A COMPARISON OF 6-TEST STATISTICS FOR DETECTING MULTIVARIATE NONNORMALITY WHICH UTILIZE THE MULTIVARIATE SQUARED-RADII STATISTIC

This study presents tabulated emprically-derived critical values for H awkins' test for non-normality, and compares the power of this test to five other test statistics designed to detect multivariate non-normal ity, all of which are functions of the multivariate squared-radii stat istic. The power comparison has been accomplished using a Monte Carlo simulation with two sample sizes, two observation dimensions, and ten multivariate nonnormal distributions. Among the six test statistics co nsidered in the present study, the one proposed by Hawkins (1981) has proven to be the best omnibus test statistic for detecting multivariat e non-normality. Empirically calculated critical values for Hawkin's t est statistic for detecting multivariate non-normality are given as an appendix.