Multivariate analysis versus multiple univariate analyses.

TLDR

In behavioral science, researchers debate whether to precede multiple ANOVAs with a MANOVA to control Type I error, noting that multivariate analysis can identify system constructs, select variable subsets, and assess variable worth, yet many studies use either multiple ANOVAs alone or a MANOVA followed by ANOVAs, as shown by journal surveys. The article examines which ANOVA techniques are appropriate for research situations where variance analysis methods are applicable. Univariate ANOVA is used for a single outcome variable, whereas multivariate ANOVA applies.

Abstract

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