Distributions of the direction and collinearity factors in discriminant analysis

Abstract

AbstractExact tests devised by Bartlett and Williams for the adequacy of a single discriminant function in the case of several groups are applicable to a wide range of problems in multivariate analysis. The appropriate likelihood criterion is factorized into direction and collinearity factors; and the exact distribution of these factors under the conditions of only one non-zero canonical correlation was first given by Bartlett in the general case of any numbers of dependent and independent variables, making use of geometrical arguments.In this paper the factors are expressed directly in terms of the matrices occurring in the multivariate analysis of variance table; and the results are derived by an analytical method making use of matrix transformations and rectangular coordinates.