ETA, DISCO, ODISCO, and F

Abstract

Two coefficients are proposed for measuring the extent of overlap in distributions as a direct function of the variance between the arithmetic means (»disco« and »odisco «). They are designed to answer such questions as: »Given the value of a numerical variable x, to which population should an individual be assigned so that minimum error would be incurred?« This is just the reverse of the question addressed by ANOVA. These coefficients are shown to be analytic in x and they are related to. Pearson's eta and Fisher's F. Extensions of these coefficients (designed for univariate, one way discrimination) to k-way and multivariate discriminant analysis and measurement of »interaction « are suggested.