Multivariate Analysis Versus Multiple Univariate Analyses

The argument for preceding multiple analysis of variance (ANOVAS) with a multivariate analysis of variance (MANOVA) to control for Type I error is challenged. Several situations are discussed in which multiple ANOVAS might be conducted without the necessity of a preliminary MANOVA. Three reasons for considering a multivariate analysis are discussed: to identify outcome variable system constructs, to select variable subsets, and to determine variable relative worth. The analyses discussed in this article are those appropriate in research situations in which analysis of variance techniques are useful. These analyses are used to study the effects of treatment variables on outcome/response variables (in ex post facto as well as experimental studies). We speak of an univariate analysis of variance (ANOVA) when a single outcome variable is involved ; when multiple outcome variables are involved, it is a multivariate analysis of variance (MANOVA). (Covariance analyses may also be included.) With multiple outcome variables, the typical analysis approach used in the group-comparison context, at least in the behavioral sciences, is to either (a) conduct multiple ANOVAs or (b) conduct a MANOVA followed by multiple ANOVAS. That these are two popular choices may be concluded from a survey of some prominent behavioral science journals. The 1986 issues of five journals published by the American Psychological Association were surveyed:sults of the survey are given in Table 1. A few comments about these results would be appropriate. First, only one count was made per article, even though some articles reported analyses for multiple experiments or studies. Only the main analysis for an experiment was considered; so-called preliminary analyses were not tallied. Sometimes there were only two groups involved; in this case, multiple t tests were considered multiple ANOVAS, and a Hotelling T 2 analysis was considered a MANOVA. For the second analysis approach (MAN-OVA plus ANOVAS), interpretations or explanations were invariably based on the multiple ANOVAS. In six articles in which multiple ANOVAS were used, three justifications for not doing a MA-NOVA were given: (a) low outcome variable intercorrelations; (b) small number of outcome variables; and (c) small design cell frequencies. After a MANOVA, multiple ANOVAS were often used implicitly or explicitly to assess relative variable importance. Reasons given for conducting multiple ANOVAS after a MANOVA 302 were (a) to clarify the meaning of significant discriminators; (b) to explain the results of the MANOVA; and (c) to document effects reflected by the MANOVA. In one case, …