Discriminant Functions when Covariances are Unequal and Sample Sizes are Moderate

A Monte Carlo study (Wahl 1971) is compared to the study of Marks and Dunn (1974) which investigated the ability of three discriminant functions, the quadratic, best linear, and Fisher's linear discriminant function, to classify individuals into two multivariate normally distributed populations with unequal covariance matrices. Parameters that were varied in all of the studies include the distance between populations, covariance matrices, number of variables, sample size and population proportion. Our results, when related to those of Marks and Dunn, indicate sample size to be a critical factor in choosing between the quadratic and linear functions.