ABSTRACT
Multivariate analysis of variance (MANOVA) is a statistical model that is appropriate for both experimental and non-experimental research contexts where the relations between one or more explanatory (independent) variables and multiple outcome (dependent, response) variables are of interest. While in general explanatory variables may be quantitative or qualitative (see Chapter 3, this volume, on canonical correlation), 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. As presented here, MANOVA is viewed as an extension of the univariate general linear model (see Chapter 1, this volume, on between-groups ANOVA) to examine population differences on one or more linear composites of correlated outcome variables. The correlations among the outcome variables suggest that one or more constructs might underlie the observed measures (here, “constructs” are conceptualized somewhat differently than in a structural equation modeling context; see Chapter 28, this volume). Composites are weighted combinations of the observed variable scores with the estimated weights chosen to maximize group separation. 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. The purpose of a multivariate analysis of variance therefore is to identify, define, and interpret the constructs determined by the linear composites separating the populations being compared. The careful selection of the outcome variables to study is essential for a meaningful analysis. A researcher may begin a study having some idea regarding the underling constructs, but often unanticipated constructs are identified. MANOVA can be used to support the researcher’s beliefs regarding the assessed constructs as well as to reveal hidden constructs underlying the observed outcome measures.
