Behavior of the Product-Moment Correlation Coefficient When Two Heterogeneous Subgroups Are Pooled1

Abstract

An equation was derived to determine the relationship between the pooled within-subgroup correlation coefficient, rw, and the correlation coefficient obtained from the total group data, rt. It was, thus, possible to assess the amount of distortion introduced by pooling heterogeneous subgroups. As a basis for deciding whether to pool two subgroups in order to calculate rt, a two-stage procedure was recommended: (1) comparison of the two within-subgroup r's; and (2) comparison of rt and rw. On the basis of results for the second stage test, distortion in rt was shown to be a function of the pattern of subgroup mean differences, total group sample size, and the magnitude of rw. Implications were discussed.