One of the more arcane arguments in the race-IQ debate, concerns the correlation between the Black-White mean difference and heritability estimates within both Black and White populations. The argument from the hereditarian side goes something like this: Aptitude tests differ in their heritabilities; some tests are more environmentally influenced and other tests are more genetically influenced. A genetic hypothesis would predict that tests found to be more heritable for Blacks would also be more heritable for Whites and that the Black-White difference would correlate positively with indexes of heritability (and negatively with indexes of environmentality). In contrast, most formulations of the environmental hypothesis predict that the Black-White difference would correlate negatively with indexes of heritability (and positively with indexes of environmentality). A number of studies, using sibling correlations (Jensen, 1973 pg. 107-117; Jensen, 1998) and inbreeding depression (Jensen and Rushton, 2010) as indexes of heritability, have borne out the genetic hypothesis’ prediction. Just as the highly heritable differences within populations correlate with genes (the correlation being the square root of the heritability estimate), the between population difference also correlates with genes within populations. This argument has been made a number of times. Jensen spent several pages on it in his 1973 book, Educability and Group differences (pg. 113-177) and mentioned it briefly in The G-factor (pg. 471-472). Michael Levin elaborated on it in Why Race Matters and mentioned it elsewhere. For example, in “The Race concept: a Defense,” he argued:
There are also apparent heritable differences in psychological functioning, particularly in phenotypic IQ, a valid, unbiased proxy for intelligence (Neisser et al., 1996)…. While systematic review of the question of genetic factors in these discrepancies is inappropriate here (see Hocutt & Levin, 1999; Levin, 1997), two lines of evidence support genetic involvement firmly enough to warrant retaining broad racial categories pending further inquiry. The first is the correlation of the size of white/African-American mean differences on IQ subtests with (within-group) subtest heritability, a result difficult to explain by means of environmental variables, for these variables would have to produce larger effects as sensitivity to environment dwindles.
More recently, Rushton has brought this argument to the fore in The rise and fall of the Flynn Effect as a reason to expect a narrowing of the Black–White IQ gaps. Previously, Rushton and his co-authors extended the argument globally. In Genetic and environmental contributions to population group differences on the Raven’s Progressive Matrices estimated from twins reared together and apart, they reason:
In 55 comparisons, group differences were more pronounced on the more heritable and on the more environmental items (mean rs=0.40 and 0.47, respectively; Ns=58; ps<0.05). After controlling for measurement reliability and variance in item pass rates, the heritabilities still correlated with the group differences, although the environmentalities did not. Puzzles found relatively difficult (or easy) by the twins were those found relatively difficult (or easy) by the others (mean r=0.87). These results suggest that population group differences are part of the normal variation expected within a universal human cognition.” (Rushton et al., 2007.)
The environmentalist response has been varying. Some, like Flynn and Nisbett, tried to create a Reductio ad absurdum by showing that heritability estimates were also positively correlated with the secular increase. But this attempt has met with failure (Rusthon and Jensen, 2010; see Flynn’s concession in The spectacles through which I see the race and IQ debate). More recently, it has been argued that the positive correlation is a function of multi-collinearity. The reasoning goes: Within populations, g and heritability correlate, so between population differences in g necessarily also lead to a correlation with heritability. Revelle et al (2011), for example, make this case:
Related to this is the so – called “ Spearman hypothesis, ” which claims that, if factor loadings on a variable are correlated with heritability and also with between – group
differences, then the between – group differences must be genetic. A simple thought
experiment shows why this is not true. Consider variables measuring overall height.
Of these, some will be better measures of height than others, perhaps because of
reliability issues, perhaps because the others are less valid. In this case the factor loadings on the general factor of height will be correlated with their heritability values. In addition, those measures that represent the better measure of height will show the biggest between – group differences in height. Indeed factor loadings, heritabilities, and between – group differences will be highly correlated, even though the between group difference is due to nutrition.” (Revelle et al., 2011. Individual differences: An up to date historical and methodological overview)
In A genetic origin of Black-White mean IQ differences? Weak inferences based on ambiguous results, Kan (et al.) makes this same case, just more elaborately. As he illustrates, a environmentally induced g difference would lead to the found correlation just as a genetically induced differences would.
