The authors consider multivariate analysis of variance procedures based on the multivariate spatial ranks. Two models are considered: the location-family model and the fully nonparametric model. Procedures for testing main and interaction effects are given for the 2 × 2 layout.

The problem of testing equality of two normal covariance matrices, [Sigma]1 = [Sigma]2 is studied. Two alternative hypotheses, [Sigma]1 [not equal to] [Sigma]2 and [Sigma]1 - [Sigma]2 0 are considered. Minimal complete classes among the class of invariant tests are found. The group of...