsky, D. (2009). Trust as a mediator of the relationships between poverty, racial composition, and academic achievement: Evidence from Michigan's public elementary schools. Educational Administration Quarterly, 45(2), 292–311.


Goddard, R. D., Sweetland, S., & Hoy, W. K. (2000). Academic emphasis of urban elementary schools and student achievement in reading and mathematics: A multilevel analysis. Educational Administration Quarterly, 36(5), 683–702.


Goldstein, H. (1986). Multilevel mixed linear model analysis using iterative generalized least squares. Biometrika73(1), 43–56.


Granovetter, M. (1985). Economic action and social structure: The problem of embeddedness. American Journal of Sociology, 91(3), 481–510.


Hanushek, E. A. (1989). The impact of differential expenditures on school performance. Educational Researcher, 18(4), 45–62.


Hart, B., & Risley, T. R. (1995). Meaningful differences in the everyday experience of young American children. Baltimore, MD: Paul H. Brookes Publishing.


Hedges, L. V., Laine, R. D., & Greenwald, R. (1994). An exchange: Part I: Does money matter? A meta-analysis of studies of the effects of differential school inputs on student outcomes. Educational Researcher, 23(3), 5–14.


Homans, G. C. (1958). Social behavior as exchange. American Journal of Sociology, 63(6), 597–606.


Hoy, W. K., & Sabo, D. J. (1998). Quality middle schools: Open and healthy. Thousand Oaks, CA: Corwin Press.


Hoy, W. K., Smith, P. A., & Sweetland, S. R. (2002). A test of a model of school achievement in rural schools: The significance of collective efficacy (pp. 185–202). In W. K. Hoy & C. Miskel (Eds.), Theory and Research in Educational Administration. Charlotte, NC: Information Age Publishing,


Jones, B. L., & Maloy, R. W. (1988). Partnerships for improving schools. New York, NY: Glenwood.


Kline, R. (2005). Principles and practice of structural equation modeling (2nd ed.). New York, NY: Guilford Press.


Kozol, J. (1991). Savage inequalities: Children in America’s schools. New York, NY: Crown.


Labaree, D. F. (1997). How to succeed in school without really learning: The credentials race in American education. New Haven, CT: Yale University Press.


Lankford, H., Loeb, S., & Wyckoff, J. (2002). Teacher sorting and the plight of urban schools: A descriptive analysis. Educational Evaluation and Policy Analysis, 24(1), 37–62.


Lareau, A. (1987). Social class differences in family-school relationships: The importance of cultural capital. Sociology of Education, 60, 73–85.


Lee, V. E., & Bryk, A. S. (1988). Curriculum tracking as mediating the social distribution of high school achievement. Sociology of Education, 61(2), 78–94.


Lee, V. E., & Burkam, D. T. (2002). Inequality at the starting gate: Social background differences in achievement as children begin school. Washington, DC: Economic Policy Institute.


Lee, V. E, & Croninger, R. G. (1994). The relative importance of home and school in the development of literacy skills for middle-grade students. American Journal of Education, 102, 286–329.


Lin, N. (2000). Inequality in social capital. Contemporary Sociology, 29(6), 785–795.


Loury, G. C. (1977). A dynamic theory of racial income differences. In P. A. Wallace & A. LaMond (Eds.), Women, minorities, and employment discrimination (pp. 153–188). Lexington, MA: Heath.


Marsden, P. V., & Hurlbert, J. S. (1988). Social resources and mobility outcomes: A replication and extension. Social Forces, 66(4), 1038–1059.


Marsh, H. W. &  Hocevar,  D. (1985). Application of confirmatory factor analysis to the study of self-concept: First- and higher order factor models and their invariance across groups. Psychological Bulletin, 97(3), 562–582.


Marzano, R., Waters, T., & McNulty, B. (2005). School leadership that works: From research to results. Alexandria, VA: Association for Supervision and Curriculum Development.


Massey, D. S., & Denton, N. A. (1993). American apartheid: Segregation and the making of the underclass. Cambridge, MA: Harvard University Press.


