Comments on Gottfredson (2012)

re: Gottfredson, L. S. (in press). Resolute ignorance on race and Rushton, Personality and Individual Differences.

Relevant passage:

Of all human traits, variation in general intelligence (g) is the functionally most important in modern life. The first question that behavior genetics tackled was “how heritable are within group differences in intelligence?” – the answer: “very.” The next obvious question is “how heritable are the between-group differences in phenotypic intelligence?” It could be easily answered using today’s analytic methods, but no scientific discipline will touch it. Most would have to be shut down completely, however, to avoid getting relevant evidence. Traits that are so useful in daily life and so heritable across generations are going to manifest themselves in many predictable ways. Rushton has marshaled relevant such evidence on intelligence to test competing hypothesis about the long standing mean IQ difference between American blacks and whites: 0% genetic vs. 50-80% genetic.

[With regards to genetic effects, Jensen and Rushton were arguing d =1. Given the with group heritabilities of 0.5 to 0.8 commonly found in the US, this implies, assuming MI, between group phenotypic differences of 0.6 to 0.8 standardized units on the account of genes. Assuming a phenotypic d of 1 between Blacks and Whites, this entails a between group heritability of 0.6 to 0.8. I note this because this simple point concerning the relationship between genetic effect, heritability, and phenotypic difference, ceteris paribus environmentally speaking, seems not to have been well articulated by HBDers and because the failure to articulate this point has led to some unnecessary confusion. ]

The latter range percentages is Jensen’s “default hypothesis,” which is that within race variation and between race variation arise from the same sources whether genetic or environmental. Accordingly, there is no Factor-X operating on all members of one race but on no members of another. (Anything that affects some but not all members of a group would show up as a within group influence). (Resolute Ignorance on Race and Rushton)

[The term “Factor-X” has been inconsistently used in discussions of mean differences. Strictly speaking, a “Factor-X,” per Jensen’s original usage, is a between group environmental factor. As a between group factor it: (a) exerts a uniform effect and (b) is not constrained by within population heritabilities (since it is not a factor that varies within groups). Apart from a “Factor X,” there are two other possible environmental scenarios which may lead to a mean between group difference: Within group variable factors and within group uniform factors. In both of these cases, the between group differences are due to the environmental factors, or a subset of them, that cause the differences within groups. As such, proposed explanations are constrained by within group heritabilities or, more specifically, by the correlation between the totality of within group environmental influences (i,e., SQRT(1-h^2)) and IQ.

The difference between these scenarios is in the distribution of effect: variable versus uniform. Because variable effects are variable, they will show up as within group variance and will substantially increase the environmental variance in one of the populations relative to that in the other. That is, if the mean difference between populations is due to within group variable factors then the heritability of IQ will noticeably differ between populations.

Most discussants have failed to distinguish between the two types of within group factor scenarios, Gottfredson (2012) just being the latest example. As such, they unwittingly leap between discussions of a Factor-X and discussions of variable within group factors. Granted, the third scenario, within group uniform factors, is somewhat implausible as it necessitates a “Factor Y.” That is, since within group factors by definition are not uniformly distributed within groups for these factors, or a subset of them, to be uniformly distributed between groups one needs to posit, in addition to the factors causing the mean difference, some between population homogenizing factor or a “factor Y” which can explain the uniform distribution. It could be argued that this possibility, and with it the within group uniform factor scenario, is so outlandish as to not warrant consideration, but one could make a very similar case against the “Factor X” scenario. Indeed, the case against “Factor X” is worse, since the presence of such a between groups factor can be statistically tested for using multi-group confirmatory factor analysis. As experts in the field have noted, the finding of measure invariance (MI) between groups implies no between group factor or “Factor X” (see: Lubke et al., 2003). And MI has been repeatedly found in the case of the B/W gap. So on the bases of both empirical and theoretical grounds, “Factor X” is untenable, while on the basis of only theoretical grounds is the within group uniform factors scenario and the “Factor Y” entailed untenable. So, there is no justification for neglecting the latter while not the former. And neglecting both obviously allows for the reduction of this issue to that of a banal empirical one: a matter of determining if MI holds and if so if within group heritabilities are equivalent.

To clarify this point: There are three possible exclusively environmental causal scenarios for the between group difference: Factor-X, in which the factors causing the between group difference are unique to one group and do not vary in that group. Under this scenario, MI will not hold. Within group variable factors, in which the factors causing the between group difference are those environmental ones, or a subset of them, that cause the differences within groups. And the aggregated effect of these factors is variably distributed between populations. Under this scenario, MI will hold and within group heritabilities will be noticeably different. Within group uniform factors, in which the factors causing the between group difference are those environmental ones, or a subset of them, that cause the differences within groups. And the aggregated effect of these factors is uniformly distributed between populations. Under this scenario MI will hold, within group heritabilities will be the same, but an implausible homogenizing “Factor Y” is needed to explain the uniformity of effect between populations. In our actual universe, the only tenable environmental account is “Within group variable factors.” In principle, one can test this hypothesis by simply comparing within group heritabilities. If within group heritabilities are consistently found to not differ in large samples which demonstrate MI than this scenario can be ruled out, and, in such a case, one is left with a genetic hypothesis. Alternatively, if heritabilities are consistently found to differ or if the results are mixed then this scenario is ruled plausible, but not proved to be the case. My review, of course, leads me to conclude that the evidence concerning group differences in within group heritabilities is ambiguous. Some large recent representative samples (e.g., Add Health) show non-trivial differences in shared environmentality and some show none (e.g., CNLSY).]

If within race IQ variation is 50-80% heritable, as it is in the West, the default hypothesis predicts that between group differences will be too. This is a readily testable hypothesis, but virtually no one with the necessary data has been willing to test it or lend the data to others who are.

Gottfredson is correct that the racial hereditarian hypothesis is readily testable. Her discussion is misleading, though, because she makes it sound as if testing the hypothesis requires special data. It doesn’t. Since, as discussed above, the difference between the populations in question is due to within group variable factors, one can use structural equation modeling applied to public use data sets which have kinship data to determine the extent to which genes condition the difference. Interested readers are encouraged to read Judea Pearl’s The Causal Foundations of Structural Equation Modeling, for background. Yes, such studies have been done and the results support a (partial) genetic hypothesis. And yes, these studies have been critiqued, (e.g., Dickens (2005) and Brody (2002)) and, more often, ignored. But the appropriate response is to publish more such studies and to test the alternative models offered — not to declare that the genetic hypothesis is untestable with publicly available data. What’s ridiculous about this debate is that largely ending it would require only the concerted effort of a few statistically minded individuals, internet access, and a copy of AMOS.

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