A CORRELATIONAL APPROACH FOR MEASURING OVERLAP OF DISTRIBUTIONS AND PROPORTION OF MISCLASSIFICATION

J. W. Tilton's overlap measure is inappropriate when the underlying relationship between the dichotomized variable, represented by 2 groups, and the continuous variable, on which the groups overlap, is assumed to be bivariate normal. Also, Tilton's measure is restricted to interpretation in terms of equal-sized distributions. 2 measures of overlap for the bivariate normal case are developed, 1 for interpretation in terms of equal-sized distributions, the other for interpretation in terms of the base-rate distributions. With underlying bivariate normality, the distributions are normal only when r is zero. Graphs are presented which show the relationships among r, overlap, and proportion of misclassification for various base rates. A table gives cutoffs that are optimum for prediction under these conditions. (PsycINFO Database Record (c) 2006 APA, all rights reserved). © 1968 American Psychological Association.