Performance Properties of the Four MANOVA Statistics

• Activity Number: 287
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 8:30 AM to 10:20 AM
• Sponsor: General Methodology
• Author(s): Bruce Brown*+ and Suzanne Hendrix and Kent Hendrix
• Affiliation(s): Brigham Young University and Brigham Young University and Meridian School
• Keywords: MANOVA ; Multivariate Tests ; p-plots ; Multivariate Visualization

Abstract

Univariate ANOVA employs a single test statistic, the F test, but MANOVA utilizes four tests of statistical significance. Contrary to popular belief, the four are complementary rather than competing methods. Rencher and Scott (1990) demonstrate that one avoids alpha inflation by following the procedure of reporting significant univariate effects only when the corresponding multivariate effect is significant. However, the multivariate test can be considered to be significant if any of these four is. It follows from their demonstration that all four should be considered, since each has conditions under which it is more powerful than the others.

The purpose of this study is to identify the conditions under which each of the four is more powerful and the ways in which a p-value profile of the four can be diagnostically reflective of data structure. In particular, simulations are used to explore the relative magnitude of these four statistics as a function of five ways in which datasets can differ: (1) dimensionality, (2) relative distances of means from one another, (3) the ratio of between to within variance, (4) homogeniety of variances, and (5) pattern of covariance structure.