Theoretical Distributions of Optima for Univariate Discrimination of Random Data*

ABSTRACT Optimal linear discriminant models maximize percentage accuracy for dichotomous classifications, but are rarely used because a theoretical framework that allows one to make valid statements about the statistical significance of the outcomes of such analyses does not exist. This paper describes an analytic solution for the theoretical distribution of optimal values for univariate optimal linear discriminant analysis, under the assumption that the data are random and continuous. We also present the theoretical distribution for sample sizes up to N = 30. The discovery of a statistical framework for evaluating the performance of optimal discriminant models should greatly increase their use by scientists in all disciplines.