Parental divorce, sibship size, family resources, and children’s academic performance

Social Science Research 38 (2009) 622–634

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Parental divorce, sibship size, family resources, and children’s academic performance Yongmin Sun a,*, Yuanzhang Li b a b

Department of Sociology, The Ohio State University-Mansfield, Mansfield, OH 44906, USA Allied Technology Group, 1803 Research Blfd., Rockville, MD, 20850, USA

a r t i c l e

i n f o

Article history: Available online 2 April 2009

Keywords: Academic performance Child well-being Family resources Family structure Parental divorce Sibship size

a b s t r a c t Using data from 19,839 adolescents from the National Education Longitudinal Study, this study investigates whether the effects of parental divorce on adolescents’ academic test performance vary by sibship size. Analyses show that the negative effect of divorce on adolescent performance attenuates as sibship size increases. On the other side of the interaction, the inverse relationship between sibship size and test performance is weaker in disrupted than in two-biological-parent families. Trends of such interactions are evident when sibship size is examined either as a continuous or a categorical measure. Finally, the observed interactions on adolescents’ academic performance are completely explained by variations in parental financial, human, cultural, and social resources. In sum, this study underlines the importance of treating the effect of parental divorce as a variable and calls for more research to identify child and family features that may change the magnitude of such an effect. Ó 2009 Elsevier Inc. All rights reserved.

1. Introduction A substantial amount of research has investigated whether parental divorce or separation affects children’s chances for educational success (e.g., Cherlin et al., 1991; Kurdek et al., 1995; McLanahan and Sandefur, 1994; Raley et al., 2005; Sun and Li, 2001; Teachman et al., 1996). A growing section of this research has now moved beyond an earlier model that depicts the consequences of parental divorce as uniform and undifferentiated for all children (Furstenberg and Kiernan, 2001). Instead, many scholars now argue that the effect of divorce on children’s educational progress may vary contingent upon children’s gender (e.g., Morrison and Cherlin, 1995; Zaslow, 1988), age (e.g., Allison and Furstenberg, 1989), race and ethnicity (e.g., Sun and Li, 2007), and the number of postdivorce family transitions (Kurdek et al., 1995; Sun and Li, 2008). Another important family feature that may potentially alter the effect of divorce, but has not yet been rigorously examined, is the number of siblings a child has (hereafter referred to as sibship size). Specifically, we expect the negative effect of divorce on children’s educational outcomes to attenuate as sibship size increases, for two reasons. First, siblings may provide emotional support and comfort to one another during family crises such as parental divorce. The fact that siblings within the same family are going through this difficult process with a child may reduce the stress of divorce on the child and therefore, ease its negative effect (Kempton et al., 1991). Second, large sibship size generally dilutes valuable parental resources available for each child in a family (e.g., Blake, 1989; Downey, 1995a) and the actual amount of parental resources divided by a given sibship size varies by the overall levels of such resources in different families. For instance, the levels of financial, human, and social resources are generally lower in disrupted than in two-biological-parent families (e.g., Coleman, 1988; McLanahan and Sandefur, 1994). Thus, a large sibship size (e.g., five siblings) in both disrupted and two-biological-parent * Corresponding author. Fax: +1 419 755 4367. E-mail address: [email protected] (Y. Sun). 0049-089X/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.ssresearch.2009.03.007

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families will dilute the same proportion of resources, but the magnitude of dilution in disrupted families will be smaller, because they have fewer resources from the outset. Based on this argument, the extent of resource disadvantages in divorced relative to two-biological-parent families should be less severe in large than in small families. Given that resource deprivation in divorced families has been identified as a key reason for academic disadvantages in such families (e.g., Astone and McLanahan, 1991; McLanahan and Sandefur, 1994), the divorce effect on children’s education should be smaller for children with many siblings than for their peers with just one or two siblings. Although prior divorce and sibship-size studies have separately investigated how resource deprivation in disrupted families and resource dilution in large households negatively affect children’s educational progress (e.g., Blake, 1981, 1989; Downey, 1995a; McLanahan and Sandefur, 1994; Park, 2008; Sun and Li, 2001; Steelman and Powell, 1989; Xu, 2008), few of these studies have integrated the interrelated effects of parental divorce, sibship size, and parental resources in their investigations. Consequently, little is known to date about whether the effect of parental divorce on children’s academic progress varies by sibship size and whether such potential interactions are further related to family resources. Using data from 19,839 adolescents from the National Education Longitudinal Study (NELS), we examine the potential interaction effects between parental divorce and sibship size on adolescents’ test performance. Specifically, we investigate: (1) whether the effect of divorce lessens in magnitude as sibship size increases; and (2) whether various levels of parental financial, human, cultural, and social resources mediate the interaction effects of divorce and sibship size.

