Behavior of the Product-Moment Correlation Coefficient When Two Heterogeneous Subgroups Are Pooled1
Alan L. Sockloff · Educational and Psychological Measurement · 1975
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.