We suggest an easy to use version of the omnibus test for normality using skewness and kurtosis based on Shenton and Bowman (1977) which controls well for size. A multivariate version is introduced. Size and power are investigated in comparison with four other tests for multivariate normality. The alternative hypothesis in the power simulations is the whole Johnson system of distributions.
Some key words: Johnson system; Kurtosis; Multivariate normality test; Skewness; Univariate normality test; Wilson-Hilferty transformation.