2. Background 2.1. Parents’ marital disruption, resource deprivation, and children’s educational performance Previous research has provided convincing evidence that childhood experience of parental divorce is likely to compromise children’s chances for educational success. Compared to their peers from married, two-biological-parent families, children from single- and step-parent families are likely to have lower GPAs and test scores (Cherlin et al., 1991; Pong, 1997; Raley et al., 2005; Sun, 2001; Sun and Li, 2001), lower chances of graduating from high school or attending college (Astone and McLanahan, 1991; Biblarz and Gottainer, 2000; Teachman et al., 1996), and a lower level of educational attainment by adulthood (Amato and Keith, 1991a; Sun and Li, 2008). One important theoretical explanation for the negative educational consequences of divorce is resource deprivation. Proponents of this perspective (e.g., Coleman, 1988; McLanahan, 1985; McLanahan and Sandefur, 1994) argue that parents’ financial, human, and social capitals are crucial to their children’s educational success. Parental divorce, however, deprives children of such parental resources. Financially, divorce often lowers the living standards for children (Duncan and Hoffman, 1985), cuts the family’s educational budget (Downey, 1995b), and increases children’s chances of moving into an economically deprived (and often academically noncompetitive) school district (McLanahan and Booth, 1989). In addition, when a non-custodial parent leaves the household after divorce, the parent (usually the father) may take away some human capital (e.g., tutoring and educational advice derived from his education) which otherwise would be available to the child. More importantly, divorce is likely to reduce parental social capital. According to Coleman (1988), social capital consists of the time and effort parents devote to their positive interactions with their children, other parents, and school personnel. Obviously, family dissolution is likely to substantially reduce the amount of time the non-custodial parent spends in monitoring and supervising the child (Furstenberg and Nord, 1985) and may even compromise the time the custodial parent spends with the child (Astone and McLanahan, 1991). Furthermore, family dissolution often reduces time that parents spend in contact with other parents and school personnel. This reduction in access to community-based social resources may also limit a family’s ability to allocate external resources for educational purposes (Coleman, 1988). Although the presence of a step-parent may somewhat compensate for the reduction of family resources in the household, the extent of such compensation is often limited (Downey, 1995b). Consistent with this resource deprivation argument, most studies indeed reported lower levels of various parental resources in single- and step-parent families than in two-biological-parent families (e.g., Downey, 1995b; McLanahan and Sandefur, 1994; Sun, 2001; Sun and Li, 2001). Shortages of family resources in these nontraditional families were found either to partially or completely account for the educational disadvantages commonly found in such households (Astone and McLanahan, 1991; Downey, 1995b; McLanahan and Sandefur, 1994; Sun and Li, 2001, 2008). The resource deprivation model can be enhanced in at least two aspects. First, while family resources are obviously important for child development, such resources do not have to come exclusively from parents. McLanahan and Sandefur (1994), for instance, point out that supplementary support provided by relatives and extended family members can be particularly valuable to children during family crises. Similarly, siblings may also provide emotional protection and support to one another after parental divorce (Kempton et al., 1991). Presumably, the presence of siblings may serve as a stress buffer in postdivorce families, because it makes children feel that they are not shouldering all the stress alone. Further, siblings may serve as confidants with whom they can share their frustrations. These stress-relief functions provided by siblings may reduce the negative effect of divorce on children’s educational outcomes. Despite this apparent potential for siblings to buffer divorce effects, only one study (Kempton et al., 1991), to our knowledge, has directly examined this interaction effect and reported that the presence of a sibling indeed reduces children’s externalizing behavior problems in disrupted families. This study, however, used a small and non-representative sample, and therefore, cannot generalize its findings to major populations.

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Second, although some prior tests of resource deprivation include sibship size either as a control or a family-resource variable (e.g., Sun and Li, 2008), such modeling only controls for the effect of sibship size on the child outcomes, and consequently does not sufficiently take into consideration that the relative resource deprivation for each child in disrupted families decreases as the sibship size increases (this argument will be elaborated in a later section). To explore the implication of this argument, we need to elucidate the deprivation model by considering how sibship size may change the extent of resource deprivation. 2.2. Sibship size, resource dilution, and children’s educational outcomes Numerous studies have also documented the inverse relationship between sibship size and children’s educational outcomes (for a review, see Steelman et al., 2002). One explanation for this inverse relationship is resource dilution. Proponents of this perspective (Blake, 1981, 1989; Downey, 2001; Powell and Steelman, 1989; Steelman and Powell, 1989) argue that different types of parental resources are not only valuable, but also finite in most families. Once the total amount of such resource is fixed, the actual share for each child largely depends on the number of children in the family. Thus, the larger the sibship size, the fewer resources each child has access to and accordingly, the lower the chance for each child’s academic success. Among many studies that have tested the dilution argument, Downey’s research (1995a) provides a comprehensive investigation. Using data from over 24,000 adolescents in the base-year sample of the NELS, Downey found that some parental resources (e.g., social resources) decrease almost linearly as the number of siblings increases, whereas others (e.g., family financial resources) decreased in a non-linear, 1/v pattern (v is the number of children). Despite such variations in the rates of dilution by resource type, the overall trend of fewer resources in large families was observed for each type of resources. In addition, variations in such resources completely explained the negative effect of sibship size on adolescents’ math performance and a large portion of its effect on their reading achievement. Proponents and critics of the dilution argument have extensively debated its conceptual merits and limitations (Downey, 2001; Downey et al., 1999; Guo and VanWey, 1999). Although it is beyond the scope of this study to clarify all these issues, two issues are relevant to this study. First, prior tests of the dilution model emphasize the proportion of family resources diluted by each additional child. This approach does not sufficiently adjust for the differences in the total amount of family resources and consequently, the differences in the magnitude of resource dilution. In the following illustration, we use two families with sharply different levels of financial investment in their children’s education to demonstrate the differences between proportion and magnitude dilutions. Based on findings from Downey’s study (1995a), we assume parents distribute their financial resources approximately equally among all children, resulting in a 1/v pattern of dilution, although the logic demonstrated through this example applies to parental social resources which may be diluted linearly (Downey, 1995a). Suppose a resource-affluent, two-biological-parent family has two children and an annual education budget of $20,000 for books, computers, tutoring, and private school tuitions, whereas a resource-deprived, disrupted household also has two children, but an annual education budget of $500. If one more child is added to each family without changing the total family budgets, the per-child share of financial resources in the first family drops from $10,000 to $6667, or a net loss of $3333 (33%), and the per-child share in the second family changes from $250 to $167, or a net loss of $83 (also 33%). Although the resource dilution by one additional child in both families remains the same in percentage (33%), the loss in magnitude (or absolute dollar value) in the first, two-biological-parent family is substantially larger (by over $3000) and may lead to a more significant reduction in educational goods or services for each child. Such a significant loss in financial resources may have a sizable effect on children’s educational outcomes. By contrast, the magnitude dilution in the disrupted family is very small (by only $83) and the actual loss of educational goods and services caused by the resource dilution is almost negligible. Assuming that it is the magnitude (not percentage) decrease in such financial resources that harms children’s outcomes, we should then expect a weaker effect of sibship size on performance in the disrupted than in the two-biological-parent family. Flipping to the other side of the same interaction, adding one child to each family in the above example also makes the per-child resource deprivation (i.e., the per-child resource difference between the two-biological-parent and disrupted families) decline from $9750 to $6500. As mentioned earlier, if resource deprivation in disrupted families is indeed a key reason for the negative effects of divorce on children’s education, such effects should be less severe in large than in small families. Obviously, prior tests of the dilution and deprivation models have not taken these factors into consideration. Second, if the availability of some parental resources to each child in the family (e.g., per child family income) approximates the function of 1/v (with v being the total number of children), the largest dilution by one additional child is always from zero to one (Downey, 2001). Following this argument, children with no siblings (hereafter, referred to as only children) should always outperform peers with one sibling by a large margin. This hypothesis, however, is not supported by most research, which often found that only children perform similarly to or even less well than peers in two-child homes (e.g., Belmont and Marolla, 1973; Blake, 1989). This only-child exception often disrupts an otherwise linearly inverse relationship between sibship size and performance (Belmont and Marolla, 1973). Obviously, factors other than resources may be related to the performance of only children and therefore, are responsible for their unique performances.

