Spearman’s hypothesis tested on the admixture data in Scarr et al.

The relevance of Spearman’s Hypothesis to the nature-nurture debate is startlingly obvious, yet, nonetheless, a number of commentators fain not to comprehend it. (Take, as example, behavioral geneticist Wendy Johnson.) The idea is mind numbingly simple:

(1) Given a hypothesized genotypic difference between groups in a trait (genetic d), the magnitude of the phenotypic differences between groups will be positively related with within population heritability estimates of the measures of this trait in absence of countervailing or confounding environmental influences. The relationship between within group heritability and phenotypic differences given some genetic d is shown below:


(2) Mutatis mundis an environmental differences and a negative relation, assuming that the environmental differences between groups represent a random sampling of the environmental differences which cause variance within groups.

(3) The heritability (or: one-minus-environmentality) estimate of subtests are indexed by g-loadings (as the correlation between the two is 1). This is a non-trivially interesting finding as we could live in a world in which environmentality was equally or more related to g-loadings than heritability — but we don’t. It just so happens that the sum of all environmental influences on cognition tends to exert less effect on more g-loaded tests.

Points (1) and (2) are simple mathematical derivations. Point (3) is an interesting empirical finding. The upshot of these points taken together is that a consistent finding of a Jensen effect (a positive correlation between the magnitude of group differences and g-loadings) supports — in the sense that this is what would be predicted by — the position that genetic differences are driving a group difference. Obviously, a Jensen Effect could be environmentally accounted for, but the point is that an accounting for must be done, since only a subset of environmental influences can induce such an association and since the simplest environmental model would predict an anti-Jensen Effect (for example, as on the Flynn effect). To render more clear this latter statement: by the simplest environmental model, the environmental factors causing a group difference would be a random sampling of the within group cognitive affecting environmental factors, factors which, on average, have — by (2) — a greater influence on the less heritable, less g-loaded sub tests. That is, a random sampling of environmental differences would not be expected to cause a Jensen Effect, an effect which represents a correlation between within population genetic influences on tests and group differences. Thus, when a Jensen Effect is found, some environmental explaining is needed. (Obviously, one can “explain” a Jensen Effect by simply positing g driven differences (e.g., Revelle et al (2011); Kan et al. (2011)), but this doesn’t explain why differences are g-driven in the first place; were a g difference itself brought about by differences in a random sampling of the environmental influences that affect cognition within populations, then one would expect an anti-Jensen Effect (for the reason discussed above); an accounting, then, is still needed: one has to explain how the environmental differences surreptitiously produced g differences — i.e., without producing the characteristic anti-g loaded correlation; obviously one can do this; one just has to propose that the group differences are caused by those specific environmental effects that cause g-loaded differences e.g., fetal alcohols syndrome — but the burden is on environmentalists to specify the causal factors because a generic environmental account is insufficient.)

So, the relationship between the magnitude of a group difference and g/genetic loadings is informative. At very least, the presence of such a positive relationship indicates that group differences are not due to either a random sampling of the environmental factors which affect cognition within populations or those specific types of factors which have been shown to consistently produce anti-Jensen Effects.

For this reason, continual exploration of “Spearman’s hypothesis” is warranted.

Now, Jason Malloy has brought to my attention a couple of group differences that could be explored. Most recently, he has noted:

John Loehlin once noted that even though fullscale IQ scores did not vary with ancestry in Sandra Scarr’s crude admixture study (Scarr et al, 1977), the subtest patterns did, in fact, show a genetic correlation. Black ancestry correlated with memory performance, while white ancestry correlated with abstract problem solving (Loehlin 2000, pp.187-188).

As far as I am aware, no one has formally tested Loehlin’s conjecture that there was a Jensen Effect on the association between cognitive ability and admixture in the Scarr et al. 1977 study. That study, the results of which were utterly consistent with a typically proposed genetic hypothesis (i.e., genetic d =1), was discussed in detail elsewhere. Listed below are the tests given to the study population, the mean test differences reported between the upper and lower most Caucasian African Americans, the correlations between African Ancestry and differences in the African American sample, the mean Black-White differences in the larger sample, the Black and the White g-loadings as reported in Jensen (1985) (cf. Scarr (1981)), and the averaged Black-White g-loadings. The correlation between the admixture d/r and the Black g was about +0.85. Thus Loehlin’s conjecture was borne out. It’s worth noting that others have found similarly high Jensen Effects on indices of admixture in the African American population. Meng Hu, over at Human Varieties has noted: “Clearly, the g-factor contributes to the differences, but not the non-g dimension. The conclusion is that white ancestry advantage among blacks is a Jensen effect, as well as skin color among blacks (Dalliard, Jan.29.2013).”


So, I find that interesting — as far as these things go. Later on I will discuss some other found Jensen and anti-Jensen Effects. Perhaps the pattern of effects will shed some light on the mysterious cause of the B/W gap. Perhaps not, though. Whatever the case, the differential places number 4 on the social science’s top 10 list of fundamental and transformative issues, so it can hardly be said that continual dilettante interest in it’s nature in unwarranted (as I am sometimes told).

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2 Responses to Spearman’s hypothesis tested on the admixture data in Scarr et al.

  1. Jason Malloy says:

    This is a perfect opportunity to link to the new masters thesis by Daniel Metzen @ U of Amsterdam:

    The Causes of Group Differences in Intelligence Studied Using the Method of Correlated Vectors and Psychometric Meta

    “The purpose of the present study was to test a fundamental hypothesis:
    Only variables under genetic influence are strongly and positively related to general intelligence, or g, and variables not under genetic influence are not. We conducted analyses on a manifold of variables to test this hypothesis (see Table 66). The hypothesis was strongly supported: variables under genetic influence, namely heritabilities and most group differences, showed moderate to strong, positive correlations with g; the meta-analytical correlation of brain volume with g was weak to modest. All other phenomena showed no strong positive correlation with g … These findings in combination suggest a strong genetic component in [ethnic] differences with regard to general intelligence…”

  2. 猛虎 says:

    Woodley sent me this. A very important finding :

    “In the present study we used the data on the secular increase in simple RT described in a meta-analysis of 14 agematched studies from Western countries conducted between 1884 and 2004 to generate estimates of the rate of IQ decline. The decline estimate of −1.23 IQ points per decade from the present study falls within the range of those produced in previous studies employing the magnitude of the dysgenic effect on IQ as the basis for estimating declines (i.e. −.12 to approximately −1.3 points per decade). Our estimate is the first to be based on the use of real data rather than inference, however.”

    Were the Victorians cleverer than us? The decline in general intelligence estimated from a meta-analysis of the slowing of simple reaction time.
    Michael A. Woodley, Jan te Nijenhuis, Raegan Murphy, 2013.

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