I happened to recently reread the passage below found in Neven Sesardic’s “Making Sense of Heritability”:
Sesardic is discussing what has been termed the sociologist’s fallacy. You can read James Flynn’s discussion of this here. On second take, I noticed a more fundamental error occurring than the one discussed by both Flynn and Sesardic.
Sesardic’s characterization is correct. If we match groups on outcomes such as education, and if, on matching, we find a reduction in the magnitude of the IQ gap, knowing nothing else, it’s impossible to tell if the matching produced the IQ reduction by increasing the environmental similarity or by increasing the genetic similarity between groups.
An important point left unelucidated, though – and an obvious one when it is — is that the environmental and genetic explanatory models of the effect of matching presuppose different models of mean differences. Imagine two models. In model one, which we shall call a deviational model, group A is uniformly depressed in IQ with respect to group B by some set of factors. By uniformly, here, we mean across the board or nearly so. That is, almost all member of group A are affected equally by the factors causing the mean difference. In model two, which we shall call a distributional model, the effect is not spread out equally across members of the groups. It’s variable. Some members of our group A are affected more and some less and some not at all.
Now, for an environmental explanatory model of the effect of matching to be correct, our model of mean differences necessarily has to be a distributional one, as in this model only are there some Group A individuals for which the depressing effect is reduced or removed by having environmental effects removed. It is only in this model that environmental similarity is increased. This is obvious, of course, when considered.
It’s also obvious that we are not dealing with a distributional model of mean difference in the case of the Black-White difference. No – or very few – Blacks are not depressed in IQ relative to Whites. None are reaching their supposed genetic potential of W + X, where W is the white IQ mean and X is the Black individual’s deviation from the Black mean. We know this, of course, because the heritabilities of IQ in both populations are approximately the same and because the phenomena of differential regression is no less at the far right end of the bell curve than at the far left end. This last point needs clarifying. If you match Whites and Blacks for IQ, the White siblings and offspring will regress towards a mean of 100 while the Blacks siblings and offspring will regress towards a mean of 85. This differential regression is an index of the depressing effect (genetic or environmental) causing the group deviation. But this effect is no less at the far right of the bell curve than at the far left. To see the implications of this, imagine if 15% of the Black population wasn’t depressed in IQ and if the other 85% was and was so equally. If so, 15% would be depressed in IQ 0 SD relative to the White mean and the remaining 85% would be depressing 1.18 SD, thus producing an average Black-White difference of 1 SD. Were this the case, at an IQ of 130, given a normal distribution, we would have roughly 2.1% x 15% of unaffected Blacks (= 0.315) and 0.069% x 85% of affected Black (= 0.059). The ratio of unaffected to affected Blacks at this IQ would be over 5 to 1. Were this the case, the sib regression difference (at 130) would be less than one fifth of what it was at an IQ of 85, since this differential regression indexes our depressive effect. And yet it is not. This, of course, merely illustrates what we already know based on similar heritability estimates: we are working with a deviational and not distributional model. (The only additional piece of information that the phenomena of differential regression gives us is that the Black and White differences must be due to shared environmental factors. The math does not add up otherwise; this is somewhat of a tautology, of course, as a deviational model, if caused by environmental factors, will necessarily be caused by environmental factors acting between families, between populations.)
Differential regression in the NLSY ’79 and the CNLSY
Now, were we to propose that the effect affecting the Black population was normally distributed — which is the mostly likely environmental scenario — we would also expect to find a narrowing — and indeed convergence — of the sibling regression lines at the far right end of the distribution. Skeptical readers can model the situation for themselves with the aid of excel’s normal distribution function.
The above means that the effect of matching is a genetic one. Matching Blacks and Whites on outcomes matches them on genotypic IQ. This isn’t to say that the mean difference is therefore genetic; it is just to say that the cause of the difference is uniform; as such, statistically controlling for differences has no chance of controlling for environment. Again, environmental factors, or sets of them, could be at work uniformly depressing the Black IQ relative to the White. Now, this being said, correlational research is still informative. Statistical controlling indicates which outcomes could possibly causally explain the differences. For an outcome to cause the difference, there needs to be a mean difference in it and it need to be correlated with IQ within the populations in question. For example, research shows that motivation correlates with tests scores. But it also shows that the mean level of motivation for Blacks is generally greater than or equal to the mean level of motivation for Whites. So differences in motivation are likely not a cause of the mean difference. Alternatively, total wealth differs greatly between Blacks and Whites in the US, but this variable is virtually uncorrelated with IQ within populations. So differences in total wealth are likely not a cause of the mean difference Basically, the outcomes that have been shown to partially statistically explain the difference are the most likely candidates for the supposed environmental cause of the gap. If this is the case, it might be asked, why did we make the point above, concerning the nature of the explanatory effect. The reason is two fold:
Firstly, knowing that we are working with a deviational model is informative. For one, it means that a genetic explanation is tenable; for another, it means that an environmental explanation needs to account for why no or few Blacks have realized their hypothetical genetic potential relative to Whites. Our environmental hypothesis pictures Whites as balloons that have risen near to the ceiling and Blacks as balloons that are tethered to the floor. While having the same mean amount of helium and potential to rise, Blacks, it is argued, float nearer to the ground because they are held down. But by what factors? Elsewhere, we saw that the explanation is not motivation, peer effects, market discrimination, or racist attitudes. And we saw that Blacks underperform despite extensive institutional discrimination for them. Inevitably it will be argued that the IQ gap is caused by the various outcome gaps such as the income gaps. But such explanations seem queer because it’s now usually conceded that Black IQ is antecedent to Black outcomes. This is why matched for IQ Blacks frequently have a better outcome profile than Whites. For example, matched for IQ, Blacks are more educated than Whites:
Quote: “The bachelor’s degree gap between White and Black adults was overwhelmingly due to a higher share of Black adults scoring in the lower deciles of the test score distribution. Black adults in the top two deciles were nearly 30 times as likely to obtain a Bachelor’s degree as their peers in the bottom decile….