Moolenaar, N. M. (2012). A social network perspective on teacher collaboration in schools: Theory, methodology, and applications. American Journal of Education, 119(1), 7–39.


Morgan, S. L., & Sørensen, A. B. (1999). Parental networks, social closure, and mathematics learning: A test of Coleman's social capital explanation of school effects. American Sociological Review, 64(5), 661–681.


National Center for Educational Statistics. (2012). National Assessment of Educational Progress. Retrieved from http://nces.ed.gov/nationsreportcard/about/


National Center for Educational Statistics (2013).  Enrollment and percentage distribution of enrollment in public elementary and secondary schools, by race/ethnicity and region: Selected years, fall 1995 through fall 2023. Retrieved from http://nces.ed.gov/programs/digest/d13/tables/dt13_203.50.asp


Oakes, J. (2005). Keeping track: How schools structure inequality. New Haven, CT: Yale University Press.


Orfield, G. (2001). Schools more separate: Consequences of a decade of resegregation. Cambridge, MA: Harvard University Civil Rights Project


Orfield, G., & Lee, C. (2005). Why segregation matters: Poverty and educational inequality. Cambridge, MA: Harvard University Civil Rights Project.


Penuel, W., Riel, M., Krause, A., & Frank, K. (2009). Analyzing teachers' professional interactions in a school as social capital: A social network approach. Teachers College Record, 111(1), 124–163.


Perna, L. W., & Titus, M. A. (2005). The relationship between parental involvement as social capital and college enrollment: An examination of racial/ethnic group differences. Journal of Higher Education, 76, 485–518.


Pil, F. K., & Leana, C. (2009). Applying organizational research to public school reform: The effects of teacher human and social capital on student performance. Academy of Management Journal, 52(6),

1101–1124.


Pong, S. (1998). The school compositional effect of single parenthood on 10th-grade achievement. Sociology of Education, 71(1), 23–42.


Portes, A. (1998). Social capital: Its origins and applications in modern sociology. Annual Review of Sociology, 24, 1–24.


Putnam, R. D. (1993). Making democracy work: Civic traditions in modern Italy. Princeton, NJ: Princeton University Press.


Putnam, R. D. (2001). Bowling alone: The collapse and revival of American community. New York, NY: Simon and Schuster.


Ream, R. K. (2003). Counterfeit social capital and Mexican-American underachievement. Educational Evaluation and Policy Analysis, 25, 237–262.


Rivkin, S. G., Hanushek, E. A., & Kain, J. F. (2005). Teachers, schools, and academic achievement. Econometrica, 73(2), 417–458.


Roza, M., Hill, P. T., Sclafani, S., & Speakman, S. (2004). How within-district spending inequities help some schools to fail. Brookings Papers on Education Policy, 7, 201–227.


Small, M. L. (2009). Unanticipated gains: Origins of network inequality in everyday life. Oxford, UK: Oxford University Press.


Stanton-Salazar, R. D. (1997). A social capital framework for understanding the socialization of racial minority children and youths. Harvard Educational Review, 67, 1–40.


Stanton-Salazar, R. D. (2011). A social capital framework for the study of institutional agents and their role in the empowerment of low-status students and youth. Youth & Society, 43(3), 1066–1109.


Sui-Chu, E. H., & Willms, J. D. (1996). Effects of parental involvement on eighth-grade achievement. Sociology of Education, 69, 126–141.


Teachman, J. D., Paasch, K., & Carver, K. (1996). Social capital and dropping out of school early. Journal of Marriage and the Family, 58(3), 773–783.


Van Laar, C., & Sidanius, J. (2001). Social status and the academic achievement gap: A social dominance perspective. Social Psychology of Education, 4(3–4), 235–258.


APPENDIX A


Structural Equation Modeling


Structural equation modeling uses the correlation matrix to model relationships in data. In order to understand the formulas, it is necessary to define some terms.

