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Understanding How FamilySocioeconomic Status Mediates theMaternal Intelligence–Child CognitiveOutcomes Relationship: A ModeratedMediation AnalysisD. Diego Torres aa Houston Education Research Consortium , Kinder Institute forUrban Research, Rice University , Houston , Texas , USAPublished online: 12 Nov 2013.

To cite this article: D. Diego Torres (2013) Understanding How Family Socioeconomic Status Mediatesthe Maternal Intelligence–Child Cognitive Outcomes Relationship: A Moderated Mediation Analysis,Biodemography and Social Biology, 59:2, 157-177

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Biodemography and Social Biology, 59:157–177, 2013Copyright © Society for Biodemography and Social BiologyISSN: 1948-5565 print / 1948-5573 onlineDOI: 10.1080/19485565.2013.833804

Understanding How Family Socioeconomic StatusMediates the Maternal Intelligence–Child Cognitive

Outcomes Relationship: A ModeratedMediation Analysis

D. DIEGO TORRES

Houston Education Research Consortium, Kinder Institute for Urban Research,Rice University, Houston, Texas, USA

In a model of moderated mediation using matched data from the 1979 NationalLongitudinal Survey of Youth and the 1979 National Longitudinal Survey of Youth,Children and Young Adults, I test (1) whether family socioeconomic status (SES) medi-ates the maternal intelligence-child cognitive outcomes relationship and (2) the extent towhich this mediating impact is dependent on the level of maternal intelligence. Resultsreveal that the mediating impact of SES on the maternal intelligence–child cognitiveoutcomes relationship varies as a function of the level of maternal intelligence. Thepositive effect of higher SES on children’s academic ability decreases as the cognitiveability of mothers increases, such that children in low IQ households benefit most fromhigher SES, while children in high IQ households benefit somewhat less.

The covariance between socioeconomic status (SES) and phenotypic IQ is well known inthe field of behavioral genetics (Gottfredson 2011). About 30 percent of the variance inthe primary factors that comprise SES indices is explained by cognitive ability (Neisseret al. 1996:82). Gottfredson (1997), Jensen (1998), and Rowe (1997) have highlighted thattests of intelligence, in both the civilian and military spheres, reveal individuals’ abilityto appropriate difficult material and expose the rate at which individuals can learn newmaterial. Taken together, these two factors are strongly predictive of the type of employ-ment individuals can perform well and therefore the amount of income they are likely toearn. Research also shows that higher levels of cognitive ability are required in more pres-tigious occupations (Gottfredson 1997:87), and the more prestigious the job, the greaterthe level of remuneration. Moreover, the predictive validity of general cognitive ability forboth job performance and training rises with the overall complexity of the work being done(Gottfredson 1997:82).

Since one of the most studied relationships in social science research is that of parentalSES with children’s cognitive and academic development (Astone and McLanahan 1991;Bankston and Caldas 1998; Smith, Brooks-Gunn, and Klebanov 1997; Taylor, Dearing,and McCartney 2004), properly understanding the relationship between parental SES and

The author would like to extend thanks to those who provided their insights and feedback duringthe preparation of this manuscript: David J. Harding, of the University of California at Berkeley, andBarbara A. Anderson, Brian A. Jacob, and Yu Xie, all of the University of Michigan–Ann Arbor.

Address correspondence to D. Diego Torres, Houston Education Research Consortium, KinderInstitute for Urban Research, Rice University, 6100 Main Street, MS-28, Houston, TX 77005. E-mail:ddtorres@rice.edu

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phenotypic parental IQ, as well as the ways in which high levels of one might alter oraugment the downward pressure of the low levels of the other on children’s academic per-formance, is important to the formation of effective policies aimed at closing the classgap in educational outcomes. If, however, much of the existing social science literature,particularly in the field of sociology, has viewed the variation in the measures of SES orsocial class—for example, years of education, income, and career prestige—as well as theirassociations with child cognitive outcomes, as completely environmental in origin (Rowe,Vesterdal, and Rodgers 1998), researchers will need to appreciate the fact that part of thevariation is genetic. To the degree that parental SES is associated with children’s cognitiveand academic development (e.g., school grades, psychometric test scores), the relationshipis likely genetically moderated, given that an underlying heritable characteristic relates tothe correlated factors.

For those who have at least recognized the implications that the covariance betweenSES and phenotypic IQ poses to stratification research, their analyses in the past coupleof decades have tended to pit the one against the other rather than investigate the opportu-nity that this covariance offers to test interesting hypotheses with respect to their combinedeffects on children’s life chances (Rowe, Vesterdal, and Rodgers 1998). The origin of thiscontention dates back to the publication of Herrnstein and Murray’s (1994) The Bell Curve:Intelligence and Class Structure in American Life and the rejoinders to it. The main argu-ment proffered in that text is that social background is of decreasing importance and thatmeasured intelligence matters more to individuals’ likelihood of committing crime; beingunemployed, in poverty, or on welfare; or providing substandard care for their children, fac-tors that are associated with fewer years of completed education and, hence, the range ofcareer opportunities available. Fischer et al. (1996), arguing that Herrnstein and Murray’sanalysis overstates the importance of IQ as a predictor of outcomes, carried out phenotypicregression analyses on the same data used by Herrnstein and Murray, entering a host ofadditional “environmental” characteristics that the authors did not, and showed the effectof IQ to be nearly equal to, not greater than, that of social context. A general criticismof both sets of analyses, though, is that they are incapable of explaining the underlyingsources of variation between SES and phenotypic IQ (Jensen 1998; Rowe 1994). Whetherresearchers are studying the relationship of phenotypic parental IQ to child cognitive out-comes or parental SES to child cognitive outcomes, controlling for parental SES in thecase of the former relationship or for phenotypic parental IQ in the case of the latter rela-tionship leads to the removal of, respectively, shared genetic and shared environmentalvariance. Except in comparisons of monozygotic and dizygotic twins or other clever natu-ral experiments, partialing out the true effect of measured parental intelligence on children’scognitive outcomes is perhaps impossible to do well, given the broad array of environmentaland genetic factors that can be controlled for. Inasmuch as the goal of research with regardto these relationships is to separate the sources of variance, then, phenotypic regressionanalyses are not the optimal choice of method. Assuming a causal path from phenotypicparental IQ to child cognitive outcomes that is perhaps mediated by parental SES, how-ever, it may still be possible to test, using phenotypic regression methods, whether and howsaid mediation varies across levels of phenotypic parental IQ, a question that has yet to beadequately addressed in the literature.

