A COMPARISON OF SIX TEST STATISTICS FOR DETECTING MULTIVARIATE NON-NORMALITY WHICH UTILIZE THE MULTIVARIATE SQUARED-RADII STATISTIC

摘要

This study presents tabulated emprically-derived critical values for Hawkins' test for non-normality, and compares the power of this test to five other test statistics designed to detect multivariate non-normality, all of which are functions of the multivariate squared-radii statistic. The power comparison has been accomplished using a Monte Carlo simulation with two sample sizes, two observation dimensions, and ten multivariate non-normal distributions. Among the six test statistics considered in the present study, the one proposed by Hawkins (1981) has proven to be the best omnibus test statistic for detecting multivariate non-normality. Empirically calculated critical values for Hawkin's test statistic for detecting multivariate non-normality are given as an appendix.