3. The present study The present study investigates the interaction effect of parental divorce and sibship size on children’s academic performance. This investigation is based on minor modifications of both resource dilution and resource deprivation models. We first

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incorporate parents’ marital disruption status into the dilution model. Because family resources are generally more abundant in two-biological-parent than in disrupted families (Coleman, 1988; McLanahan and Sandefur, 1994), we suggest that the magnitude of parental resources diluted by a given number of additional siblings will be larger in two-biological-parent than in disrupted families. Given the positive relationship between the magnitudes of parental resources and child performance, the oft-cited inverse relationship between sibship size and child performance is likely to be weaker in disrupted than in two-biological-parent families. Meanwhile, we also incorporate the notion of sibship size into the deprivation perspective and argue that the level of resource deprivation for each child (i.e., the per-child resource differences between two-biological-parent and disrupted families) decreases as the sibship size increases. Given such patterns of decreasing resource deprivation by sibship size and the potential for siblings to serve as stress buffers (Kempton et al., 1991), another well-cited inverse relationship between parental divorce and children’s educational achievement is likely to be weaker in large than in small families. To examine these hypothetical interrelationships, this study investigates two specific research questions. First, we investigate the main effects of parental divorce, sibship size, and their interactions on adolescents’ reading and math achievements. In addition to replicating the well-established negative effects of divorce and sibship size on child performance, we expect the negative slope of sibship size on performance to be flatter in disrupted than in two-biological-parent families, resulting in an attenuating disruption effect as the sibship size increases. Second, we examine whether variations in parental resources mediate the potential interaction effect between parents’ divorce and sibship size on children’s academic performance. If the differences in sibship-size slopes on children’s performance between two-biological-parent and disrupted families are indeed attributable to different magnitudes of resource dilution, the potential interaction effects on children’s performance should be reduced or eliminated when variations in parental resources are held constant. By incorporating a wide range of financial, human, cultural, and social resource measures into the analysis, we are able to test whether such interactions on performance are indeed related to parental resources. 4. Method 4.1. Sample Data used for this study came from the base-year wave of the NELS. Collected by the National Center for Educational Statistics (NCES), the NELS used a nationally representative sampling pool of 26,432 American 8th graders in 1988, of whom 24,599 students participated (with a response rate of 93.1%). The study surveyed both the 8th graders and their parents. Students also took a set of academic tests. We chose the base-year NELS because the sample pool contained more cases than the two recent NCES data sets (the Early Childhood Longitudinal Study—Kindergarten Cohort and the Education Longitudinal Study of 2002). The large sample size of the NELS was crucial for our analyses of interactions because it provided enough cases in each subcategory of divorce status and sibship size. Furthermore, numerous prior divorce and sibship-size studies have used the NELS study to test the resource deprivation and dilution arguments (e.g., Downey, 1995a,b; Pong, 1997; Sun and Li, 2001). By using the same data set, we could examine whether the negative educational consequences of parental divorce that are documented in these studies indeed vary by sibship size and whether many measures of parental resources tested by prior work indeed mediate the potential interaction effects. For the purpose of maintaining a large sample, we restricted our analyses to the base-year data even though the NELS had multiple waves of data, because using longitudinal data in the first three waves (which covered a time interval of four years) would have resulted in a loss of over 8000 cases. In addition, the major advantage of a longitudinal design is to allow a test of how an increase in sibship size may be related to a decline in child performance across the multiple waves (Guo and VanWey, 1999). Unfortunately, the NELS does not have a comparable measure of total sibship size across its first three waves and thus precluded such an analysis. Among all the 8th graders in the base-year pool, 21,920 had student- and parent-survey data, and also participated in at least one academic test. From this pool, we excluded 2081 cases (or 9.5% of the original pool) in the following categories: (a) cases whose biological parents were widowed, never married, or cohabitating (n = 1290, or 5.9% of the pool); (b) cases who lived with neither biological parent (n = 660, or 3%), and (c) cases whose parent-survey respondent was not a parent or parent’s partner and therefore, did not report the marital status of the 8th grader’s biological parents (n = 131, or 0.6%). The final sample included 19,839 8th graders, averaging about 14 years of age. All analyses used the base-year sampling weights, which corrected the unequal probabilities involved in oversampling certain types of schools and minority students. 4.2. Measures Table 1 provides descriptive statistics of all the dependent, independent, and intervening (parental resource) variables. Means, standard deviations, and the number of cases were provided for continuous variables, whereas frequency and percentage distributions were provided for categorical variables. Dependent variables. We used students’ IRT (Item Response Theory) scores in the reading and math tests as the dependent variables. Based on a student’s answers to test questions with different levels of difficulty and the number/type of questions omitted, the IRT scores estimate the number of right answers a student would have provided if he or she had answered all questions. Such IRT scores are often preferred in analyses of students’ test performance because they have several important advantages over raw test scores (for a discussion on these advantages, see Appendix H of the Second Follow-up: Student Component Data File User’s Manual).

