On randomization in multivariate analysis of variance (Q1091705)

When plot effects are modeled in a randomized block design in multivariate analysis of variance, the error and hypothesis matrices have independent noncentral Wishart distributions. When the noncentrality matrices of these distributions have unit rank, the distribution of resulting Wilks' statistic is doubly noncentral (linear case). It has been proved that averaging out the doubly noncentral distribution of Wilks' statistic with respect to the permutation distribution resulting from randomization, under the null hypothesis, does give the usual central distribution of Wilks' test statistic used for multivariate analysis of variance. Thus, it provides a mathematically rigorous proof for the justification of randomization, a key factor for the validity of the MANOVA test procedure.