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. Thi s problem is related to the investigation, whether graphically or anal ytically, of significant empirical departures From the overall null hy pothesis on these functions. A closed testing procedure for a sequence of relevant hypotheses is proposed. Unlike the classical procedures b ased on asymptotic distributions of the likelihood ratio statistics, t he proposed method ensures that the Type I familywise error rate does not exceed the nominal cc-level. Also, it is consistent with testing t he overall null hypothesis, while relying on tests of subsequent linea r hypotheses implied by the former. Examples are given to compare the proposed procedure with a classical one. (C) 1998 Academic Press.