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Table 1 Descriptive statistics for variables. Ma

SDa

N

26.72 35.61 2.26 51.25 0.52 1.49 4.17 1.58 2.95

8.57 11.81 1.55 20.14 0.77 1.24 1.50 1.77 1.48

19,806 19,803 19,839 19,839 19,839 19,839 19,839 19,839 19,839

Frequency

Unweighted (%)

Weighted (%)a

Categorical variables Parental divorce status Two-biological-parent families Disrupted families

13,920 5919

70.17 29.83

68.71 31.29

Number of siblings (categorical) Only children (no sibling) One or two siblings Three or four siblings Five or more siblings

1233 11,913 4529 2164

6.21 60.05 22.83 10.91

5.92 60.21 22.99 10.88

Family annual income Under $9999 $10,000–$24,999 $25,000–$49,999 $50,000–$74,999 $75,000 and up

2049 4760 7681 3021 2328

10.33 23.99 38.72 15.23 11.74

10.46 25.42 40.26 15.43 8.43

Educational savings Under $999 $1000–$5999 $6000–$14,999 $15,000 and up

12,977 3833 1739 1290

65.41 19.32 8.76 6.51

66.71 19.81 8.40 5.08

Parents’ educational attainment No high school degree High school or GED Some college College graduation Graduate/professional degree

1725 3728 7988 3260 3138

8.70 18.79 40.26 16.43 15.82

8.57 20.63 42.50 15.48 12.82

Parent attended event with child Parent attended event Parent did not attend event

13,040 6799

65.73 34.27

65.10 34.90

Continuous variables Reading test score Math test score Number of siblings (continuous) Parental occupational prestige Cultural classes Cultural activities Parent–child discussion Parent–school tie Number of other parents known

a

Means, SDs, and weighted percentages were weighted by the base-year sampling weights.

Independent variables. One key independent variable is parents’ divorce status. The NELS contained a student-reported family structure measure, classifying students’ families into two-biological-parent, single-mother, single-father, mother and stepfather/male guardian, and father and stepmother/female guardian families (students living in non-biological-parent families were excluded). We combined student-reported family structure measure and parent-reported marital status, and created a dummy variable of parental divorce status, classifying the sample members into two kinds of families (0 = married, two-biological-parent families, n = 13,920; 1 = disrupted families, n = 5919).1 In preliminary analyses, we further divided the disrupted families into single-parent and step-parent households, but found that the relationship between sibship size and performance did not differ significantly between these two kinds of disrupted families. In light of this finding, we combined these cases into the category of disrupted families in order to keep enough such families by sibship-size categories. Sibship size was measured by a student-survey item measuring the total number of brothers and sisters, including half-, step-, and adoptive siblings. We chose to use this measure instead of another parent-report item gauging the number of biological/half-/step-siblings currently living in the household, for two reasons. First, one important reason for expecting a small disruption effect in large families is that siblings may serve as stress buffers during their parents’ divorce process. Because siblings living outside an 8th grader’s household may still provide such a function through their communications with the 8th grader, these nonresident siblings should still be counted. Second, although some older biological siblings of an 8th gra1 When student and parent data contradict each other, we rely on marital status information provided by the parent, assuming that such information is more accurate.

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der were living elsewhere at the time of the survey, they might still receive parental financial resources (e.g., college tuition) and social support, both of which continued to dilute parents’ time and money from the 8th grader. Furthermore, half- and step-siblings might live in different households, but were still likely to receive resources from the 8th grader’s parents or parents’ spouses/partners. Because it is difficult to measure the exact distribution of parental resources among all children, regardless of their presence in the household, we followed most prior studies of resource dilution and measured sibship size with the total number of siblings as a continuous variable (0 = 0; 6 = 6 or more). To explore possible non-linear patterns of interactions, we also created a categorical measure with four sibship-size groups: no sibling, one to two, three to four, and five or more siblings. Four dummy variables were respectively created for these categories. Parent resources as intervening variables. Two measures of financial resources were used. Annual family income from all sources in the previous year (1987) was coded into five income categories: (a) $0–$9999, (b) $10,000–$24,999, (c) $25,000–$49,999, (d) $50,000–$74,999, and (e) $75,000 and up. Five dummy income variables were created for these income groups. In addition, the amount of money parents saved for the 8th grader’s future education (presumably for college) was measured with four dummy variables: (a) $0–$999, (b) $1000–$5999, (c) $6000–$14,999, and (d) $15,000 and up. For human capital measures, we first included the parent’s educational attainment, measured by five dummy variables: (a) no high school degree, (b) high school graduation, (c) some college, (d) college graduation, and (e) graduate/professional degree. In addition, parents’ occupational prestige (measured by the prestige index in the data) was included. For both measures of human capital, the higher level of such resources (e.g., educational attainment) of either parent or spouse/partner was taken for two-biological-parent and step-parent households. For single-parent families, the level of the custodial parent’s human capital was used. We also included two measures of cultural resources, not only because such resources promote children’s educational success (Bourdieu, 1977), but also because the level of cultural resources was likely to be low in large families (Downey, 1995a). We constructed a composite of cultural activities, measuring the frequencies with which the 8th grader visited: (a) art, (b) science, and (c) history museums (0 = has visited none; 3 = has visited all three, a = 0.79). Another composite of cultural classes measures the frequency with which students took classes outside of school in: (a) arts, (b) music, and (c) dancing (0 = attending none; 3 = attending all three classes, a = 0.50). Also used in this analysis were social resource measures, gauging the amount of time parents spent interacting with their 8th graders, school personnel, and other parents. For parent–child relationships, we first used a composite of parent–child discussion gauging the frequency with which the parent talked to the adolescent about course selection, school activities, and things studied in class since the beginning of the school year (0 = has not talked about any of these; 6 = has talked about all these topics three or more times, a = 0.60). For parent– school ties, we constructed another composite that measured whether parents: (a) belonged to PTA, (b) attended PTA meetings, (c) took part in other PTA activities, (d) worked as a volunteer in school, (e) contacted the school about fund raising, and (f) contacted the school about volunteer work (0 = having participated in none; 6 = having participated in all these activities, a = 0.78). Also included was an item which asked the student whether either parent had attended a school event with the student in the current school year (0 = no; 1 = yes). Finally, for parent–parent ties, we used the number of other parents the 8th grader’s parent knew by first name (0 = 0; 5 = 5 or more). Control variables. In our analyses, we controlled for six characteristics of students and their schools, because these variables were reported in prior research to be correlated with students’ performance and/or with parental divorce. The controls included students’ gender, racial/ethnic background, disability status (0 = no, 1 = learning/physical disability), native language (0 = English, 1 = other languages), geographic locality (urban, suburban, rural), and type of school attended (public, Catholic, other private school). 4.3. Missing value strategies In order to save the cases with missing values on independent variables (i.e., resource and control variables), we used Rubin’s multiple imputation (MI) technique (Rubin, 1987). In MI, each missing value on a particular variable is replaced by a set of m > 1 maximum-likelihood estimates drawn from their predictive distributions based on non-missing values on all related variables. Specifically, we used the PROC MI in SAS and included all the dependent and independent variables in MI to inform the imputation. After the imputation, only imputed values on the missing independent variables were kept, whereas imputed values on missing dependent variables were excluded. This strategy is known as MI with deletion, which helps to reduce biases from misspecification of the MI model (von Hippel, 2007). Given that the percentage of missing values on each independent variable in our data set was below 10%, we imputed 10 (m = 10) estimates for each missing value because 10 estimates gave at least 99% efficiency of estimation (see Schafer and Olsen, 1998). In all analyses presented in this study, we estimated statistics (e.g., means, percentages, regression coefficients, and standard errors) using 10 sets of data and reported summary statistics based on the formulae provided by Rubin (1987).