For instance, research in the field of behavioral genetics—which typically makes use ofthe twin design and other sibling analyses instead of phenotypic regression analyses, meth-ods that can actually separate the sources of variance just discussed—contends that childrenraised in more advantaged homes have more opportunities to engage in the environmentalexperiences that assist them in reaching their genetic potential for cognitive growth, while

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A Moderated Mediation Analysis 159

children from disadvantaged homes do not (Bronfenbrenner and Ceci 1994; Dickens andFlynn 2001). McGue (1997) has published research supporting this genotype by environ-ment interaction, finding that parental SES positively moderates children’s cognitive ability.Turkheimer et al. (2003) has found the heritability of cognitive ability to be greater by afactor of seven in high SES families compared to low SES families. More recently, work byHarden, Turkheimer, and Loehlin (2007) and Tucker-Drob et al. (2011) has shown, respec-tively, the presence of a genotype by environment interaction effect on cognitive abilityamong adolescents and among infants. This research indicates that the influence of highparental SES is likely associated with a stronger correlation between the measured cog-nitive abilities of parents and those of their children. Given the positive effect of parentalSES on children’s cognitive ability, it at least seems apparent that the cognitive ability ofdisadvantaged children from low cognitive ability homes is likely to rise along with thelevel of parental SES, something social scientists have long argued. What remains unclearis whether the effects of higher parental SES on the phenotypic parental IQ–child cognitiveability relationship are the same at all values of the phenotypic parental IQ.

The Present Study

The social environments that parents provide for their children is not independent of par-ents’ cognitive ability, and, to the degree that environmental variables such as parental SESpredict children’s academic performance, part of that effect is explained by the phenotypicexpression of heritable genetic traits. The important question is whether the indirect effectof phenotypic parental IQ on child cognitive outcomes through parental SES is conditionalon phenotypic parental IQ. This article aims to test a model of moderated mediation, aconceptual model that is shown in Figure 1 (Preacher, Rucker, and Hayes 2007). Whereasmodels of simple mediation and simple moderation have been employed in the past toexamine the phenotypic parental IQ–child cognitive outcomes relationship, this is the firstresearch that integrates the assumptions of both models into one model of moderated medi-ation. I hypothesized an indirect effect of phenotypic parental IQ on children’s academicperformance through parental SES that is conditional on the level of phenotypic parental IQ.

Given the findings of the genotype by environment interaction in the field of behavioralgenetics in particular, I also posited that the indirect impact of phenotypic parental IQ

Parental IQ(X)

Parental SES(M)

Child Outcome(Y)

Parental IQ × Parental SES(X × M)

a1 b1

b2

c’

Figure 1. Conceptual moderated mediation model in which the independent variable moderates themediated path.

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160 D. D. Torres

on children’s academic performance via parental SES should be larger at lower levels ofphenotypic parental IQ and smaller at higher levels of phenotypic parental IQ. That is, Ianticipated larger returns to children’s psychometric test scores as a result of higher parentalSES when phenotypic parental IQ was low and smaller returns as a result of higher parentalSES when phenotypic parental IQ was high.

Methods

Sample

In order to test the strength of the indirect effect of phenotypic parental IQ on children’s aca-demic outcomes via parental SES, I use matched mother-child data from the 1979 NationalLongitudinal Survey of Youth (NLSY79) and the 1979 National Longitudinal Survey ofYouth, Children and Young Adults (NLSY79-CYA). The original NLSY79 sample included12,686 individuals who were between the ages of 14 and 21 as of January 1, 1979;6,283 of these individuals were female. Of these 6,283 women, 451 were in the militaryand were subsequently dropped from future surveys in 1984. Because of financial con-straints, another 901 women from the economically disadvantaged white oversample weredropped from future surveys in 1990. With the passage of time and the attendant growth inNLSY79 women’s family size, the weighted mother-child data begins to be representativeof a cross-section of women in the United States.

Child cognitive assessments, my primary outcomes of interest, were administered bien-nially to the children of the NLSY79 women beginning in 1986. Taking eight rounds ofdata from 1986 to 2000, I retained from separate datasets (one for each of the relevantoutcomes) the most recent round for which a valid score was recorded for a respondent asof the completion of the 2000 survey, excepting those individuals whose most recent validscore was recorded in 1986. This restrictive measure was employed so that each individualcontributed at least two scores across the eight rounds of data for any given outcome, onescore to serve as the dependent variable in my models, the other the prior year’s score toserve as a control. Half of the scores for each outcome observed came from the 1998 and2000 survey years, while the other half were distributed across the five rounds prior to1998, going back to 1988. Preliminary analyses comparing regression models between ear-lier and later years and by year separately showed consistent, if slightly different, estimates.Therefore, for each outcome of interest, all the data were combined into a single model ofmoderated mediation. Many of the NLSY79 mothers represented multiple children in 2000.

It is important to note here that although childbearing is estimated to be 90 percentcomplete for the NLSY79 cohort as of the completion of the 2000 survey round, concernsmay arise in some quarters about two related facts. First, whereas previously it was thecase that many of the NLSY79-CYA children were born to teen mothers, by 2000, thetrend has changed to one in which more children are being born to women in their 20s and30s (see Center for Human Resource Research 2002a). Second, it is reasonable to expectto see differences in socioeconomic status between families of children born earlier to pre-dominantly younger mothers and families of children born later to older mothers. Statedmore clearly, the youngest children in the sample are more likely than their older peers tohail from middle class rather than poor households, a fact that necessitates treating within-sample age comparisons with caution. NLSY79-CYA documentation suggests, however,that it is increasingly reasonable by 2000 to generalize to the broader child population,despite these concerns.

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A Moderated Mediation Analysis 161

Dependent Measures

Measures of children’s performance, returned as a raw score, are provided for three of thefive subtests of the Peabody Individual Achievement Test, Revised (PIAT-R)— the read-ing recognition, reading comprehension, and mathematics subtests—and for the PeabodyPicture and Vocabulary Test-Revised (PPVT-R); these scores constitute the child cognitiveoutcomes of interest. The complete battery of Peabody assessments, outlined in greaterdetail later, is both well normed and standardized, and both the PIAT-R and the PPVT-Rhave high test-retest reliability, are strong in predictive validity, and have been shown tocorrelate well with other measures of cognitive ability.

