| Many multivariate statistical methods call upon the assumption of multivariate normality. However, many applied researchers fail to test this assumption. This omission could be due to either ignorance of the existence of tests of multivariate normality or confusion about which test to use. Although at least 50 tests of multivariate normality exist, relatively little is known about the power of these procedures. The purpose of this study was to examine the power of 13 promising tests of multivariate normality under a variety of conditions. Monte Carlo simulations were used to generate 10,000 data sets from 27 multivariate distributions, including the multivariate normal distribution, normal mixtures, elliptically contoured distributions, and heavily skewed distributions. The test statistic for each procedure was calculated and compared with the appropriate critical value. The number of rejections of the null hypothesis of multivariate normality was tabled for each situation. No single test was found to be the most powerful in all situations. The use of the Henze-Zirkler test is recommended for a formal test of the null hypothesis of multivariate normality. The use of supplementary procedures such as Mardia's measures of skewness and kurtosis and the chi-square or beta plot is also recommended for diagnosing the cause of the non-normality. |
