How the Power of MANOVA Can Both Increase and Decrease as a Function of the Intercorrelations Among the Dependent Variables

This article directly addresses explicit contradictions in the literature regarding the relation between the power of multivariate analysis of variance (MANOVA) and the intercorrelations among the dependent variables. Artificial data sets, as well as analytical methods, revealed that (a) power increases as correlations between dependent variables with large consistent effect sizes (that are in the same direction) more from near 1.0 toward -1.0, (b) power increases as correlations become more positive or more negative between dependent variables that have very different effect sizes (i.e., one large and one negligible), and (c) power increases as correlations between dependent variables with negligible effect sizes shift from positive to negative (assuming that there are dependent variables with large effect sizes still in the design). Implications for the reliability of dependent variables and strategies for selecting these variables in MANOVA designs are discussed.