Simultaneous test procedures in multivariate analysis of variance

Abstract

This paper presents procedures for multivariate analysis of variance which simultaneously test for significance all variables together as well as all subsets of variables, or the differences between all samples as well as between the samples of any subgroup. These procedures ensure a predetermined probability of making no type I error on any of the tests and are coherent in preserving the implication relations which exist between hypotheses on different groups of samples. The procedure using Roy's maximum characteristics root statistics is found to be preferable to all other procedures of this kind.