Abstract
It has been proposed that a correlation between a vector of factor loadings of intelligence tests and a vector of group differences on these same tests (=correlation of vectors) indicate that the group difference is mainly in g. In the present simulation, we show that there is an inverse sigmoid association between the difference between population means on a latent variable and the correlation of vectors and that the appearance and precision of this association is moderated by sample size and the standard deviation of factor loadings. In high powered studies, a weak correlation of vectors would falsify, while a strong correlation would not be able to verify, a hypothesis about a sizeable difference between population means.
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