5. Results 5.1. Descriptive analyses Before turning to the two research questions, we first report the means and standard deviations of two test performance measures and the number of cases in each of the 14 subcategories of divorce status and sibship size (see Table 2). Simple t-tests

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Table 2 Descriptive statistics of adolescents’ reading and math performance by parental divorce status and by sibship size.a Family type

Reading

Math

Number of siblings 0

Number of siblings

2

3

4

5

6 or + 0

1

2

3

4

5

6 or +

Two-biological-parent families Mean 28.53 28.63 Std 8.49 8.55 n 803 5032

27.41 8.42 3979

26.37 8.35 1994

25.47 8.40 894

24.45 7.84 480

23.98 8.35 718

37.39 11.53 802

38.16 11.93 5034

37.07 11.95 3981

35.72 11.66 1992

34.53 11.61 891

32.79 10.56 478

31.94 11.03 719

Disrupted families Mean Std N

25.69 8.51 1428

24.91 8.61 999

24.45 8.14 633

23.96 7.99 376

23.65 8.08 587

34.85 11.35 427

34.28 11.49 1456

33.46 11.43 1429

32.47 10.81 997

32.43 10.82 637

32.14 10.52 374

31.29 11.09 586

0.48

0.32

2.54*** 3.88*** 3.61*** 3.25*** 2.10*** 0.65

0.65

27.25 8.68 428

Mean differences 1.28* by divorce status

1

26.08 8.44 1455

255*** 1.72*** 1.46*** 1.02*

a

All means were weighted by base-year sampling weights. p < 0.05. ** p < 0.01. *** p < 0.001. *

are also conducted to estimate mean performance differences between children in two-biological-parent and disrupted families by each sibship size cell. To present the trends of sibship-size slopes, these means of test scores are also plotted in Fig. 1. As shown in Fig. 1, the means of reading and math performances in disrupted families decline almost linearly as sibship size increases. Similarly, the inverse relationships between sibship size and the two test performances in two-biological-parent families are also approximately linear, although these patterns are somewhat disrupted by the performance levels of only children. Consistent with several prior studies (e.g., Blake, 1989), only children in two-biological-parent families perform somewhat less well than peers in two-child households. Despite this, the overall sibship-size slopes on both reading and math performances are generally flatter in disrupted than in two-biological-parent households. Consequently, the mean performance differences between two-biological-parent and disrupted families (i.e., the divorce effect) are generally greater in magnitude in small than in large families. In fact, this difference in both reading and math is very small in magnitude and no longer statistically significant when adolescents have five or more siblings (see the bottom row of Table 2). Although these general trends are consistent with our earlier expectation for an interaction effect, the reader is reminded that these findings are not adjusted for family financial and social resources. In order to examine these trends rigorously, we turn to multivariate models. 5.2. Differences in divorce effect by continuous measure of sibship size We start the multivariate analyses with our first research question: Does the effect of parental divorce on children’s academic performance vary by sibship size, net of background features of students and their schools? Before we answer this question, we replicate prior studies by examining the main effects of parental disruption and sibship size on adolescent performance. Such an analysis provides baselines of these two main effects that help the reader interpret the interaction effects in subsequent models. Because our descriptive analyses show an approximately linear relationship between sibship size and adolescent performance, we first include sibship size as a continuous variable in this analysis. Specifically, we use OLS models2 and respectively regress students’ reading and math performances on parents’ disruption status, sibship size, and the six controls. Table 3 summarizes the findings in Model 1. As shown in Model 1, adolescents from disrupted families score 1.03 and 2.09 points lower than peers in two-biologicalparent families in reading and math tests respectively (p < 0.001), net of the effects of sibship size and other control variables. We also estimate the sizes of these two effects as 0.13 SD for reading3 and 0.19 SD for math based on an equation for estimating adjusted effect sizes in regressions (Keef and Roberts, 2004). These divorce effects are somewhat larger than the average of such effect on test performances reported in a prior meta-analysis (Amato and Keith, 1991b).4 In addition, prior re-

2 An alternative approach is seemingly unrelated regression (SUR), which takes into consideration the correlated errors associated with analyzing multiple correlated dependent variables in a set of regressions. In our current case, however, the SUR does not offer this advantage because all the independent variables used to predict reading and math are identical in each subsequent model. Thus, OLS models are used instead for all subsequent analyses. 3 Based on the equation presented in Keef and Roberts (2004), we calculate the size of divorce effect as: g = (Md  Mi)/r ^, where Md  Mi is the adjusted mean difference in test performance between disrupted and two-biological-parent families after the effects of the other covariates have been pffiffiffiffiffiffiffiffiffiffitaken into account and r ^ is the standard deviation of the regression residuals. This r ^ is often estimated by the squared root of mean squared errors (or MSE) reported in regression analyses. For instance, as shown in Model 1 of Table 3, the coefficient of divorce status is 1.03 points for reading and Root MSE (not presented in the table) is 7.96. Thus, the size of adjusted divorce effect, g = 1.03/7.96 = 0.13 (SD). 4 A separate analysis without controlling for other covariates estimates raw divorce effects as 0.23 SD for reading and 0.29 SD for math, both of which are larger than the averaged raw divorce effect on test performance (0.16 SD) reported in Amato and Keith (1991b).

