chapter  4
Multivariate Analysis of Variance: Differences Among Several Groups on Several One-Way (Univariate) Analysis of Variance
ByMeasures
Pages 58

Multivariate Analysis of Variance: Differences Among Several Groups on Several Measures The use of Hotelling’s I 2 is limited to comparisons of only two groups at a time. Many studies, such as the one that provided the data presented in Data Set 4 (chap. 3), involve more than just two independent groups of subjects. Just as doing a series of six univariate t tests to test all the differences on a single variable among four experimental groups would be inappropriate because of the inflation of Type I error this produces, so would a series of six T analyses of the differences in mean response vectors among these same groups be just as inappropriate for the same reason. The answer to the problem of multiple experimental groups in the univariate case is (univariate) analysis of variance (Anova); the solution to the multiple comparison problem when there are two or more outcome measures as well as two or more groups is multivariate analysis of variance (Manova). Before we discuss Manova, it might be well to review the basic rationale and computational formulae of Anova.