Dimensionality in Manova Tested by a Closed Testing Procedure

The decision on dimensionality of the space spanned by general linear functions of the parameter matrix of a MANOVA model is considered. This problem is related to the investigation, whether graphically or analytically, of significant empirical departures from the overall null hypothesis on these functions. A closed testing procedure for a sequence of relevant hypotheses is proposed. Unlike the classical procedures based on asymptotic distributions of the likelihood ratio statistics, the proposed method ensures that the Type I familywise error rate does not exceed the nominalα-level. Also, it is consistent with testing the overall null hypothesis, while relying on tests of subsequent linear hypotheses implied by the former. Examples are given to compare the proposed procedure with a classical one.