The total number of child scores available for each of the four outcomes is as follows.The reading recognition subtest of the PIAT-R consisted of 6,756 child scores, the readingcomprehension subtest consisted of 5,987 child scores, the mathematics subtest consistedof 6,767 child scores, and the PPVT-R consisted of 5,427 child scores. The total number ofNLSY79 mothers represented in each of the four subtests was, respectively, 3,335, 3,073,3,334, and 2,850. Children’s mean age ranged from a low of 11.61 years on the PPVT-R toa high of 12.69 years on the reading comprehension subtest of the PIAT-R.

PIAT-R Reading Recognition. The reading recognition subtest of the PIAT-R, which con-sists of 84 items of increasing difficulty from the preschool to the high school level,measures, among children age five and up, how well children recognize words and how wellthey pronounce the words recognized. Children are assessed on their ability to match letters,name names, and read single words. The completion rate for the PIAT-R reading recog-nition subtest is a little less than 90 percent, with little difference between racial/ethnicgroups. A disparity in completion rates does, however, exist between children of differentages; the oldest and youngest children have below average completion rates compared tochildren in the middle ages of childhood. Regarding achieved scores, the weighted dis-tribution for the 2000 survey reveals that white children had a mean percentile score of67.3, with Hispanics following at 57.7 and blacks still lower at 50.2, a trend that is similaracross all rounds of the NLSY79-CYA data. The corresponding mean standard scores were109.1 for whites, 104.4 for Hispanics, and 100.2 for blacks (Center for Human ResourceResearch 2002b). NLSY79 documentation highlights the point that scores on this subtestare increasingly confounded with acculturation factors once children leave the early gradesof formal schooling.

PIAT-R Reading Comprehension. The reading comprehension subtest of the PIAT-R, whichconsists of 66 items of increasing difficulty, measures children’s ability to derive meaningfrom sentences read silently. Children are assessed on their ability to choose from amongfour possible picture answers the best portrayal of a sentence’s meaning. The PIAT-R read-ing comprehension subtest is only administered to children who score 15 or higher on thePIAT-R reading recognition subtest. Completion rates for this measure are lowest relativeto the other PIAT-R subtests considered in this study, though, like them, it reveals littleevidence of racial/ethnic disparities. The racial/ethnic disparities in mean percentile andraw scores on the 2000 PIAT-R reading comprehension subtest were not dissimilar to thosefound with respect to the 2000 PIAT-R reading recognition subtest. White children hadhigher mean percentile and standard scores (61.5 and 105.4, respectively) than Hispanicchildren (48.3 and 98.9), who, in turn, had higher mean scores than blacks (41.3 and 95.4;Center for Human Resource Research 2002b).

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162 D. D. Torres

PIAT-R Mathematics. Consisting of 84 multiple-choice questions of increasing difficultythat range from basic numeral recognition and addition to more complex trigonometry, themathematics subtest of the PIAT-R measures children’s knowledge of concepts and skillstaught in mainstream mathematics education. While the test has an overall completion rateof 91 percent, the rate is lower among children older than 11 years of age. Completion ratesdo not vary by race/ethnicity. Racial/ethnic differences did, however, arise with respect tothe mean percentile and standard scores in 2000. Again, whites outperformed Hispanics,who outperformed blacks.

PPVT-R. Dunn and Dunn (1981) describe the PPVT-R as measuring “an individual’s recep-tive (hearing) vocabulary for standard American English [that] provides, at the same time,a quick estimate of verbal or scholastic aptitude.” Consisting of 175 vocabulary items ofincreasing difficulty, the PPVT-R assesses children’s ability to choose from among fourpicture answers the best portrayal of a word’s meaning. Of all the Peabody measures,the PPVT-R revealed the greatest racial/ethnic disparities in mean percentile and standardscore outcomes for 2000. The mean percentile score for whites was more than 20 pointshigher than the mean percentile score for Hispanics and more than 30 points higher than themean percentile score for blacks. The mean standard score on the PPVT-R was 103.3 forwhite children, which was almost 15 points higher than the 88.4 mean standard scoreachieved by Hispanic children and nearly 20 points higher than the 82.5 mean standardscore achieved by black children. Interestingly, these differences remain strong even aftercontrolling for demographic and socioeconomic controls.

Independent Measure

Maternal AFQT. Maternal percentile score on the Armed Forces Qualification Test(AFQT), which consists of word knowledge, paragraph comprehension, arithmetic reason-ing, and mathematics knowledge assessments of the Armed Services Vocational AptitudeBattery (ASVAB), serves as an indicator of phenotypic parental IQ. The AFQT, admin-istered to most of the original members of the NLSY79 cohort, is used by the U.S.Department of Defense to predict maximal performance and to match military recruitsto job tasks they can do well (Armor and Sackett 2004; Hoewing 2004). As such, it is avery good proxy for the score an individual might receive on a formal test of intelligence,which also has high predictive validity for job trainability, job performance, and the abilityto quickly appropriate and manipulate knowledge in dynamic environments (Gottfredson1997; Jensen 1998). Indeed, both the AFQT and formal tests of intelligence are highly cor-related with one another, with r averaging about .8 (Herrnstein and Murray 1994). AFQTscores’ ability to explain nearly 65 percent of the variation in IQ, and vice versa, suggeststhat both tests are measuring the same underlying trait.

The measured intelligence of parents is expected to correlate well with their children’spsychometric test scores, consistent with the behavioral genetics literature that shows cog-nitive ability to have a substantial heritable component (Jensen 1998; Rowe 1994). Whileheritability tends to be highest at older ages, research by Rodgers, Rowe, and May (1994)that uses the same dataset used here suggests that it is a sizable 50 percent in childhood andadolescence. Maternal intelligence should also correlate well with parental SES, which hasan independent effect on children’s academic performance. I treat intelligence as precedingin time both parental SES and children’s ability, though, as I will address in the discus-sion, it is also reasonable to reverse this relationship. Intelligence is hypothesized to haveboth a direct impact on child cognitive outcomes and an indirect effect on child cognitiveoutcomes via parental SES.

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A Moderated Mediation Analysis 163

Mediator

Parental Socioeconomic Status (SES). An SES index was created by standardizing, for allrounds, the sum of the z-transformed values of (1) the natural log of net family income plusone; (2) the highest grade of the NLSY79 woman and her spouse; and (3) the maximumDuncan SEI value, first transformed to deciles, of either the NLSY79 woman or her spouse.Cronbach’s alpha, a gauge of the reliability of multi-item scales, returned a value in theexcellent range of about 0.92, indicating that a shared underlying trait is being measuredby these composite indices.

