Although the multivariate normal assumption is common to many of the multivariate statistical methods used to analyse psychological data, its tenability is rarely examined. It is possible to derive a goodness‐of‐fit test of this assumption, but in practice sample sizes will not be large enough to make complete testing feasible. In such a situation a partial testing procedure is advocated, together with studies of robustness. A numerical example is given illustrating how the partial testing procedure may detect instances of distributions which have normally distributed marginals but which are not multivariate nor