In his classic work, Educability and Group Differences, Arthur Jensen presented a number of lines of evidence in defense of his thesis that the Negro-White difference in psychometric intelligence had a congenital component. On the basis of full sibling correlations and relations, Jensen offered the following arguments:

(a1) The full sibling correlations for Blacks and Whites are comparable; (a2) unshared environmental hypotheses, such as nutritional ones, would predict otherwise (pg. 338-339).

(b1) The full sibling correlations for Blacks and Whites are comparable; (b2) a shared environmental hypothesis of group differences would predict otherwise, assuming that the within population heritablities were the same (pg. 108-109).

(c1) The average absolute difference between full siblings is no greater for Blacks than for Whites; (c2) unshared environmental hypotheses, such as nutritional ones, would predict otherwise (pg. 338-339).

(d1) When matching Blacks and Whites on IQ, one sees differential sibling regression, a differential regression which does not decrease with increasing IQ; (d2) an environmental hypothesis of group differences would not predict this (pg. 118-119).

He reasoned that were the difference between groups due to unshared environmental effects there would be significant between group differences in the full sibling intraclass correlations and in the average absolute sibling differences (a-c). He also reasoned that full sibling correlations would be different were group differences due to shared environmental effects given similar within population heritabilities (b). Finally, he saw the pattern of differential (full) sibling regression as inconsistent with a purely environmental hypothesis (d). To evaluate these arguments, we took a look at the full sibling correlations and differences in the NLSY97 and NLSY79. The results are shown below.


The averaged absolute Black-White, Hispanic-White, and Black-Hispanic differences in intraclass correlations were 0.094, 0.035, and 0.078. The averaged absolute intrapair Black-White, Hispanic-White, and Black-Hispanic differences were 0.03, 0.075, and 0.045. To make sense of the numbers, we took the White NLSY1997 sibling pairs and subtracted various amounts with a standard deviation of 0.4*the magnitude of the amount subtracted. The purpose was to simulate the effect of a relatively normally distributed environmental depressive effect. We modeled the following scenarios: 100% unshared, 100% shared, 50% shared/50% unshared, and 75% shared/25% unshared. In the case of the 50% shared/50% unshared model, for example, 0.5 SD with a SD of 0.2 was subtracted from both siblings and 1 SD with a SD of 0.4 was additionally subtracted from one of the pair; the average effect then added up to 1 SD. The figure below shows the results. (Bolded in red are modeled findings which don’t fit the race/ethnicity results at all; unbolded in red are modeled findings which don’t fit the race/ethnicity results very well.)



Unshared environmental effects had a large impact on both intraclass correlations and on average absolute intrapair differences. They decreased the former and increased the latter. Average absolute intrapair differences were particularly sensitive to unshared effects. In the 75% shared/25% unshared model, the unshared effects showed up as a 0.13 (+/- 0.05) SD increase in the sibling differences. This magnitude of effect is inconsistent with that found between Blacks and Whites and is marginally inconsistent with that found between Hispanics and Whites. In contrast to unshared effects, shared environmental effects tended to increase the intraclass correlations (which isn’t too surprising since these correlations index the amount of variance between families to within and since a variable shared effect by definition increases the between family variance). The amount of increase due to large shared effects, though, was marginal. For example, while in the 100% unshared model, the ICC decreased 0.71, rendering it negative, in the 100% shared model the ICC increased only 0.073. Naturally, shared environmental effects also had no impact on average absolute sibling differences.

Generally, these results support Jensen’s arguments (a) and (c) but not his argument (b) (on the account of b2). That is, the full sibling correlations and differences are inconsistent with a medium to strong unshared environmental explanation for the B/W gap. Specifically, based on the differences in average absolute sibling differences, the upper limit for the contribution of unshared environment is around 15%. The results are not, however, inconsistent with a shared environmental explanation, since variable shared environmental effects have little impact on intraclass correlations.

With regards to Jensen’s argument (d), I discussed the issues involved elsewhere. I noted that the slope of the differential regression lines found, in the case of Blacks and Whites, is not consistent with a pure shared environment hypothesis. I left the door open for a hybrid shared/unshared model, though. To explore this issue further, I looked at the differential regression lines base on the 100% shared and 75% shared/25% unshared models. These are shown below:



As found before, in a 100% shared model with modest standard deviations there is a narrowing of regression differences with increasing IQ (i.e., a convergence of regression lines on the right end). This narrowing isn’t noticeable, though, in the case of a 75% shared/25% unshared model. The increased within family variability seems to offset the effect of the increased between family variability on the slopes of the regression lines. We noted above that the unshared contribution for the B/W gap can be at most only around 15%. This leads us to ask: Would a 85% shared/15% unshared model also show no narrowing? I didn’t bother to test this, knowing that such a model would be statistically indistinguishable from any plausible genetic one. With regards to differential regression, the conclusion then is that the patterns found are consistent with some plausible environmental models e.g., 85% shared/ 15% unshared. Therefore, Jensen’s argument (d) like his argument (b) needs to be rejected. Overall, the comparative sibling similarities provide strong evidence against environmental hypotheses which propose moderate to large unshared environmental effects, but they do not provide evidence against those which propose mostly (but not fully) shared environmental effects — and these latter are precisely the arguments that are mostly (though not always) proposed.

How can we investigate further? We might expect that a large difference due to variable shared environmental factors would noticeably increase between family variance. To see if so, I looked at the variance between sum sibling scores (sibling 1+siblng 2). Variable shared environmental factors modestly increased sum sibling variance. This is shown at the bottom of the second chart above. In comparison, Blacks and Whites showed small sum sibling variance differences in the NLSY97 and modest ones in the NLSY79 (though, for the latter sample, going in the reverse direction and indicating reduced variance for Blacks relative to Whites). The modest NLSY79 differences could be construed as evidence for a between race shared environmental effect insofar as Whites showed more between family variance than did Blacks; from this perspective, the results are odd, though, since there was a trivial Hispanic-White difference in the summed sibling variance; as such, to make the above argument, one would have to maintain that Hispanics also had an equally superior environment relative to Blacks, a claim which doesn’t accord with the found Black-Hispanic-White IQ and SES differences in the NLSY79. Generally, as noted by Jensen (1973) pg. 187, comparing between family variance is problematic as this variance is influenced by a wide range of genetic and environmental factors and as it is subject to a great deal of variability between samples. As such, such comparisons do not lend one much analytic leverage.

We reach, then, the same impasse that we have so many times before. While it’s not difficult to disentangle unshared environmental from genetic and shared environmental (between group) effects, it is to disentangle genetic from shared environmental ones.