It is important to understand potential sources of group differences in the heritability of intelligence test scores. On the basis of a basic item response model we argue that heritabilities which are based on dichotomous item scores normally do not generalize from one sample to the next. If groups differ in mean ability, the functioning of items at different ability levels may result in group differences in the heritability of items, even when these items function equivalently across groups and the heritability of the underlying ability is equal across groups. We illustrate this graphically, by computer simulation, and by focusing on several problems associated with a recent study by Rushton et al. who argued that the heritability estimates of items of Raven's Progressive Matrices test in North-American twin samples generalized to other population groups, and hence that the population group differences on this test of general mental ability (or intelligence) had a substantial genetic component. Our results show that item heritabilities are strongly dependent on the group on which the heritabilities were based. Rushton et al.'s results were artefactual and do not speak to the nature of population group differences in intelligence test performance.