Abstract

A technique for the formal construction of statistical distributions in multivariate Edgeworth populations is applied to investigate the effects of moderate multivariate nonnormality on the test statistics used in connexion with the general linear model, in particular, Wilks's likelihood ratio criterion. The first-order approximation to the sampling distributions under nonnormality are shown to involve Mardia's measures of multivariate skewness and kurtosis, together with a supplementary skewness measure. Correction terms for tests at the 5% level are constructed for one-way analysis of variance, and the resulting approximations are compared with simulation results for a range of bivariate distributions.

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