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, r_w , and the correlation coefficient obtained from the total group data, r_t . 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 r_t , a two-stage procedure was recommended: (1) comparison of the two within-subgroup r's; and (2) comparison of r_t and r_w . On the basis of results for the second stage test, distortion in r_t was shown to be a function of the pattern of subgroup mean differences, total group sample size, and the magnitude of r_w . Implications were discussed.

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