A New Test for Multivariate Normality and Homoscedasticity

Abstract

Given data X ij j = 1 to n i i = 1 to g, one may wish to test whether the X ij are normal with common covariance matrix. Letting X i . denote the mean of the ith group and S the pooled covariance matrix, the quantities V ij = (X ij – X i .)′S −1(X ij – X i .) are used in the test. The exact null distribution of V ij is noted, and the Anderson-Darling statistic is proposed for testing whether the data fit this null distribution. The new test has acceptable power, is flexible, and is easily implemented.