[39_21811.htm_g/00004.jpg]

where x is the observed (exogenous) variable, Λx are the factor loadings, ξ is the true score associated with the latent factor, and δ is the error component associated with the exogenous variable.

[39_21811.htm_g/00006.jpg]

where y is the observed (endogenous) variable, Λy are the factor loadings, η is the true score associated with the factor, and ε is the error component associated with the exogenous variable.

[39_21811.htm_g/00008.jpg]

where ηi are the latent endogenous variables, Γ relates the endogenous variables to exogenous variable, and Β relates the endogenous latent variables to each other. These terms can be considered betas like those produced by multiple regression.


The variance/covariance matrix can be partitioned into 3 unique blocks. The exogenous variables correlations, the endogenous variables correlations, and the block where the exogenous and endogenous variables correlate as shown (Σxyyx).

[39_21811.htm_g/00010.jpg]

 These blocks can be defined as:

[39_21811.htm_g/00012.jpg]

[39_21811.htm_g/00014.jpg]

[39_21811.htm_g/00016.jpg]

Where Φ is the variance/covariance matrix of the exogenous factors, [39_21811.htm_g/00018.jpg]is the variance/covariance matrix of the endogenous factors, and both ψ and Θε are disturbance terms (For further details on the theory of structural equation modeling, see Kline, 2005). Once the correlation matrix is partitioned and various constraints are imposed in the modeling processes the relationships (or betas) and factor loadings for the latent factors can be estimated.


Once the model is estimated it is imperative to determine “goodness of fit.” Goodness of fit compares the estimated correlation matrix produced by the model to the observed correlation matrix produced by the data. Small differences between these correlation matrices imply that the model approximates reality, as expressed by the data, well.


The chi-square test takes the overall difference between the observed correlation matrix produced by the data and the correlation matrix produced by the model, converting that difference to a chi-square distributed variable. A low chi-square means the correlation matrices are very similar, implying that the model approximates or fits the data well.


RMSEA or root mean square of approximation assesses model fit by taking the chi-square distributed variable and correcting for the sample size and the degrees of freedom (number of constraints) in the model. A low RMSEA implies that the model created correlation matrix is similar to the observed correlation matrix.


TLI or Tucker-Lewis index takes the difference between the chi-square value produced from the worst possible model (constraining all variables to have NO correlation with any other variable) and from the chi-square value produced by the user supplied model, and then divides that difference by the worst possible chi-square value. If there is good fit the result should be close to 1.


CFI or comparative fit indices takes the chi-square value and subtracts the number of constraints from it. It also does this for the worst possible model mentioned along with the TLI model. It takes the difference between those two models and divides by the number produced by the worst possible model. Once again, if the number resulting is near 1 then that implies good model fit.


No fit index is robust in all situations; therefore a variety are used and reported.




Cite This Article as: Teachers College Record Volume 119 Number 7, 2017, p. 1-29
https://www.tcrecord.org ID Number: 21811, Date Accessed: 10/24/2021 11:44:30 AM

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About the Author
  • Serena Salloum
    Ball State University
    E-mail Author
    SERENA SALLOUM is an Assistant Professor of Educational Leadership at Ball State University. Her research interests focus on how the social context of schools contributes to academic achievement, with a particular emphasis on collective efficacy. Recent work has been published in the Elementary School Journal and Education Administration Quarterly.
  • Roger Goddard
    Ohio State University
    E-mail Author
    ROGER GODDARD is the Novice G. Fawcett Chair in Educational Administration and Professor at The Ohio State University. His research interests include social cognitive theory, efficacy beliefs, organizational theory, school leadership, experimental design, and hierarchical linear modeling. Recent publications have appeared in Educational Evaluation and Policy Analysis and the American Journal of Education.
  • Ross Larsen
    Brigham Young University
    E-mail Author
    ROSS LARSEN is an assistant professor at BYU in the Instructional Psychology and Technology department. His research interests include innovative methodological solutions to applied problems, structural equation modeling, and missing data analysis. His publications have appeared in Structural Equation Modeling: A Multidisciplinary Journal and Behavior Research Methods.
 
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