Spearman's hypothesis

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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.[1] 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.[2]

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.[3] 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."[4]

Jensen went onto 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.[5] 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.[6] 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.[7][8]

Other related hypotheses

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 reported that the found psychometric meta-analytic correlation between g-loadings and heritability estimates was 1.[9][non-primary source needed] As such, Spearman's hypothesis and this hypothesis are related.

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.[10]

Hereditarians, including Jensen, have also argued that Spearman's hypothesis (both formulations) supports their hereditarian position with regards to racial and ethnic differences.[2] 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.[11] 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.[12] 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.[13]

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.[14] Ashton and Lee (2005) argue that MCV can produce spurious results.[15] 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.[16]


  1. Jensen, A. R. (1985). The nature of the black–white difference on various psychometric tests: Spearman's hypothesis. Behavioral and Brain Sciences, 8(02), 193–219.
  2. 2.0 2.1 Hunt, E., & Carlson, J. (2007). Considerations relating to the study of group differences in intelligence. Perspectives on Psychological Science, 2(2), 194–213.
  3. te Nijenhuis, J. (2012). Jan te Nijenhuis. The Flynn effect, group differences, and g loadings. Personality and Individual Differences.
  4. Miele, Frank (2002). Intelligence, Race and Genetics. Conversations with Arthur R. Jensen. Westview Press. Paperback edition first published in 2004 by Westview Press. ISBN 0-8133-4274-0 (pbk). Page 138.
  5. Dolan, C. V., Roorda, W., & Wicherts, J. M. (2004). Two failures of Spearman's hypothesis: The GATB in Holland and the JAT in South Africa. Intelligence, 32(2), 155–173.
  6. Jensen, A. R. (1987). Further evidence for Spearman's hypothesis concerning black–white differences on psychometric tests. Behavioral and Brain Sciences, 10(03), 512–519.
  7. te Nijenhuis, J., van Vianen, A. E., & van der Flier, H. (2007). Score gains on g-loaded tests: No g. Intelligence, 35(3), 283–300.
  8. Steppan, M. (2010). Protestantism and intelligence: Max Weber and the Rindermann-paradox. The International Journal of Educational and Psychological Assessment, 5, 134–154.
  9. Rushton, J. P., & Jensen, A. R. (2010). The rise and fall of the Flynn Effect as a reason to expect a narrowing of the Black–White IQ gap. Intelligence, 38(2), 213–219.
  10. Jensen, A.R. (1998). The g Factor: The Science of Mental Ability. Westport, CT: Praeger. ISBN 0-275-96103-6, p. 371-383.
  11. Gottfredson, L. S. (2005). What if the hereditarian hypothesis is true?. Psych. Pub. Pol. and L., 11, 311–605.
  12. Gottfredson, L. S. (2007). Shattering logic to explain the Flynn effect. Cato Unbound.
  13. Lua error in Module:Citation/CS1/Identifiers at line 47: attempt to index field 'wikibase' (a nil value).
  14. Dolan, C.V. and Lubke, G.H. (2001). Viewing Spearman's hypothesis from the perspective of multigroup PCA: A comment on Schönemann's criticism. Intelligence 29, 231–245.
  15. Ashton, M. C., & Lee, K. (2005). Problems with the method of correlated vectors. Intelligence, 33(4), 431–444.
  16. Flynn, J. R. (2010). The spectacles through which I see the race and IQ debate. Intelligence, 38(4), 363–366.