An Omnibus Test for Univariate and Multivariate Normality*

Abstract 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.