Group Heterogeneity And Pearson's r

Abstract

For many who deal with correlation (as students, teachers, or applied researchers), the connection between group heterogeneity and the magnitude of Pearson's r is difficult to pin down. Confusion abounds because factors that increase score variability do not have a similar effect on r. Three such factors are considered in this paper, with the point made that an increase in ß_r (and/or in ß_y) can be associated with an increase or a decrease in r-or possibly with no change in r whatsoever! A helpful distinction is also drawn between (a) properties of the persons or objects that define one's population of interest and (b) properties of the numbers assigned to those persons or objects (or a sample of them) as a result of the measurement process.