Spearman's hypothesis states that the magnitude of the black-white difference in 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, argues that differences in g are the sole or major source of differences between blacks and whites observed in many studies of race and intelligence. Jensen devised the method of correlated vectors to study the hypothesis. This, and a similar relationship regarding the degree of heritability of tests and the magnitude of black-white differences on tests, have been argued to support the partially genetic explanation for black-white average IQ differences.
Various criticisms have been advanced and the validity of the arguments remain unresolved.
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In his 1927 book The Abilities of Man, Charles Spearman discussed briefly the results of an American study where a sample of white and black schoolchildren were given a diverse battery of mental tests. There was a gap favoring whites in all tests, but its magnitude varied considerably across the tests. Spearman noted that the gap was at its largest in tests thought to be particularly good measures of g.[1]
Based on Spearman's insight, Arthur Jensen set out to formalize and test the hypothesis in the 1980s. He argued that the correlations between the g-loadings of various tests and the magnitude of the black-white gap on them would provide strong evidence for the validity of the hypothesis. He proposed strong and weak forms of the hypothesis, with the former stating that differences in g are the sole cause of the gap, and the latter stating that g is the main cause of the gap. In order to test this, he developed the method of correlated vectors, and, in a series of studies, demonstrated that the correlations obtained (+0.6, on average) supported the weak form of the hypothesis. However, Jensen has argued that the correlations would be substantially higher if certain corrections for statistical artifacts were made.[1]
Closely related to Spearman's hypothesis is the relationship between how high heritability a test has and how large the racial gaps are for that test. The degree of heritability can be estimated by, for example, examining how much inbreeding depression from cousin marriages affect a test or how much siblings differ from one another on a test. The method of correlated vectors can be used to compare the degree of heritability and magnitude of racial gaps for several tests. Rushton and Jensen argued that the results were similar as to those found when examining the relationship between degree of g-loading and magnitude of racial gaps. This also occurs across nations. The effect of inbreeding depression on different tests calculated from cousin marriages in Japan predicted the magnitudes of black-white IQ gaps on different tests in the United States.[2]
Jensen has argued that if Spearman's hypothesis is proven correct, it would, at least partially, answer the question why the black-white gap varies across different IQ tests. Moreover, it would prove that the main source of the differences between whites and blacks in IQ tests is the same as the main source of differences between individuals within each racial group, namely g. This would suggest that to understand the nature of the black-white gap, one would have to understand the nature of g.[1] In 2002, Jensen stated that he had now tested Spearman's hypothesis on 25 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."[3]
Rushton and Jensen argue that a test's g-loading also correlates 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, support the view that g is biological and heritable. Therefore, the supposed confirmation of Spearman's hypothesis, and the similar relationship for heritability, support, they argue, the theory that average racial IQ differences are partially genetic.[4]
One criticism of Spearman's hypothesis has concerned the Flynn effect. Flynn earlier argued that the most g-loaded and heritable tests are those that have seen the highest increases due to the Flynn effect. Using Jensen's argument this could then be taken as evidence that the Flynn effect is substantially due to genetic causes, which is absurd. Rushton and Jensen have argued that a more complete analysis shows that higher g-loading or heritabiliy are either unrelated to the Flynn effect or are negatively related with relatively smaller increases for such tests. Flynn in a 2010 reply stated regarding his earlier argument that "Today I would not be surprised or disturbed if a wider array of evidence negated this result" but that this is irrelevant since the basic assumption, that confirmation of Spearman's hypothesis would support the partially genetic theory, is basically flawed (as explained in a later section). [2][5]
Peter Schönemann has argued that positive correlations predicted by Spearman's hypothesis are likely only psychometric artefacts which also arise with measures which have nothing to do with 'general ability', for example, the number of toys and books a child has. He claims that these positive correlations will arise with any set of moderately correlated random data, once the sample is split into high and low groups.[6] According to Dolan and Lubke, Schönemann's analysis is incorrect. Using simulations, they show that the correlations are not positive by mathematical necessity.[7]
Dolan and Hamaker in 2001 reanalyzed the data from a previous study that had used the statistical method invented by Jensen (the method of correlated vectors) with a more recent and improved method (multigroup confirmatory factor analysis). They argue that the method of correlated vectors is dependent on the existence of g and if more complex models are used the results are unclear. As such, "we cannot accept Spearman's hypothesis as an 'empirically established fact".[8]
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 did in fact exist. Furthermore, several more recent studies using multigroup confirmatory factor analysis have supported Spearman's hypothesis in the US and South Africa for black-white IQ gaps and in Serbia for Romani-white IQ gaps. They also argue that the heritability of a test correlates with the g-load of the test which support the existence of a genetic g.[2]
Spearman's hypothesis is not without its critics. Psychologists Hunt and Carlson[9] write:
One of the most widely cited pieces of evidence (although not the only one) for biological differences in intelligence, sometimes referred to as Spearman's hypothesis (Jensen, 1998), rests on an indirect argument constructed from three facts. The first is that various IQ measures are substantially correlated, providing evidence for general intelligence. Although tests do vary in the extent of their g loading, factor structures are similar over several test batteries (Johnson, Bouchard, Krueger, McGue, & Gottesman, 2004). The second is that, within Whites, the g factor appears to have a substantial genetic component (see citations in Rushton & Jensen, 2005a). The third fact is that the g loadings of tests are substantially and positively correlated with the difference between the mean White and African American score on each subtest within a battery of tests. This analysis has been referred to as the "method of correlated vectors" (Jensen, 1998). Because it has also been well established that general intelligence has a substantial genetic component, results from the method of correlated vectors have been offered as putative evidence that the "default hypothesis" ought to be that about 50% of the variance in the African American versus White difference reflects genetic differences in a potential for intelligence (Jensen, 1998; Rushton and Jensen, 2005a).
They[9] further summarize criticisms of this position:
Technical objections have been made to the method of correlated vectors and to a somewhat stronger condition: that if the within-group correlations between measures are identical across groups, the between-group differences must arise from the same cause as the within-group correlations (Widaman, 2005). 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.
Nisbett writes that the argument is based mainly on the g-loadings for the subtests of the WISC. With the exception of one subtest the differences in g-loading are very small. Furthermore, the argument is based on crystallized g. If instead looking at fluid g, then the subtests with the highest g-loading are the ones which have increased the most due to the Flynn effect. This, argues Nisbett, argues against high g-loading being due to genetics. Even if using crystallized g, then blacks have gained almost as much on a highly crystallized g-loaded test as on IQ tests in general, which contradicts what the hereditarians would predict, that blacks would gain much less on highly g-loaded tests.[10]
Rushton and Jensen have disputed this and argue in a response to Nisbett that a more complete analysis show consistent results for black-white differences on the Flynn effect and g-loadings supporting a genetic role.[11]
Flynn (2010) has criticized the basic assumption that confirmation of Spearman's hypothesis would support the partially genetic explanation for black-white average IQ differences. He argued that also only environmental causes for average group IQ differences would cause the differences to be greater for more complex tasks. Using the example of basketball, he argued that the differences between two unequally trained groups would be less for skills involving less complexity, such as layups, than they would be for more complex skills such as long-distance jump shots. Furthermore, he argued that complex tasks tend to be more affected by genetic differences in inherited traits and therefore have higher heritability. Thus, also only environmentally caused group differences would cause the gaps to be larger for more heritable tasks.[5]