Control Measures

In addition to the typical demographic covariates of race/ethnicity, sex, and age includedin each of the four models measuring the conditional indirect effect of maternal AFQTon children’s test scores through parental SES, I also included as a control respondents’previous grand mean centered raw scores.

Data Analysis Plan

Missing values of the four independent measures constituting the basis for the creationof the parental SES indices were handled via multivariate imputation by fully conditionalspecification (FCS) (Raghunathan et al. 2001) using SPSS Statistics 19.0. Also referredto as multiple imputation by chained equations (MICE), FCS imputes missing valueson a variable-by-variable basis given, or conditional on, information on all the variablesobserved. The imputations are generated through a sequence of regression models, differ-entiated by the type of variable being imputed (e.g., continuous, binary, categorical), inwhich the covariates include both observed and imputed values for a given individual.

Subsequent to the imputation procedure, indirect (or simple mediation) and condi-tional indirect effects (or moderated mediation) were assessed in each of the four outcomes.Descriptions of the procedures used follow.

Simple Mediation. While Preacher, Rucker, and Hayes (2007:211) note that a “significantunconditional indirect effect [or simple mediation] does not constitute a prerequisite forexamining conditional indirect effects [or moderated mediation],” I nonetheless carriedout preliminary analyses for each of the four outcome measures outlined previously byconfirming that maternal AFQT has a strong and significant independent effect on chil-dren’s psychometric test scores and then testing whether the direct effect was mediated byparental SES (Figure 2). To assess the strength of the mediating impact of parental SES onthe maternal AFQT–child cognitive outcomes relationship and to avoid issues arising fromnonnormally distributed data, I used the product-of-coefficients strategy with bootstrapping(Preacher and Hayes 2004; Preacher, Rucker, and Hayes 2007).1 The indirect effect, then,

1While the product-of-coefficients strategy assumes that the point estimate of the indirect effectis normally distributed, this is usually not the case, even in large samples in which the expectation ofthe point estimate is that it tends toward normality. The standard error used to determine the statisticalsignificance of a1b1 is therefore problematic. Bootstrapping overcomes the problems associated withthe product-of-coefficients strategy by quantifying the indirect effect as the product of the mean boot-strapped sample estimates of the regression coefficients, with the optimum lower limit of bootstrapresamples being 5,000. Confidence intervals are produced using the estimated standard error of themean indirect effect, and ranges excluding zero signify that mediation exists.

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164 D. D. Torres

Parental IQ(X)

Parental SES(M)

Child Outcome(Y)

a1b1

c’

Figure 2. A model of simple mediation.

was estimated by first regressing parental SES on maternal AFQT (M) and then regressingchildren’s scores on parental SES, controlling for maternal AFQT (Y):

M = a0 + a1X + r (1)

Y = b0 + c ′X + b1M + r (2)

Sample indirect effects were then quantified as products of the mean bootstrapped sampleestimates of the regression coefficients a1 and b1, where a1 refers to the slope coefficient ofM regressed on X and b1 refers to the conditional coefficient of Y regressed on M. Giventhat the unconditional indirect effect is generally given as c – c’, where c denotes the effectof X on Y in the absence of M and c’ denotes the effect of X on Y in the presence of M, c –c’ and a1b1 are equivalent (MacKinnon, Lockwood, and Williams 2004).

Moderated Mediation. Preacher, Rucker, and Hayers (2007) note several cases in whichthe magnitude of an indirect effect may depend on a moderator. Regarding the graphicalrepresentation of simple mediation in Figure 2, one can imagine cases in which some fourthvariable (W) impacts (1) the a1 path, (2) the b1 path, or (3) both the a1 and b1 paths.Additionally, W may also impact only (4) the a1 path, while a fifth variable (Z) affects theb1 path. For the purposes of this study, I focused on how the indirect effect of maternalAFQT on children’s academic performance via parental SES might depend on maternalAFQT. This is a case of the independent variable itself functioning as the moderator of theb1 path (see Figure 1 in this article and Model 1 in Preacher, Rucker, and Hayes 2007:194).

As in the preliminary examination of simple mediation addressed previously, I testedthe hypothesis of moderated mediation in two regression analyses using bootstrapping.First, I regressed parental SES (M) on maternal AFQT (X) (see Equation 1). I then regressedchildren’s test scores (Y) on maternal AFQT (X), parental SES (M), and the interactionbetween maternal AFQT (X) and parental SES (M),

Y = b0 + c ′X + (b1 + b2X) M + r (3)

The dependent variable model represented in Equation 3 differs from that represented inEquation 2, in that it now elucidates how the regression of Y on M can be seen as conditionalon X. The hypothesis of moderation, or causal interaction, in the terminology of Wu andZumbo (2008), goes beyond what is assumed in a simple interaction between two maineffects in stressing that the mediating effect of M is expected to vary at the values of the

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A Moderated Mediation Analysis 165

moderator, X (Morgan-Lopez and MacKinnon 2006). The aim of moderated mediation isnot to highlight the combined effect of X and M on Y—which is what statistical interactionachieves—but to elucidate how the moderator, also the main predictor in the case of thepresent analyses, alters the established causal relationship of M and Y . Given a direct effectof maternal AFQT on parental SES in the mediator model, a significant interaction effectbetween maternal AFQT and parental SES in the dependent variable model suggests, then,that mediation was indeed moderated.

In cases in which a significant interaction was found to exist, I probed the indirect effectby completing regression analyses at the mean and ±1 SD of maternal AFQT to ascertainthe extent to which the indirect effect varied as a function of maternal AFQT. Since the

conditional indirect effect is quantified as f(θ |X

)= a1

(b1 + b2X

), the values of X at the

mean and ±1 SD were simply inserted into this equation. I used 95 percent bias-correctedbootstrapping to achieve more precise confidence intervals on which to judge statisticalsignificance from zero. Preacher, Rucker, and Hayes (2007) also suggest an extension ofthe Johnson-Neyman approach to moderated mediation analysis, because it allows for easyidentification of the value of the moderator for which the indirect effect is just statisticallysignificant (α = 0.05). Additional values of the moderator that are below α = .05 constitutethe region of significance for the indirect effect, while values greater than α = .05 indicatestatistical nonsignificance.

Results

Descriptives

Table 1 shows the means and standard deviations for maternal AFQT, parental SES, and thefour Peabody measures. While the full range of the AFQT is represented among mothersin the dataset, it is interesting that the mean percentile score of the present sample is onlyabout 35. This squares, though, with the fact addressed previously that many of the womenrepresented were early childbearers, who tend, on average, to have lower cognitive abilitythan their delaying peers. It is true that by 2000, more of the women bearing children wereolder, but this trend is not yet fully reflected in the child data; hence, the obviously lowmean maternal AFQT percentile score.

