Spearman's hypothesis has two formulations. The original formulation was that the magnitudes of the black-white differences on tests of cognitive ability positively correlate with the tests' g-loading. The subsequent formulation was that the magnitude of the black-white difference on tests of cognitive ability is entirely or mainly a function of the extent to which a test measures general mental ability, or g.
The hypothesis, first formalized by Arthur Jensen in the 1980s based on Charles Spearman's earlier comments on the topic, stated that the magnitude of the differences is directly related to the magnitude of the g-loadings of a test. Jensen devised the method of correlated vectors (MCV) to study this hypothesis and published his research in his paper, "The nature of the black–white difference on various psychometric tests: Spearman's hypothesis", a paper which elicited 29 comments from experts in the field. Some subsequent research has confirmed Jensen's original findings and has extended the hypothesis to other ethnic and racial groups. In 2002, Jensen stated that he had now tested Spearman's hypothesis—the original formulation—on twenty-five large independent samples, and it had been confirmed on every one. Based on all these studies, he asserted, "the overall probability that Spearman's hypothesis is false is less than one in a billion."
Jensen went on to argue that the finding of a positive correlation between group differences and g-loadings strongly supported the hypothesis that the group differences were largely in general mental ability—the later formulation of Spearman's hypothesis. The validity of this inference has been much debated. Jensen and others provided alternative tests for the hypothesis that the group differences were largely in general mental ability. These include a method devised by Robert Gordon which involves creating a group difference factor and then determining the congruence coefficient between the general intelligence factor and the group difference factor.
Later studies showed that Spearman's hypothesis is not confined to black-white differences, nor is it merely an American phenomenon. A positive correlation between score gap size and g loading has been observed in comparisons of European populations with Roma communities, Central Asian populations, Native Americans, and more. Spearman's hypothesis has also been observed in academic achievement tests, which indicates that it is not a unique characteristic of intelligence tests. Others have used Jensen's method of correlated vectors to test whether other group differences are related to a test's g-loading, such as differences between test-training groups and non-training groups, between Protestants and Catholics in Europe, between cohorts, and so on.
Closely related to Spearman's hypothesis is the hypothesis that the magnitude of certain group differences correlate with within group heritability estimates. Jensen and Rushton, for example, reported in 2010 that the found psychometric meta-analytic correlation between g-loadings and heritability estimates was 1. This finding has been challenged by more recent studies, such as one by Voronin, te Nijenhuis, and Malykh, which finds negative correlations between g-loadings and heritability in two samples of Russian twins. Another 2015 study, this one conducted in Korea, also found no clear link between heritability and g-loadings of IQ subtests.
In 1998, Rushton proposed the term Jensen effect to refer to the positive and statistically significant correlation between the vector of many biological variables and that of the g-loadings of different subtests.
Implications of Spearman's hypothesis
Jensen argued that Spearman's hypothesis explains why the black-white gap varies across different IQ tests. He also argued that were Spearman's hypothesis proven correct it would establish that the main source of the difference between whites and blacks on IQ tests is the same as the main source of the differences between individuals within each racial group, namely g. If so, he argued, to understand the nature of the black-white gap, one would have to understand the nature of g.
Hereditarians, including Jensen, have also argued that Spearman's hypothesis (both formulations) supports their hereditarian position with regards to racial and ethnic differences. There are two arguments based on the two formulations of Spearman's hypothesis. The first is that a correlation between group differences and g-loadings is what one would expect if differences were predominantly genetically conditioned but not if differences were culturally conditioned. The second is that g differences are deeply biologically and genetically rooted within populations and, as such, it's reasonable to postulate that they could be so rooted between populations. As for this latter point, Rushton and Jensen argued that a test's g-loading also correlated with scholastic and workplace performance, heritability estimates determined from twin studies, inbreeding depression scores calculated in children of cousin-marriages, brain evoked potentials, brain pH levels, brain glucose metabolism, as well as nerve conduction velocity, reaction time, and other physiological factors. This, they argue, supports the view that g is biological and heritable. Therefore, a confirmation of Spearman's hypothesis and the similar relationship for heritability would support, they argued, the theory that the average racial IQ differences were partially genetic.
Criticism of Spearman's hypothesis
Spearman's hypothesis and the arguments that invoke it have received multiple criticisms, including criticisms of Jensen's method of correlated vectors, of the inference that the first formulation of Spearman's hypothesis supports the second, and of genetic and biological arguments made on the basis of Spearman's hypothesis.
First, Jensen's MCV has been criticized with regards to the original formulation of Spearman's hypothesis. Peter Schöneman and others argue that MCV produces tautological results. However, according to Dolan and Lubke (2001), Schönemann's analysis is incorrect; using simulations, they show that the correlations are not positive by mathematical necessity. Ashton and Lee (2005) argue that MCV can produce spurious results. However, according to te Nijenhuis et al. (2007), one can use psychometric meta-analysis to negate this problem.
Second, Jensen's MCV has been criticized with regards to the claim that it supports the later formulation of Spearman's hypothesis. Dolan et al. (2004) argue that MCV lacks specificity: that is, that instances not including g differences could create a positive correlation between the magnitude of the group differences and the g-loadings. Dolan et al. (2004) note that they are specifically criticizing MCV as a way of proving that group differences largely or totally represent g differences; they don't argue against Spearman's hypothesis as originally formulated and they do not argue that the larger body of evidence does not support Spearman's hypothesis as later formulated. Hunt and Carlson summarize criticism:
The essence of these objections is that the method of correlated vectors does not consider alternative hypotheses concerning the latent traits that might give rise to the observed difference in test scores. When a more appropriate method of analysis, multigroup confirmatory factor analysis, is applied, it has been found that Spearman's hypothesis (i.e., that the difference is due to differences in general intelligence) is only one of several models that could give rise to the observed distributions in test scores (Dolan, 2000). These findings render the method of correlated vectors ambiguous—which is not the same as saying that the Jensen-Rushton position is incorrect. Our point is that the argument for the default hypothesis is an indirect one. It would be far better if a direct causal argument could be made linking racial/ethnic genetic differences to studies of the development of the brain.
However, Rushton and Jensen (2010) argued that this criticism misses the point because there was no absolute claim that g had been proven—only that the results were what would have been expected if a g difference did in fact exist. Moreover, te Nijenhuis et al. (2007) note that the method proposed by Dolan et al. (2004) is not without limitations:
A principle of meta-analysis is that the amount of information contained in one individual study is quite modest. Therefore, one should carry out an analysis of all studies on one topic and correct for artifacts, leading to a strong increase of the amount of information. 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. An alternative methodological approach is to limit oneself to the rare datasets enabling the use of structural equations modeling. However, from a meta-analytical point of view, these studies yield only a quite modest amount of information.
Third, arguments based on Spearman's hypothesis have been criticized. Some have argued that culturally caused differences could produce a correlation between g-loadings and group differences. For example, Flynn argues that the most g-loaded and heritable tests are those that have seen the highest increases due to the Flynn effect. More generally, Flynn (2010) has criticized the basic assumption that confirmation of Spearman's hypothesis would support a partially genetic explanation for IQ differences. He argues that environmental causes for average group IQ differences would cause the differences to be greater for more complex tasks.
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