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Fig. 1. Means of reading and math test scores by divorce status and sibship size.

Table 3 Unstandardized regression coefficients of regressions of adolescents’ academic performance on parental divorce status, sibship size (continuous), and interactions. Independent variables

Reading Model 1a ***

Math Model 2a ***

Model 1a ***

Model 2a

Intercept Parental divorce status Sibship size (continuous) Female status Asian American African American Hispanic American Native American Adolescent has disability Native language not English Urban locality Rural locality Catholic school Other private school Divorce  sibship size (continuous)

28.99 1.03*** 0.52*** 1.74*** 0.44 4.96*** 3.47*** 4.87*** 4.32*** 2.32*** 0.55*** 0.97*** 2.13*** 3.85***

29.27 1.66*** 0.62*** 1.74*** 0.44 4.96*** 3.45*** 4.85*** 4.33*** 2.28*** 0.56*** 0.97*** 2.15*** 3.84*** 0.26***

40.41 2.09*** 0.54*** 0.56*** 3.04*** 7.89*** 5.69*** 6.84*** 6.28*** 1.96*** 0.91*** 1.58*** 0.86** 4.89***

40.74*** 3.07*** 0.70*** 0.57*** 3.04*** 7.88*** 5.65*** 6.81*** 6.29*** 1.89*** 0.91*** 1.57*** 0.88** 4.88*** 0.41***

R2 N

0.14 19,806

0.14 19,806

0.14 19,803

0.14 19,803

a

All coefficients were weighted by the NELS base year weights. p < 0.05. ** p < 0.01. *** p < 0.001. *

search reports that such academic disadvantages among 8th graders in divorced families may increase during high school years (Sun and Li, forthcoming) and may lead to low socioeconomic attainments in early adulthood (Amato and Keith, 1991a; Sun and Li, 2008). Meanwhile, after effects of other covariates are held constant, each additional sibling is estimated to be associated with a decline around 0.52 points in both reading and math (the effect sizes are 0.07 SD for reading and 0.05 SD for math,

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p < 0.001). Overall, these findings on the inverse divorce and sibship-size effects are consistent with those documented in prior divorce and sibship-size studies. In light of these findings, we include in Model 1 the interaction term of parental disruption status  sibship size. As shown in Model 2, the main divorce effects on two performance measures are negative and highly significant, indicating that, net of other effects, only children (when sibship size = 0) in disrupted families respectively score 1.66 and 3.07 points lower in reading and math than only children in two-biological-parent families (the effect sizes are respectively 0.21 and 0.28 SD). Meanwhile, among adolescents in two-biological-parent families (i.e., when divorce status = 0), each additional sibling lowers adolescents’ reading and math performances by about 0.62 and 0.70 points respectively (or 0.08 SD for reading and 0.06 SD for math in effect size). More important to this study, both interaction effects are positive (0.26 points in reading and 0.41 points in math) and highly significant (p < 0.001). These findings suggest that, net of the effects of the controls, the inverse slopes of sibship size on both math and reading performances are significantly flatter in disrupted than in two-biological-parent families. Put differently, the negative effect of divorce on child performance is estimated to attenuate by 0.26 and 0.41 points respectively in reading and math with each additional sibling. It needs to be noted that although this interaction effect appears to be small (around 0.03 SD), its magnitude can cumulate to a modest level when sibship size increases substantially.

Table 4 Unstandardized regression coefficients of regressions of adolescents’ academic performance on parental divorce status, sibship size (categorical), interactions, and parental resources. Independent variables

Reading Model 1a,b ***

Math Model 2a,b ***

Model 3a,b ***

Intercept Parental divorce status

28.29 1.05***

28.39 1.45***

17.55 0.03

Sibship size (categorical) Only childrenc 1 or 2 siblings (reference)c 3 or 4 siblingsc 5 or more siblingsc

0.37A 0.00A 1.18***,B 2.00***,C

0.25A 0.00A 1.38***,B 2.51***,C

0.39A 0.00A 0.53**,B 0.67**,B

Model 1a,b ***

Model 2a,b ***

Model 3a,b

39.75 2.08***

39.89 2.64***

23.96*** 0.21

0.07A 0.00A 1.31***,B 2.35***,C

0.50***,B 0.00A 1.47***,B 3.41***,C

0.19A 0.00A 0.20A 0.65*,B

Family income $10,000–$24,999 $25,000–$49,999 $50,000–$74,999 $75,000 and up

0.86*** 1.59*** 1.14*** 1.27***

1.28*** 2.22*** 2.56*** 3.73***

Money saved $1000–$5999 $6000–$14,999 $15,000 and up

0.61*** 0.51* 1.27***

0.90*** 0.90** 1.58***

Parental education attainment High school degree Some college College degree Graduate degree Parent occupational prestige Cultural classes Cultural activities Parent–child talk Attending school event Parent–school ties # of parents known

1.00*** 1.86*** 3.62*** 5.69*** 0.02*** 0.79*** 0.41*** 0.91*** 0.47*** 0.09 0.02

1.26*** 2.34*** 5.20*** 8.33*** 0.03*** 0.94*** 0.39*** 1.16*** 1.25*** 0.10 0.11*

