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It is common practice to assume that the dependent variables in differential prediction studies, and analysis of variance and co-variance designs are characterized by certain psychometric properties which are invariant across the subgroups of interest. More specifically, the accuracy of the results of such analyses depends on the assumption that the dependent variables are measuring the constructs in the same metrics with equivalent reliabilities across all subgroups. Systematic procedures are outlined for testing these assumptions.
Rock et al. (Sun,) studied this question.