A cursory look at the pairwise correlations shown in Table 2 reveals statistically signifi-cant pairwise correlations among the dependent, main independent, and mediator variables.Maternal AFQT explains just less than 30 percent of the variance in parental SES, about

Table 1Means and standard deviations for main predictor, mediator, and children’s raw scores

on the Peabody instruments

Variables Mean SD

Maternal AFQT (n = 3,363) 34.723 26.573Parental SES (n = 3,363) −0.038 2.563PIAT-R Reading Recognition (n = 6,756) 53.118 15.954PIAT-R Reading Comprehension (n = 5,987) 49.199 12.308PIAT-R Mathematics (n = 6,767) 48.537 12.911PPVT-R (n = 5,427) 108.633 20.633

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Table 2Pairwise correlations for maternal AFQT, parental SES, and children’s raw scores (all

measures)

Variables (1) (2) (3) (4) (5) (6)

Maternal AFQT (1) 1Parental SES (2) 0.529 1PIAT-R Reading Recognition (3) 0.259 0.188 1PIAT-R Reading Comprehension (4) 0.352 0.248 0.741 1PIAT-R Mathematics (5) 0.295 0.190 0.717 0.643 1PPVT-R (6) 0.395 0.270 0.586 0.629 0.574 1

Note: All pairwise correlations are significant at the p < .001 level.

7 percent of the variance in reading recognition performance, 12 percent of the variance inreading comprehension performance, about 9 percent of the variance in mathematics per-formance, and about 16 percent of the variance in children’s performance on the PPVT-R.The percentage of variance in child cognitive ability explained by maternal AFQT com-ports with findings in the literature (Plomin et al. 2001). It should be apparent from thecorrelations shown that although a huge portion of parental SES is explained by maternalAFQT, the relationship between parental SES and children’s test scores is indicative of apossible mediating effect of parental SES on the maternal AFQT–child cognitive outcomesassociation. If maternal AFQT explains about 30 percent of the variance in parental SES,and if parental SES explains about 5 percent of the variance in children’s ability (aboutthe average r2 value across the four pairwise correlations of parental SES and the Peabodymeasures), it is likely that, in addition to the direct effect of maternal AFQT on child scores,there is an indirect effect of maternal AFQT through parental SES. The pairwise correla-tions among the PIAT-R measures reveal that about 41 percent to more than half of thevariance is explained between any two measures, with these values being significant at thep <.001 level. The associations between any of the PIAT-R measures and the PPVT-R isslightly lower than the associations found among the PIAT-R measures alone, but more thanone-third up to 40 percent of the variance between one test and the other is still explained.

Simple Indirect Effect

Significant mean indirect effects of maternal AFQT on children’s test scores via parentalSES were found for each of the four Peabody measures. The total indirect effect was β =0.0218 (SE = 0.0038), with a bias-corrected and -accelerated 95% CI from 0.0142 to0.0292 for the reading recognition subtest of the PIAT-R. The direct effect remained sta-tistically significant (β = 0.1647, p <.001), however, suggesting only partial mediationof the maternal AFQT–children’s reading recognition score relationship. For the readingcomprehension portion of the PIAT-R, the indirect effect was β = 0.0215 (SE = 0.0033),with a 95% CI from 0.0152 to 0.0282, although again, the direct effect remained strongand significant (β = 0.1465, p <.001). The total indirect effect was β = 0.0142 (SE =0.0031), with a 95% CI from 0.0082 to 0.0203 for the mathematics subtest of the PIAT-R.Maternal AFQT still exerted a significant direct impact of β = 0.1447 on children’s math-ematics performance (p <.001), despite partial mediation. Finally, regarding the PPVT-R,the total indirect effect was β = 0.0446 (SE = 0.0053) with a 95% CI from 0.0345 to0.0553. And like the other assessments, the direct effect of maternal AFQT on children’s

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A Moderated Mediation Analysis 167

PPVT-R percentile score remained statistically significant when the mediator, parental SES,was included in the regression (β = 0.2273, p <.001).

Maternal AFQT exerted a stronger influence on each of the respective child cognitiveoutcomes when not controlling for parental SES. When parental SES was controlled for,however, the total effect of maternal AFQT was reduced by about 12 percent on the readingrecognition subtest, about 13 percent on the reading comprehension subtest, about 9 percenton the mathematics subtest, and about 16 percent on the PPVT-R.

Conditional Indirect Effect

I tested the hypothesis of moderated mediation, or conditional indirect effects, on each out-come first by regressing parental SES (M) on maternal AFQT (X), the a1 path denotedin Equation 2, and then by regressing child percentile scores on maternal AFQT (X), thec’ path, parental SES (M), the b1 path, and the interaction between maternal AFQT andparental SES (the b2 path). When they supported the hypothesis of moderated mediation,significant interactions between maternal AFQT and parental SES were probed at specificvalues of the moderator (i.e., maternal AFQT) to ascertain whether and how the indi-rect effect differed as a function of the moderator. Results for regression analyses of theconditional indirect effect for all four outcomes are shown in Table 3.

PIAT-R Reading Recognition. Results from the regression analysis revealed that parentalSES was predicted by maternal AFQT; the coefficient represented in the a1 path indi-cated that a one percentile increase in maternal AFQT is associated with a β = 0.020(p <.001) standard deviation increase in parental SES. Children’s reading recognitionscores were predicted by maternal AFQT (c’ path; β = 0.150, p 0.001), parental SES (b1

path; β = 1.774, p <.001), and the maternal AFQT by parental SES interaction (b2 path;β = –0.023, p < .01), with approximately 44 percent of the reading recognition ability vari-ance being explained. Stated more clearly, the c’ path highlighted that a one percentile pointincrease in maternal AFQT is associated with an increase of just smaller than one-seventhof a raw point in children’s ability on the reading recognition test, the b1 path showed that aone standard deviation increase in parental SES above the mean parental SES is associatedwith an appreciation of 1.77 raw points on the reading recognition test, and the b2 pathelucidated that there is a declining mediating impact of parental SES on children’s readingrecognition scores the higher up the maternal AFQT ladder a child’s parent is.

