An Omnibus Test for Univariate and Multivariate Normality

We suggest a convenient version of the omnibus test for normality, using skewness and kurtosis based on Shenton and Bowman ["Journal of the American Statistical Association" (1977) Vol. 72, pp. 206-211], which controls well for size, for samples as low as 10 observations. A multivariate version is introduced. Size and power are investigated in comparison with four other tests for multivariate normality. The first power experiments consider the whole skewness-kurtosis plane; the second use a bivariate distribution which has normal marginals. It is concluded that the proposed test has the best size and power properties of the tests considered. Copyright (c) Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2008.