A Test to Determine Closeness of Multivariate Satterthwaite′s Approximation

The distribution of a nonnegative linear combination of mean square matrices associated with a balanced multivariate mixed model can be approximated by a central Wishart distribution. A necessary and sufficient condition for this approximation to be exact is presented. A multivariate test statistic is then developed to determine the closeness of the approximation for a given data set.