In light of the significant relationship between maternal AFQT (the main indepen-dent variable) and parental SES (the mediator variable), the significant interaction term, b2,supported the hypothesis of moderated mediation. I therefore examined whether this condi-tional indirect effect was significant at specific values of the moderator, which in this case isalso the independent variable. Table 4 shows the bootstrapped results testing the hypothesisthat the conditional indirect effect equals zero at the mean and ±1 SD of the moderator.The bias-corrected 95% CIs revealed that parental SES had its strongest impact on readingrecognition raw scores for children with mothers at low values of AFQT. Children born tomore intelligent mothers—that is, those one standard deviation above the mean AFQT—donot appear to benefit from being in a family with higher SES. The indirect effect at onestandard deviation above the mean maternal AFQT was less than half the indirect effectat the mean of maternal AFQT and less than one-third the indirect effect at one standarddeviation below the mean maternal AFQT.

Using the extension of the Johnson-Neyman approach to moderated mediation, theconditional indirect effect of maternal AFQT on children’s PIAT reading recognition score

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Tabl

e3

Res

ults

ofre

gres

sion

anal

yses

for

the

cond

ition

alin

dire

ctef

fect

sof

mat

erna

lAFQ

Ton

child

ren’

sra

wsc

ores

(all

mea

sure

s)

Med

iato

rva

riab

lem

odel

Rea

ding

reco

gniti

onR

eadi

ngco

mpr

ehen

sion

Mat

hem

atic

sPP

VT

βSE

βSE

βSE

βSE

Pred

icto

rC

onst

ant

−1.3

58∗∗

∗0.

048

−1.3

75∗∗

∗0.

058

−1.3

81∗∗

∗0.

048

−1.3

48∗∗

∗0.

056

Mat

erna

lAFQ

Tsc

ore

(a1

path

)0.

020∗∗

∗0.

000

0.01

9∗∗∗

0.00

10.

020∗∗

∗0.

000

0.01

9∗∗∗

0.00

1

Dep

ende

ntva

riab

lem

odel

Con

stan

t18

.438

∗∗∗

0.79

425

.475

∗∗∗

0.78

722

.407

∗∗∗

0.63

570

.251

∗∗∗

1.11

9M

ater

nalA

FQT

scor

e(c

’pa

th)

0.15

0∗∗∗

0.00

80.

138∗∗

∗0.

007

0.13

7∗∗∗

0.00

60.

207∗∗

∗0.

011

Pare

ntal

SES

(b1

path

)1.

774∗∗

∗0.

256

1.54

0∗∗∗

0.22

71.

001∗∗

∗0.

204

3.76

7∗∗∗

0.34

8M

ater

nalA

FQT

Scor

e×

Pare

ntal

SES

(b2

path

)−0

.023

∗∗∗

0.00

6−0

.013

∗∗∗

0.00

5−0

.010

∗∗∗

0.00

5−0

.048

∗∗∗

0.00

8

Not

e:∗∗

∗ p<

.001

;∗∗p

<.0

1;∗ p

<.0

5.

168

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Tabl

e4

Boo

tstr

appe

din

dire

ctef

fect

sof

mat

erna

lAFQ

Ton

child

ren’

sra

wsc

ores

atth

em

ean

and

±1

SD(a

llm

easu

res)

PIA

T-R

Rea

ding

Rec

ogni

tion

PIA

T-R

Rea

ding

Com

preh

ensi

on

Mat

erna

lAFQ

Tβ

SEL

LB

Ca

UL

BC

bβ

SEL

LB

CU

LB

C

−1SD

0.03

2∗∗∗

0.00

50.

022

0.04

20.

028∗∗

∗0.

004

0.02

00.

037

Mea

n0.

020∗∗

∗0.

004

0.01

30.

028

0.02

2∗∗∗

0.00

30.

015

0.02

8+1

SD0.

009

0.00

50.

000

0.01

70.

015∗∗

∗0.

004

0.00

70.

023

PIA

T-R

Mat

hem

atic

sPP

VT-

R

βSE

LL

BC

UL

BC

βSE

LL

BC

UL

BC

−1SD

0.01

9∗∗∗

0.00

40.

011

0.02

60.

067∗∗

∗0.

006

0.05

30.

081

Mea

n0.

013∗∗

∗0.

003

0.00

70.

019

0.04

3∗∗∗

0.00

50.

033

0.05

4+1

SD0.

008∗

0.00

40.

000

0.01

60.

019∗∗

∗0.

006

0.00

70.

031

Not

e:∗∗

∗ p<

.001

;∗∗p

<.0

1;∗ p

<.0

5;N

=5,

000

boot

stra

pped

sam

ples

.a LL

BC

refe

rsto

the

low

erle

velo

fthe

bias

-cor

rect

ed95

perc

entc

onfid

ence

inte

rval

.bU

LB

Cre

fers

toth

eup

per

leve

lof

the

bias

-cor

rect

ed95

perc

entc

onfid

ence

inte

rval

.

169

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170 D. D. Torres

Maternal AFQT Percentile10 30 50 70 90

Con

diti

onal

Ind

irec

t E

ffec

t

–0.02

0.00

0.02

0.04Region of Significance

95% Confidence Band

Figure 3. Moderated indirect effect of maternal AFQT percentile scores on children’s PIAT-Rreading recognition raw scores through parental SES with 95 percent confidence bands.

through parental SES was shown to be significant between the first (p <.001) and just belowthe fifty-eighth (p >.05) percentile of maternal AFQT. Not only did the returns to higherparental SES on children’s reading recognition scores tend to decrease with increasing val-ues of maternal AFQT, but they actually disappeared at the very highest levels of maternalAFQT.

Figure 3 shows the indirect effect of maternal AFQT on children’s reading recogni-tion scores vis-à-vis parental SES, plotted at all ranges of the moderator with attendant95 percent confidence bands. The vertical line indicates the upper boundary of the regionof significance, while the horizontal line represents an indirect effect of zero. The lowerdashed line representing the lower confidence band approaches zero when the upper limitof the region of significance is reached.

PIAT-R Reading Comprehension. In agreement with the results yielded from the regressionanalysis for the reading recognition outcome, the analysis for the reading comprehensionscores also revealed that parental SES was predicted by maternal AFQT (Table 3). Thecoefficient represented in the a1 path indicated that a one percentile increase in maternalAFQT is associated with a β = 0.019 (p <.001) standard deviation increase in parental SES.The c’ path suggested that a one percentile point increase in maternal AFQT is associatedwith an increase of about one-seventh of a raw point in children’s reading comprehension(β = 0.138, p <.001), about the same effect as was shown in reading recognition analy-sis. Whereas the reading recognition data showed that a one standard deviation increasein parental SES above the mean is associated with an appreciation of 1.77 raw points onthe reading recognition test, however, the coefficient for the b1 path for the reading com-prehension data was somewhat reduced; the gain to children’s reading comprehension rawscore from a one standard deviation increase in parental SES was only about 1.5 (p < .001).

