Discriminant functions for linear comparisons of means when covariance matrices are unequal

Situations exist, as in the biological example of discriminant analysis for natural hybridization, cited in the text, where (a) not all populations have equal variances, and (b) comparisions based on single degrees of freedom must be planned. This paper presents a statistical methodology of estimating discriminant functions for linear comparisons among k(<2) multivariate normal populations, and of testing their significance, when these populations have unequal covariance matrices.     

Percentage Points of Multivariate t Distribution with Zero Correlations and their Application

The k-variate t distribution plays an important role in the application of Multiple Comparison Procedures, Ranking and Selection Procedures, and Estimation of Ranked Parameters. This distribution was considered by several authors in the past and is now widely used. In this paper, tables of some percentage points of the multivariate t distribution are tabulated for given probability level γ = 0.80, 0.90, 0.95, and 0.99; population size k = 2(1)20; and degrees of freedom v=2(1) 30(5)60 with common correlation coefficient ? = 0. The accuracy of the percentage points is specifically determined (and is up to the fourth decimal place). An application of these tables is considered for interval estimation of the largest mean of k(≧2) normal populations.