Reducing the large academic achievement test gap between Black and White males is critical to all future efforts to close the Black-White college degree attainment gap.”
Source: The educational attainment of the nation’s young black men and their recent labor market experiences: what can be done to improve their future labor market and educational prospects
IQ is driving the education and SES gap, not education and SES the IQ gap.
Of course, it will be argued by some that the IQ gap is due to differences in rearing environments. Accordingly, the adult IQ gap of generation #1 is antecedent to the social outcome gap of generation #1; this social outcome gap is antecedent to the childhood rearing environment gap of generation #2; and this childhood rearing environment gap is antecedent to the adult IQ gap of generation #2.
Ok, the first problem with this model is that the math doesn’t add up. The shared environmentality of IQ in childhood is about 0.4. In adulthood it’s about 0.15. If the Black-White adult IQ gap of generation #1 was 1.1 SD and if the correlation between adult IQ and cognitively relevant childhood rearing environment was the empirically found average of about 0.8, then, assuming that all of the association between parental IQ and childhood environment represented an environmental effect (i.e., no covGE, conditioned on the child’s genotype), the rearing environment gap could be no more than 1.1 SD x 0.8. And the gap in childhood and adulthood would be, respectively 0.8 x 1.1 x SQRT (0.4) and 0.8 x 1.1 x SQRT(0.15). Or 0.6 and 0.3 SD. Parental IQ differences of generation #1 can’t possibly account for more than one third of the adult differences of generation #2.
More relevant ….this still doesn’t explain why a noticeable number of Blacks have not realized their genetic potential to the same extent as Whites. A noticeable number of Blacks are capable of realizing there genetic potential relative to other Blacks. Hence the heritability of IQ, by adolescence, is three times the shared environmentality within the Black population (60% to 20%). Blacks sibling balloons with more helium rise above those with less, despite sharing the same family environment. So why are not some Blacks capable of realizing their genetic potential relative to Whites? One can’t explain this curiosity simply by pointing to mean shared family differences between populations, since these mean differences with populations don’t create the same uniform effect within racial populations. One needs a casual mechanism to account for the uniformity in addition to one or a set of them to account for the mean difference. That is, that the difference is deviational and not distributional is non-trivially interesting. It needs some explaining.
Second, knowing that the effect of controlling for outcomes is a genetic and not an environmental effect means that we must face the constraints placed on environmental explanations by the low shared environmentality of IQ. This constraint has been lucidly articulated by Jensen 1973; 1998. To causally environmentally account for a one standard deviation difference, given a shred environmentality of no more than 15%, one needs to posit 2.5 standardized units of environmental effect (1/ (square root 0.15)). This is the same as saying that one needs to maintain that Blacks live in a cognitive affecting environment characteristic of that experienced by the most deprived 1% of Whites.
(This is actually an underestimate of the “environmental differences” needed, since the external factors typically labeled “environment”, are extensively genetically conditioned. The magnitude of the “environmental differences” needed would be:
= d /(SQRT c^2 of IQ)/ (SQRT c^2 of “environment”)
Now, previous attempts to escape this logic have failed; for example, James Flynn has made a reduction ad absurdum by comparing the Black-White difference to the secular difference; but the secular differences has largely turned out to be a function of psychometric bias (Must, & van Vianen, 2009; Wicherts et al., 2004; Beaujean, & Osterlind, 2008, etc.) and the residual magnitude of the difference that actually represents true latent ability differences is utterly compatible with the massive amount environmental differences between generations. The generational differences stand in stark contrast to the Black-White differences both in IQ and in environment. Indeed, a generous appraisal might put the latent ability Flynn effect (as opposed to the manifest score Flynn effect) at 0.1 SD per decade. In Flynn effect metrics, then, the Black-White latent ability difference is equivalent to a century of environmental differences. One century!! Few would honestly maintain that the actual Black-White environmental difference is that tremendous. Now, most sociologists have simply ignored this point, feeling it sufficient to point to the results of correlational studies. Since the IQ difference could be statistically explained, it has been argued, the magnitude of the cognitively conditioning outcome differences must be at least 2.5+ SD. But, as we have seen, this does not follow because the effect of controlling is primarily a genetic, not environmental one.
To summarize: when matching Blacks and Whites for environmental factors, we are matching them for genes. We know this because the within population heritabilities are about the same and because the phenomena of differential regression is no less at the far left end of the bell curve than at the far right end. This means that Black individuals are uniformly depressed – no Black balloons are reaching the ceiling — which, we said, is curious given the dearth of environmental accounts for this curiosity. This also means that showing that the difference can be statistically explained does not shown that the environmental difference between Blacks and Whites is sufficiently large enough to causally explain the differential. It is estimates that in the metrics of the Flynn effect, the B/W difference amounts to an incredible environmental difference of one century.