Category: Psychometrics (Page 3 of 3)

A few New Analyses

Hu (2013, September, 5; 2013, July, 5; 2013, August, 18) has raised some interesting points. I will comment on a few of them here and present several new analyses.

Cultural Loading, Heritability, and the BW gap

As Meng Hu noted, Kan et al. (2011) showed that subtest cultural-loadings, as they estimated them, correlated both with the magnitude of the B/W subtest gaps and with subtest heritability estimates. The authors interpreted these associations as support for a GxE hypothesis of individual differences and offered a model similar to that proposed by Flynn and Dickens (2001). Moreover, Kan et al. (2011) saw the associations between cultural-load and heritability and between cultural-load and the magnitude of the BW gap as problematic for what they termed a biological g model. Below, I will show that g-loadings fully mediate the association between cultural loadings and the two other variables noted and therefore that what is in need of explanation is only the association between cultural-loadings and g-loadings. I will then proceed to offer an account for this.

First, I looked to see if g-loadings mediated the association between the BW gap and cultural loadings. They did. Then I looked to see if cultural-loadings mediated the association between the BW gap and g-loadings. They did not fully. The results are shown below. As reliability estimates were not presented for all subtests, I ran the analysis with and without reliability corrections. Continue reading

Investigation of the relationship between mental retardation with heritability and environmentality of the Wechsler subtests

The present analysis is an extension of Spitz’s earlier (1988) study on the relationship between mental retardation (MR) lower score and subtest heritability (h2) and g-loadings. These relationships were found to be positive. But Spitz himself haven’t tested the possibility that MR (lower) score could be related with shared (c2) or nonshared (e2) environment. I use the WAIS and WISC data given in my earlier post, and have found that MR is not related with c2 and e2 values. These findings nevertheless must be interpreted very carefully because the small number of subtests (e.g., 10 or 11) is a very critical limitation.

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A Meta-Analysis of Jensen Effect on Heritability and Environmentality of Cognitive Tests Using the Method of Correlated Vectors

A correlation between the g factor and indices of heritability (h2) gives support for the genetic g hypothesis but, on the other hand, the interpretation may appear questionable if g correlates with shared (c2) and/or non shared (e2) environment to the same extent. The results from the present meta-analysis tend to support the hereditarian hypothesis.

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Hollow Flynn Effect in Two Developing Countries and A Further Test of the Debatable Black-White Genetic Differences

Studies of the nature of the Flynn Effect are usually done in developed countries (e.g., Rushton, 1999; Wicherts, 2004; Nijenhuis, 2007; for an ‘Overview of the Flynn Effect’, see Williams, 2013). There are two recent data on two developing countries (Khaleefa, 2009; Liu, 2012). The reported numbers on subtests gains can be studied using either MCV or PC analysis. Next, we will see that shared (c²) and non-shared (e²) environments, as measured by Falconer’s formula, are unrelated to heritability (h²) of the WAIS and WISC subtests. Culture load, heritability, g-loadings, and black-white differences tend to form a common cluster (on PC1) that is different from the pattern of loadings shown by shared and non-shared environment.

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Re-analysis of Jensen’s study of Capron and Duyme adoption data

The french adoption study, by Capron & Duyme (1989, Table 2; 1996, Table 3), attempted to show that IQ can be improved by adoption. Their numbers displayed an IQ gain of 15 or even 20 points (WISC-R). To recall, Jensen (1997) analyzed Capron and Duyme adoption data (1996) with N=38, a study often cited by environmentalists as evidence against the hereditarian hypothesis. In Adoption Data and Two g-Related Hypotheses, Jensen shows that IQ difference owing to the adoption of children from low-SES parents by high-SES families is not g-loaded while at the same time the IQ difference owing to low-SES versus high-SES biological families loaded in fact on the g factor or PC1. Plus, the SES-difference of adopted families correlated at only 0.099 with SES-difference of biological families.

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Similarity in the g factor structure between- and within-families across racial groups in the NLSY97 and NLSY79

In Bias in Mental Testing (1980, pp. 546-548), Arthur Jensen showed that a congruence coefficient test from a factor analysis of the within- (WF) and between-family (BF) correlations among blacks and whites could yield an identical g factor structure. A similarity in factorial structure for these four groups having been evidenced, he writes :

These correlations are statistically homogeneous; that is, they do not differ significantly from one another. Thus it appears that the g loadings of these seven tests show a very similar pattern regardless of whether they were extracted from the within-family correlations (which completely exclude cultural and socioeconomic effects in the factor analyzed variance) or from the between-families correlations, for either whites or blacks. … This outcome would seem unlikely if the largest source of variance in these tests, reflected by their g loadings, were strongly influenced by whatever cultural differences that might exist between families and between whites and blacks.

Jensen (1980, Table 4) has been replicated by Nagoshi and Johnson (1987, pp. 310-314). I will replicate those earlier tests using NLSY97 and NLSY79. As Jensen (1998, pp. 99-100) noted, the congruence coefficient (CC) can be interpreted as being an index of factor similarity.

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Is Psychometric g a Myth?

As an online discussion about IQ or general intelligence grows longer, the probability of someone linking to statistician Cosma Shalizi’s essay g, a Statistical Myth approaches 1. Usually the link is accompanied by an assertion to the effect that Shalizi offers a definitive refutation of the concept of general mental ability, or psychometric g.

In this post, I will show that Shalizi’s case against g appears strong only because he misstates several key facts and because he omits all the best evidence that the other side has offered in support of g. His case hinges on three clearly erroneous arguments on which I will concentrate. Continue reading

Pigmentocracy: A Longitudinal Approach


We have shown, amongst other things, that pre-market measures of IQ substantially statistically explain the association between color and outcomes in the US. This implies that the adult color-outcome differences are substantially caused by IQ differences, rather than vice versa. To investigate this issue further, I have taken a longitudinal approach.

As background, it is well established that the year to year correlation for IQ is mediated by general intelligence on the psychometric level and by shared genes and shared environment on the causal levels. The latter two sources contribute to the longitudinal stability of IQ. Unshared environment, on the other hand, does not. This situation is illustrated in the table immediately below. As is shown, the longitudinal stability of IQ scores for both Blacks and Whites is conditioned by genetic and shared environmental effects. For the Add Health sample, in particular, unshared environment contributes only to longitudinal change.


(From: Beaver, et al. (2013). The genetic and environmental architecture to the stability of IQ: Results from two independent samples of kinship pairs. Intelligence, 41(5), 428-438.)

It follows then that if differences are due to shared genes and shared environment, as we propose, then the IQ-color association should be largely on a factor common across ages. Moreover, IQ at earlier ages should explain some of the IQ-color correlations at a latter ages. Overall, the association between color and IQ should have longitudinal stability. It is, of course, not necessary that it does. If, for example, labor marker color discrimination was leading to outcome differences which were, in turn, leading to IQ difference, the pre-market and post-market color-IQ correlations would not be mediated by a common factor. Likewise, if idiosyncratic individual factors such as peer group influences were conditioning the differences, one would not expect longitudinally stable color associated IQ differences (since such idiosyncratic influences don’t condition longitudinally stable IQ differences).

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