Divorce  sibship size Divorce  only childrend Divorce  1 or 2 siblingsd Divorce  3 or 4 siblingsd Divorce  5 or 6 siblingsd R2 N a

0.14 19,806

0.99X,Y 0.00X 0.67*,Y 1.25**,Y

0.39X 0.00X 0.11X 0.17X

0.14 19,806

0.27 19,806

0.14 19,803

1.35X,Y 0.00X 0.61X 2.51***,Y

0.44X 0.00X 0.28X 0.78Y

0.14 19,803

0.29 19,803

All coefficients are weighted by the NELS base year weights. Control variables in all three models include: students’ sex, race, disability status, native language, school location, and school type. c Adjusted mean differences in performance with different superscripted A, B, and C are statistically significant at p < 0.05 level. d Interaction effects with different superscripted X and Y are statistically significant at p < 0.05 level. * p < 0.05. ** p < 0.01. *** p < 0.001. b

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5.3. Differences in divorce effect by categorical measure of sibship size In the last section, the interaction effect of parental divorce and sibship size is assumed to be linear. To explore possible nonlinear interaction patterns, we re-conduct OLS analyses and respectively regress reading and math scores on controls, parental divorce status, and the three dummy measures of sibship size: no sibling, three or four siblings, and five or more siblings. Adolescents with one or two siblings serve as the reference group, because in 1988 most American children under age 18 had one or two siblings (US Census Bureau, 1988). Table 4 summarizes these findings in Mode 1. We then include into Model 1 the three interaction terms of divorce  each of the three dummy sibship size variables (Model 2). To indicate statistical significance between adjusted performance means, superscripted A, B, and C are used next to the coefficient of each sibship-size category. Adjusted group means designated with different superscripted letters are statistically significant from one another at p < 0.05. Similarly, superscripted X and Y are used to indicate statistically significant (p < 0.05) differences in interaction effects. Because the coefficients of control variables are almost identical to those presented in Table 3, they are not reported in Table 4. As shown in Model 1, the effects of parental divorce are highly significant (1.05 points for reading and 2.08 points for math). Except for adolescents with no siblings, adolescents in large sibship-size groups score significantly lower than peers in small sibship-size categories (e.g., the levels of reading and math performances are significantly lower among adolescents with five or more siblings than among their peers with three or four siblings, with p < 0.05, as showed by the different superscripted letters of B and C). In addition, adolescents with no siblings perform better than peers with three or more siblings (showed by different superscripted letters), but the performance levels between households with no siblings and one or two siblings are statistically non-significant. Overall, these findings are consistent with our earlier findings based on the continuous measure of sibship size, suggesting that parental divorce and large sibship size both have negative effects on adolescent performance. In Model 2, the main effects of parental divorce and large sibship-size categories remain statistically significant. More important to this study, the interaction effects show three patterns, with the first two observed among adolescents with at least one sibling. First, excluding the category of only children, the negative effects of divorce on both reading and math performances consistently attenuate as sibship size increases across the remaining three sibship-size categories. Among six possible pairs of group differences in divorce effect (three two-group comparisons  2 test performance measures), four are statistically significant. The most striking differences are between adolescents with one or two (the reference group) and their peers with five or more siblings. Compared with the former group, the negative effects of divorce in the latter group are 1.25 and 2.51 points smaller for reading and math respectively (the effects sizes are 0.16 and 0.23 SD, p < 0.01). Between the category of one or two and that of three or four siblings, the negative effect of divorce on reading in the latter group is lower by 0.67 points (p < 0.05), although the same pattern of a smaller divorce effect in the latter group (by 0.61 points) is not statistically significant for math. Similarly, compared with that for peers with three or four siblings, the smaller divorce effect for adolescents with five or more siblings is statistically significant for math (as showed by superscripted X and Y), but not for reading (as showed by the same superscripted Y). It needs to be pointed out again that the two non-significant differences are still consistent with the overall pattern of small divorce effects in large sibship-size categories and are likely to reach a statistically significant level if the current sample contains more divorced cases in large sibship-size categories. Second, excluding the category of only children, the negative effect of divorce on adolescents’ reading performance attenuates almost linearly as sibship size increases by each category (e.g., from one or two siblings to three or four). For math, the negative effect of divorce first attenuates marginally from the oneor-two group to the three-or-four group (by 0.61 points) and then, substantially from the category of three or four siblings to that of five or more, revealing a trend of exponential decline. Finally, the divorce effects in only-child group are not significantly different from those in any of the other three sibship-size groups. This is likely to be caused by the unique performance pattern and the relatively limited number of divorced cases in one-child households. In summary, our analyses using a categorical sibship-size measure largely confirm the same pattern of interaction effects among adolescents with at least one sibling. Such interactions are particularly evident between families with one or two siblings and those with five or more. Overall, these findings are consistent with our earlier expectation for such interaction effects. 5.4. The intervening effects of parental resources If the levels of academic disadvantages in disrupted families decrease as sibship size increases, is this observed interaction effect attributable to variations in parental resources? To answer this question, we include all the parental resource measures (Model 3). Except for two social resource measures (parent–school ties and the number of parents known), all the remaining parental resource measures have a statistically significant and positive effect on both performance measures. These findings suggest that a high level of most parental resources indeed promote academic progress. With the inclusion of parental resource measures, the main effects of parental divorce are reduced to a statistically non-significant level. This suggests that in households with one or two siblings (the reference group), the negative effect of divorce on child performance is entirely due to variations in family resources.5 Similarly, the main effects of large sibship-size categories are also largely reduced, suggesting

5 In a separate analysis, we include each type of resources individually into the regression equation and find that financial resource mediates the largest amount of divorce effects, followed by human, social, and cultural resources.

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that in two-biological-parent families (when divorce status = 0), the negative effect of large sibship size is partially attributable to low resource levels in large families. More important to this study, when all resource measures are taken into consideration, the interaction effects of parental divorce and sibship-size categories are all reduced to non-significant levels. These findings are consistent with our earlier expectations, suggesting that the interaction effects between parental divorce and sibship size are completely due to the variations in parental resources among families with different divorce statuses and sibship sizes.

