Interpretation of differential deficits: the case of aging and mental arithmetic

A fundamental issue in research on individual differences is the type of evidence sufficient to justify an inference of selective or distinct deficits in relevant theoretical processes. It is proposed that an important consideration is the extent to which the individual differences in 1 variable are independent of those in another variable. Specifically, the suggestion presented here is that a strong conclusion of selective impairment requires evidence that there is significant group-related variance in 1 variable after the variance in the other relevant variable is controlled. Furthermore, an inference that the groups are equivalent on a particular theoretical process requires evidence that the variable presumed to reflect that process has sufficient unique variance to justify the claim that a distinct process is being assessed. The proposed methods are illustrated with two studies comparing adults of different ages in mental arithmetic tasks.