Multivariate Analysis of Variance

Multivariate analysis of variance (MANOVA) is a statistical model that is appropriate for both experimental and non-experimental research where associations between one or more explanatory (independent) variables and multiple outcome (dependent, response) variables are of interest. While outcome and explanatory variables may, in general, be quantitative or qualitative, this chapter focuses on the analysis and interpretation of statistical models involving only qualitative explanatory variables, that is, variables that are used to group the available units, typically human participants, and only quantitative outcomes. As presented here, MANOVA, used with descriptive discriminant analysis (DDA), is viewed as an extension of the univariate general linear model (see Chapter 1, this volume, on between-subjects ANOVA) where the purpose is to examine population differences on one or more linear composites of correlated outcome variables. The correlations among the outcomes are assumed to be due to one or more constructs that underlie the observed measures (here, “constructs” are conceptualized somewhat differently than in a structural equation modeling context; see Chapter 33 this volume). With MANOVA, composites are weighted linear combinations of the observed variable scores with the estimated weights specifically designed to maximize group separation. That is, the composite variables are created in such a way as to obtain the largest differences in group means on the composite variables. These composites are called linear discriminant functions and each function defines an independent construct. It is the difference between populations on these constructs that is of primary interest to the researcher.