6. Discussion Prior divorce and sibship-size studies have respectively developed a parental resource perspective to respectively explain why parents’ divorce or a large sibship size is negatively related to children’s education. This study links these two research interests by examining whether parental divorce and sibship size interact in their effects on adolescents’ academic performance, and whether such interactions are related to parental resources. Our analyses based on a continuous measure of sibship size demonstrate a significant interaction effect between divorce and sibship size on adolescents’ academic performance. As expected, the inverse relationship between sibship size and performance is generally weaker in disrupted than in two-biological-parent families. Put differently, the inverse effect of divorce on child performance decreases as sibship size increases. When sibship size is broken down by categories, the same trend of interaction effects is still consistent among adolescents with at least one sibling, with most interaction effects between two sibship-size groups being statistically significant. Such interaction effects are particularly evident between adolescents with one or two siblings and their peers with five or more siblings. Interestingly, the analysis also reveals that the pattern of decrease in divorce effect by sibship size is linear for reading, but exponential for math. A closer analysis (not tabulated here) shows that these different patterns are due to a sharper drop in math than in reading performance in two-biological-parent families when sibship size increases to five and beyond. The precise cause of these differences is unclear. However, this finding invites future studies to investigate different effects of sibship size on different areas of educational outcomes. Our analyses also indicate that the observed interaction effects between divorce and sibship size are completely attributable to variations in parental financial, human, cultural, and social capitals. Findings from a separate analysis (not tabulated here but available to the reader upon request) indicate that the magnitudes of resource reduction by additional siblings in most of our family resource indicators are consistently smaller in disrupted than in two-biological-parent households. In other words, the divorce-related resource deprivation is indeed less severe in large than in small families. Given these similar interactions on parental resources, it is perhaps not surprising to find that variations in all parental resources completely account for the interaction effects between divorce and sibship size on test performances. In addition to these specific findings, the present study offers conceptual insights into the sibship size and divorce literatures. For future studies of resource dilution, our findings suggest that the sibship-size effect can generally be expected to be smaller in any resource-deprived than in resource-affluent families. Following this logic, we should expect variations in sibship-size effects across different racial/ethnic and socioeconomic groups. More importantly, the dilution model needs to develop a general strategy to adjust for the total amount of family resources so as to allow a more meaningful comparison of resource dilution. For the divorce literature, the findings suggest that in reality, the extent of resource deprivation may vary by many different individual or familial factors such as sibship size, race/ethnicity, and the availability of alternative resources. Such variations may play a critical role in shaping different experiences of children during their parents’ divorce process. In general, this study joins a group of recent divorce studies in highlighting the importance of treating the divorce effect as a variable and calling for more research to identify child and family features that may mitigate the magnitude of such an effect. Finally, our findings also suggest policy implications. For instance, policy makers often promote family policies that strengthen marriage as a strategy to fight against poverty (Lichter, 2001). Our findings suggest that a shortage of parental financial and social resources is indeed related to poor academic performance of children from disrupted families. One potential strategy to minimize such negative effects of divorce on children is to compensate for the reduced family resources in disrupted families with school- and community-based social resources and support. In fact, school-based and court-connected programs designed to help children adjust to parental divorce can be very effective (Geelhoed et al., 2001), because they not only teach coping skills, but also provide social support and emotional comfort. This strategy of mobilizing substitutive resources outside a divorced family should also be taught in the divorce education classes that are now provided by many court systems in order to encourage divorcing parents to seek such help for their children. Furthermore, school- and court-based counseling programs should also encourage children with no or a few siblings to form support groups so that these children may share their feelings, experiences, and support with other participants. At least five limitations of the present study need to be noted. Drawing from a resource dilution model, we assume that educational resources are more or less equally distributed among children in most families. Some families, however, may deliberately devote more resources to some children than others, independent of sibship size. Moreover, sibship density and birth order of children have also been found to lead to a somewhat unequal distribution of family resources (Powell and Steelman, 1993). All these may compromise the logics of the dilution and our interaction models. Unfortunately, the NELS data set does not have sibship density or other measures on uneven resource distribution. Future studies with better information on how parental resources are allocated to all children should explore the relationships between unequally distributed resources and child performance. In addition, both resource deprivation and dilution arguments assume that family

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financial resources are finite. This assumption is likely to be incorrect among the richest American households. In such families, neither parental divorce nor large sibship size is likely to reduce the amount of financial resources for children. Although a separate analysis of our data still identifies both divorce and sibship-size effects in families with an annual income of $75,000 or above (in 1988, fewer than 10% of American households had an annual income of $75,000), it would be interesting to investigate whether such effects are still evident in households with incomes in the top 5% or 1%. Unfortunately, our data set does not contain enough such families to allow this analysis. Also as a result of data limitation, we have only a limited number of social and financial resource measures. For instance, although attending travel sport camps and programs in other states and countries has become an increasingly popular way for adolescents to learn about different languages and cultures, and such programs take substantial family financial and social resources, the NELS data set does not have this variable. Thus, future studies with better measures may further explore the relationships between such activities and children’s educational outcomes. In addition, although our findings underline parental resources as an important mechanism for the interaction on educational performance, the findings do not exclude other potential intervening mechanisms. As suggested earlier, the less severe divorce effect observed in large families might also be due to the fact that siblings provide emotional support and comfort during the difficult adjustment process. Unfortunately, we are unable to directly test this hypothesis in this study because the NELS data set does not have variables that measure inter-personal relationships among siblings. Finally, half- and step-siblings are not separated from siblings born to the same biological parents in the NELS. Although sibling relationships in disrupted families and the performance levels among biological, half-, and step-siblings are discussed in prior studies (e.g., Evenhouse and Reilly, 2004; Gennetian, 2004; Ginther and Pollak, 2004), it is not clear how inter-personal relations among half- and step-siblings may modify the sibship-size effect on child performance. Once again, future studies with better measures of sibling types and inter-sibling relations may explore such modifications. In summary, this study contributes to both divorce and sibship-size literatures by integrating two resource models. 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