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.

It is not useful to repeat how the test is done. My Excel sheet (here) is in itself self-explanatory. Basically, we need to correlate the ASVAB subtests from sibling score means ((sib#1+sib#2)/2) and then from sibling score differences (sib#1-sib#2) for each racial group. Having these six sets of subtest intercorrelations in hand, we can submit them to a PC or PAF analysis. The congruence coefficient is calculated from the g-loadings for each groups. We could also indicate that, whether we use PC or PAF analysis, the result appears to be the same. Generally speaking, the variance explained by the g factor is higher with regard to the between-family correlations. In the NLSY79, the variance explained by g (PC1 or PAF1) is 64% for black BF, 47% for black WF, 68% for hispanic BF, 45% for hispanic WF, 67% for white BF, 46% for white WF. By way of comparison, in the NLSY97, the variance explained by g (PC1 or PAF1) is 62% for black BF, 44% for black WF, 59% for hispanic BF, 38% for hispanic WF, 57% for white BF, 43% for white WF.

Below is the table showing the CCs from the NLSY97 :

NLSY97 Congruence Coefficient from BF and WF correlations across racial groups

And here is the corresponding table for the NLSY79 :

NLSY79 Congruence Coefficient from BF and WF correlations across racial groups

The numbers speak for themselves. An identical structure is evidenced when the congruence is at least 0.90 or 0.95, as strict minimum. Regarding PC1, the CCs computed from principal component analyses are higher than 0.99. See the NLSY97 syntax and NLSY79 syntax for preparing the above analysis.


  1. Steve Sailer

    Off Topic but perhaps of interest, Mike Bailey calls attention to this 2009 medical study that classifies African-Americans by degree of sub-Saharan ancestry on a variety of socio-economic measures:

    • Dalliard

      There’s a better study on that. Look at Table S2 in this paper. They had a big sample (N>5,400), and there appears to be a linear negative relationship between African ancestry and various SES indicators in black Americans. Chuck wrote about it here. This is the sort of study design that race realists have been clamoring after for a while. Had this finding been published in a social science journal, it might have made a splash, but no one appears to have paid attention to it before Chuck did. In biomedical research they can freely use race as an explanatory variable without fear of being Richwined. Of course, you can explain the ancestry-SES correlation in both hereditarian and nurturist terms, but it does set limits to what is possible and plausible.

      • pnard

        “you can explain the ancestry-SES correlation in both hereditarian and nurturist terms”

        could you elaborate on how you would explain it in nurturist terms?

      • Dalliard

        Jason discussed the nurturist case with regard to IQ and white admixture here. A quote:

        Do blacks with more European admixture have higher IQs because they have more high IQ genes, or did their parents and wider society give them more IQ-boosting advantages because of their relatively European appearance? Or perhaps blacks with more white ancestry simply inherited greater amounts of cultural and material resources from their white ancestors.

        There is almost certainly also cross-assortative mating for human capital characteristics and traits that are correlated with higher white ancestry (such as light skin color and European facial morphology). The solution is, as Jason points out, to study differences between siblings. However, I’d say that even without a sibling design the SES effect may be too large to explain in terms of simple color discrimination at least.

  2. Emil OW Kirkegaard

    Nurturist explanations would be discrimination based on African visuals. It more or less perfectly mimics a genetic explanation. That’s the goal of modern nurturist explanations: to mimic genetic ones, because then they are difficult to test and falsify.

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