ABSTRACT
The ANOVA and ANCOVA tests covered in Chapter 12 are univariate tests because they only involve a single dependent variable. No matter how many independent factors are included, if there is a single dependent variable, the test is a univariate ANOVA or ANCOVA. This chapter covers multivariate ANOVA (MANOVA) and multivariate ANCOVA (MANCOVA) tests where there are two or more dependent variables. In a MANOVA test, all participants must be measured on the set of dependent variables of interest. Procedures have been proposed for replacing missing data in multivariate tests but there are no firm guidelines for dealing with this issue (Tabachnick and Fidell, 2007: 63). Therefore, it is recommended that any participant who has not been measured using the full set of dependent variables should be excluded from a study where a MANOVA test is being done. The MANOVA test applies the F test like univariate ANOVA tests do except to a single variable which is an optimal linear combination of the dependent variables of interest (Mardia et al., 1994: 2; Thomas and Nelson, 1996: 180–1). Weights are used to produce this optimal linear combination. This single combined variable is optimized to maximize any variance that can be attributed to the independent variables(s). One text suggested that MANOVA tests also involve more than one independent variable (Thomas and Nelson, 1996: 180). The argument for this is that discriminant analysis can be used where there is a single discrete independent variable. The author of this book takes a different view that discriminant function analysis and MANOVA tests have different purposes as we will see in Chapter 16. In discriminant function analysis, we hypothesize that some discrete dependent variable is influenced by a set of continuous independent variables. A single factor MANOVA test, however, tests the hypothesis that the combined set of continuous variables is influenced by the discrete factor which is the independent variable in the analysis. Whether using MANOVA tests or discriminant tests, we should always consider the conceptual model that we are testing, understanding which variables may be influenced by other variables. This will help avoid putting the ‘cart before the horse’. Other authors agreeing with this point of view include Ntoumanis (2001: 100–5) and Hinton et al. (2004: 241–50) who show how a one-way MANOVA tests can be done in SPSS.