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A Moderated Mediation Analysis 171

Maternal AFQT Percentile10 30 50 70 90

Con

diti

onal

Ind

irec

t E

ffec

t

–0.02

0.00

0.02

0.04

Region of Significance

95% Confidence Band

Figure 4. Moderated indirect effect of maternal AFQT percentile scores on children’s PIAT-Rreading comprehension raw scores through parental SES with 95 percent confidence bands.

Finally, while the coefficient for the b2 path was smaller for reading comprehension relativeto the reading recognition data, the value nonetheless implied a declining mediating impactof parental SES on the maternal AFQT–child cognitive outcomes relationship as maternalAFQT increases (β = –0.013, p <.001). About 35 percent of the reading comprehensionability variance was explained.

The significant interaction term b2 again supported the hypothesis of moderated medi-ation. Probing whether this conditional indirect effect was significant at the mean and ±1SD of the moderator, parental SES was shown to have its strongest impact on children’sreading comprehension raw scores when maternal AFQT percentile scores were low (seeTable 4). The indirect effect, however, tended to decline such that the value at one standarddeviation above the mean maternal AFQT was half that at one standard deviation below themean maternal AFQT. Values at the mean and ±1 SD of the moderator were all statisticallysignificant at p <.001

Figure 4 shows a graphical representation of the indirect effect plotted at all ranges ofthe moderator with attendant 95 percent confidence bands. The region of significance of theindirect effect had its lowest bound at the first (p <.001) percentile of maternal AFQT andits upper bound at just below the seventy-seventh (p >.05) percentile of maternal AFQT.Given that maternal AFQT percentile scores range from 1 to 99, 76.2517 is the largest valueof the moderator at which parental SES has a mediating impact. Beyond that, the mediat-ing effect of higher parental SES on the maternal cognitive ability–reading comprehensionscores relationship is negligible.

PIAT-R Mathematics. The sixth and seventh columns of the mediator variable model shownin Table 3 reveal that parental SES was predicted by maternal AFQT (a1 path; β = 0.020,p < .001). The dependent variable model shows that maternal AFQT (c’ path; β = 0.137,

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172 D. D. Torres

Maternal AFQT Percentile10 30 50 70 90

Con

diti

onal

Ind

irec

t E

ffec

t

–0.02

–0.01

0.00

0.01

0.02

0.03

0.04

Region of Significance

95% Confidence Band

Figure 5. Moderated indirect effect of maternal AFQT percentile scores on children’s PIAT-Rmathematics raw scores through parental SES with 95 percent confidence bands.

p <.001), parental SES (b1 path; β = 1.001, p <.001), and the maternal AFQT by parentalSES interaction (b2 path; β = –0.010, p <.001) all predicted children’s mathematics rawscore, with 45 percent of the mathematics ability variance being explained. While maternalAFQT had a positive direct effect on parental SES, and while parental SES had a positivedirect effect on children’s mathematics raw scores, the interaction between maternal AFQTand parental SES actually pointed to a weakening of the mediating impact of the latter asvalues of the former rose.

Given the significant interaction term, I examined how the indirect effect depended onthe value of the moderator. The bottom left panel of Table 4 shows the bootstrapped resultstesting the hypothesis that the conditional indirect effect equals zero at the mean and ±1SD of the moderator. As was the case with the reading recognition and reading comprehen-sion data, parental SES appeared to have its greatest influence on children’s mathematicsperformance at low values of maternal AFQT and decreased as maternal AFQT increased.Figure 5 shows the indirect effect to be significant from the first percentile of maternalAFQT up to about the sixtieth percentile of maternal AFQT. The lower bound of the con-fidence intervals of the bootstrapped estimates includes zero above this level of maternalAFQT.

PPVT-R. The final model in Table 3, representing the moderated mediation regression anal-ysis for the PPVT-R data, shows that parental SES was predicted by maternal AFQT (a1

path; β = 0.019, p <.001). Additionally, children’s PPVT-R raw scores were predicted bymaternal AFQT (c’ path; β = 0.207, p <.001), parental SES (b1 path; β = 3.767, p <.001),and the maternal AFQT by parental SES interaction (b2 path; β = –0.048, p <.001), with49 percent of the PPVT-R ability variance being explained. Consistent with the findingsof the other three outcomes analyzed here, parental SES had a mediating impact on the

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A Moderated Mediation Analysis 173

Maternal AFQT Percentile10 30 50 70 90

Con

diti

onal

Ind

irec

t E

ffec

t

–0.02

0.00

0.02

0.04

0.06

0.08 Region of Significance

95% Confidence Band

Figure 6. Moderated indirect effect of maternal AFQT percentile scores on children’s PPVT-R rawscores through parental SES with 95 percent confidence bands.

maternal AFQT–child academic outcomes relationship that was moderated by maternalAFQT. The bootstrapped results testing the significance of the indirect effect at the meanand ±1 SD of the moderator, shown in Table 4, indicated that the greater the levels of mater-nal AFQT, the smaller the returns to children’s academic performance as the measure ofparental SES moved higher. As also in the case of the other outcomes, there was an upperrange for the significance of the indirect effect of maternal AFQT on children’s PPVT-Rscores via parental SES. Figure 6 shows the conditional indirect effect to be significantthroughout the lower range of the moderator up until the lower dashed line representing thelower confidence band falls below zero. The region of significance for the indirect effectstarts at the first and ends just below the sixty-fifth percentile of maternal AFQT.

Discussion

Focusing on four academic measures, the present study investigated (1) whether there wasa mediating effect of the maternal cognitive ability–child cognitive outcomes relationshipby parental SES and, if so, (2) the degree to which that mediation depended on the differentlevels of maternal cognitive ability. The results buttress findings in the field of behavioralgenetics and general social stratification research. Both maternal cognitive ability (heremeasured using the AFQT) and parental SES have a main effect on children’s psycho-metric test score outcomes. Interestingly, however, while parental SES mediated some ofthe effect of maternal AFQT on children’s test scores, the effect of parental SES on chil-dren’s scores was conditional on the levels of maternal AFQT. It was apparent in each ofthe outcomes analyzed that children raised by mothers of low cognitive ability benefitedmore from higher SES environments than did their peers reared by mothers of higher cog-nitive ability. Indeed, the pattern that emerged was one in which the positive returns to themediating impact of higher parental SES on the maternal AFQT–child academic outcomes

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174 D. D. Torres

relationship declined across the range of maternal AFQT. Indeed, with respect to each ofthe assessments, the partial mediation effect of parental SES was nonexistent at the veryhighest levels of maternal AFQT, implying a limited range of the conditional indirect effect.

