March 23, 2005

Method of correlated vectors demolished

In a new Intelligence paper, Ashton and Lee demolish Arthur Jensen's "method of correlated vectors" which has been frequently used to find associations between the general intelligence factor g and other variables. The paper refers to several other criticisms of the method; I had posted about one such criticism here. The paper's conclusions:
Because of the problems outlined above, the method of correlated vectors is of limited value for identifying variables that are strongly associated with g. Even when g has a very strong relation with a given variable, the vector of that variable's correlations with intelligence subtests may be uncorrelated with the vector of those subtests' g-loadings. Moreover, the vector of g-loadings is itself heavily influenced by the nature of the subtests included in the battery, and therefore the correlations between the two vectors may vary widely across different collections of subtests. These problems do not mean that the results obtained from the method of correlated vectors must always be wrong: when the variable in question is related only to g, and when g is derived from an unbiased selection of subtests, then subtests with higher g-loadings will tend to show higher correlations with that variable, provided that sample sizes are adequate. (Even in this case, however, a very high correlation between the vectors does not rule out a rather weak association with g, as noted in Footnote 4.) But in light of the problems discussed in this article, it is clear that the method of correlated vectors can easily produce–and, indeed, already has produced–very doubtful results. These difficulties undermine the utility of this method for investigating associations between g and external variables.
Intelligence (Article in Press)

Problems with the method of correlated vectors

Michael C. Ashton et al.


The method of correlated vectors has been used widely to identify variables that are associated with general intelligence (g). Briefly, this method involves finding the correlation between the vector of intelligence subtests' g-loadings and the vector of those subtests' correlations with the variable in question. We describe two major problems with this method: first, associations of a variable with non-g sources of variance can produce a vector correlation of zero even when the variable is strongly associated with g; second, the g-loadings of subtests are highly sensitive to the nature of the other subtests in a battery, and a biased sample of subtests can cause a spurious correlation between the vectors.


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