Naturally, for this explanation to hold, one must posit g differences. Now, one would think that the existence of g differences was established. The evidence for them is rather strong. It’s difficult to explain the consistent correlations between IQ differences and g-loadings, without positing them (1). Yet, not infrequently, their existence is challenged; for example, Malda et al. (2010) recently conclude:
Our study fits in a series of studies that have given arguments to question the validity of [Spearman’s hypothesis]. The first type of argument focuses on the statistical analyses applied to test SH that are said to be too lenient (see Dolan et al., 2004). The second type of argument concerns the confounding of cognitive complexity with cultural complexity in current tests of SH. A high loading on a general cognitive ability factor does not merely imply a high cognitive complexity, but usually goes together with a high cultural complexity. Confirmations of SH that have been reported in the literature (e.g., Hartmann et al., 2007; Lynn & Owen, 1994; Te Nijenhuis & Van der Flier, 1997) may be based on this confounding in the data. We confirmed findings by Helms- Lorenz et al. (2003) which indicated that SH can only be tested when cultural complexity and cognitive complexity are both varied independently. Data from the present study and from Helms-Lorenz et al. show that when these types of complexity are unconfounded, SH is not supported. (Rugby versus Soccer in South Africa: Content familiarity contributes to cross-cultural differences in cognitive test scores.)
In light of the objections to the existence of g-differences, the correlation between heritability and group differences is not without meaning. From them we can infer g-differences in a way that we can not from the correlation between g-loadedness and group differences. Now, elsewhere Kan (2011) shows that the correlation between g-loadedness and heritability implies that g, within populations, is partially causally genetic. This is illustrated in the figure below:
A statistical model of g, within groups, predicts no correlation between heritability and g-loadedness. It follows that a statistical model of g, between groups, predicts no correlation between heritability and g-loadedness. So the correlation between heritability and group differences in IQ implies that there must be differences in causal g. The correlation would occur if:
1) there is, within groups, a causal g, which is partially genetic
2) groups differences are, in part, differences in this causal g, whether this difference arose due to genetic or environmental factors or a combination thereof
Of course, one would think that the existence of causal g differences was established. The evidence for them is rather strong, too. But… So, what does all this mean? While the correlation between the Black-White mean difference and heritability estimates does not allow for a strong inference about genetic differences, it does allow for one about causal g differences. Which is important in its own right.
1) Dolan (2000), Lubke et al. (2001), Dolan et al. (2004), Ashton and Lee (2005), maintain that the method of correlated vectors (MCV) can produce spurious results. As Dolan et al. note, while MCV established Spearman’s correlation, spearman’s correlations is necessary but not sufficient to establish g-differences, let alone that most of the differences between groups are due to g-differences (i.e. Spearman’s hypothesis). Alternatively, te Nijenhuis et al. (2007) state:
“The fact that our meta-analytical value of r=−1.06 is virtually identical to the theoretically expected correlation between g and d of −1.00 holds some promise that a psychometric meta-analysis of studies using MCV is a powerful way of reducing some of the limitations of MCV…Additional meta-analyses of studies employing MCV are necessary to establish the validity of the combination of MCV and psychometric meta-analysis. Most likely, many would agree that a high positive meta-analytical correlation between measures of g and measures of another construct implies that g plays a major role, and that a meta-analytical correlation of −1.00 implies that g plays no role. However, it is not clear what value of the meta-analytical correlation to expect from MCV when g plays only a modest role.” (Score gains on g-loaded tests: No g, 2007)”
In the case of the Black-White difference in the US, the meta-analytic correlation is approximately 0.6, so, going with te Nijenhuis et al. it seems reasonable to infer that g plays some role in the difference.