The findings here are consistent with research published by Bronfenbrenner and Ceci(1994) and Dickens and Flynn (2001), who argued that those raised in disadvantagedenvironments are at risk for failing to reach their genetic cognitive potential. That is, thecombination of having parents of low intelligence and being poor is likely a significantlygreater developmental disadvantage for children than being poor only. Conversely, beingreared in a social environment that is headed by high IQ parents, regardless of SES, is bet-ter for one’s life chances. As Flynn (2007:94) argues, “other people are the most importantfeature of our cognitive environment and . . . the mean IQ of our social environments is apotent influence on our own IQ.”

The policy implications of the conditional indirect effect explicated in this article sug-gest that money transfers to the cognitively depressed poor could increase the availability ofeducational resources and opportunities for their children that would otherwise have beenabsent because of their penury. I say “could” if only to stress the fact, as others have done,that income should not be viewed as a “‘multipurpose’ policy instrument” to improve thelife chances of children (Mayer 1997:145; Rowe 1994). While evidence from the literatureof a dampening effect of low SES on children’s cognitive ability and academic develop-ment has prompted many scholars to advocate policies such as raising the incomes of poorfamilies as a way to enhance children’s development (Duncan et al. 1998; Garbarino 1992;McLoyd 1998), if the reduction of poverty does not at the same time assist parents to attainmore education, be more involved in their children’s schools, and have relationships withtheir children’s teachers, and improve their parenting practices, such transfers will be fornaught. This will be especially true for the long-term as opposed to the short-term poor,who are quite different in their social and cultural orientations. Many adults who enterpoverty do so for a short time and are often equally competent caregivers of their childrenin trying times as in more normal circumstances. The long-term poor, in contrast, typicallyare less competent and more abusive in the rearing of their children (Seagull and Scheurer1986; Taylor et al. 1991). It is generally the case with this group that economic improve-ments should be accompanied by positive social and cultural education to counteract thenegative impacts of the nonexpectable home environments, dangerous neighborhoods, andpoor school curriculums in which their children are immersed. The assumption is clear:the behaviors of the long-term poor are not likely to be improved by increased monetaryresources alone but must be supplemented by changes in attitude and outlook that togetherround out what is measured in indices of SES.

Limitations

The present findings have a few minor limitations. The first I touched on briefly previously:most of the children represented in the data as of the completion of the 2000 survey wereborn to younger mothers. Early childbearers typically have lower cognitive ability than theircounterparts who delay family formation until later in the life course. This trend in the dataexplains the low mean maternal AFQT score reported in Table 1. An examination of theAFQT percentile scores of those women not yet represented in the child data because theyhad not begun childbearing by the 2000 survey, for instance, reveals a mean value that isalmost 13 percentile points higher than the mean reported here. It is true that more childrenare being born to older, more intelligent mothers by this time, but most of these youngstersare still quite young, which means, because they have yet to be assessed on the relevant

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A Moderated Mediation Analysis 175

outcomes, that their mothers’ AFQT percentile scores remain excluded from the final anal-yses. At any rate, if the difference in mean cognitive ability is also reflected in a large differ-ence in mean parental SES, the estimates here could perhaps be overestimated, despite thefact that the full range of maternal AFQT percentiles is represented in the data. That is, thesignificance region of the conditional indirect effect for any of the outcome measures mayin fact extend beyond the point estimated in this article if ever-higher SES levels have anincreasing mediating effect on the maternal AFQT–child cognitive outcomes relationship.

The second limitation relates to my decision to begin my causal chain at maternalAFQT. I anticipate here the common criticism of social science researchers, who wouldargue that there is no valid justification for assuming that maternal cognitive ability istemporally prior to parental SES; the causal chain could just as easily go in the oppositedirection, from parental SES to maternal intelligence. Given the findings in the fields ofbehavioral genetics and differential psychology, addressed in the opening paragraph, sucha causal direction seems counterintuitive. If the increasing complexity of the job or careerone enters is to a great extent progressively more dependent on one’s cognitive ability, itmakes sense to treat parental SES as a mediator between parental cognitive ability andchildren’s cognitive outcomes. I would concede that the criticism is a fair one, however,particularly since measures of SES do not consist only of characteristics achieved after thedevelopment of what is called intelligence. Measures of SES also take into account edu-cational attainment, which develops alongside and in concert with innate cognitive ability.It may therefore be an interesting exercise to see what would happen if the causal pathbetween maternal AFQT and parental SES were reversed. Consistent with the models runhere, however, the alternative models I ran suggest that although there is a mediating impactof maternal cognitive ability on the parental SES–child cognitive outcomes association forall the Peabody measures, this mediating impact is conditional on the level of parental SES.Stated more clearly, there is a strong positive mediating effect of maternal AFQT at lowerlevels of parental SES, but as parental SES increases, this mediating effect weakens. Thestory, then, is the same as the one I have been telling here; it is merely stated differently. It isclear that there is little added value to having either high SES parents if one’s parents havehigh intelligence or high intelligence parents if one’s parents have high SES. If, however,one is disadvantaged on one of these factors but not on the other, one will likely fare betterthan if one were disadvantaged on both factors.

Finally, many of the respondents in the NLSY79-CYA are siblings who share the samemother. This nonindependence of the data is often problematic, as it leads to inaccurateestimations of the standard errors. While not a complete solution to the issue of noninde-pendence, the use of bootstrapping methods to estimate confidence intervals, because theyoperate on fewer and weaker assumptions, is preferable to ordinary least squares regression.

Conclusion

In conclusion, both phenotypic measures such as cognitive ability and environmental mea-sures such as SES play an important role in predicting individuals’ cognitive outcomes.Neither should be ignored in interpretations of the effect of the other, but both should beseen as working best in concert. To the extent that improvements to family social statuscan lead to an expectable environment (Curtis and Nelson 2003; Bruer and Greenough2001)—that is, an environment conducive to uninhibited learning such that children achieveat a level that otherwise would have been unattainable—for children raised in low cog-nitive ability households, both family social status and parental ability must be seen asconsequential for children’s long-term academic outcomes.

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