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Multivariate Analysis of Variance (MANOVA)
Multivariate analysis of variance (MANOVA) is a statistical analysis used when a researcher wants to examine the effects of one or more independent variables (IVs) on multiple dependent variables (DVs). This method is an extension of the analysis of variance (ANOVA) model and is the most commonly used multivariate analysis in the social sciences. MANOVA tests, whether they are statistically significant or not, produce differences among levels of the IVs for multiple DVs. MANOVA tests belong to a larger family of statistical techniques known as the general linear model, which include analyses such as ANOVA, multiple types of regression, and repeated-measures designs.
MANOVA is an inferential statistical analysis. Communication researchers use this analysis to deduce a causal relationship between IVs and DVs. The researcher can then take the results of a study conducted on a smaller sample, or subset of the population, and generalize those results to a larger population. A researcher uses MANOVA to answer questions about how the combination of multiple DVs differs with respect to the chosen IVs. The researcher is hoping to find a stable pattern of cause and effect between the IVs and DVs. To briefly review, IVs refer to those variables that are manipulated or changed within the experiment and a DV is a variable that is expected to change or be affected by the IV. To answer questions about the relationship between the IVs and DVs in a MANOVA, researchers explore both multivariate effects and univariate effects. Multivariate effects refer to the influence IVs have on the combination of DVs. Univariate effects refer to how mean scores of each DV differ across the groups of the IV and, in the case of multiple IVs, the interactions between two IVs on each DV.
This entry includes a brief discussion of the differences between ANOVA and MANOVA, a basic overview of MANOVA, and the differences between one-way MANOVA and two-way MANOVA. Finally, this entry ends with some limitations to MANOVA.
ANOVA Versus MANOVA
Given that MANOVA is an extension of ANOVA, it is important to first understand how ANOVA works and then examine the reasons for choosing the two methods. One important distinction to make before discussing ANOVA versus MANOVA is the difference between multifactorial tests and multivariate tests. An ANOVA handles multiple IVs, or factors, and can therefore be called multifactorial. Being called multifactorial places the emphasis on the multiple IVs. With a MANOVA, the emphasis is on the multiple DVs (or variates) and that is thus called a multivariate test. Here the emphasis is on the multiple DVs.
A researcher running a one-way ANOVA can test for significant mean (average score for each group on the DV) differences of a single IV (also called groups or factors) with three or more levels on one DV. If the researcher has multiple IVs on only one DV, they are using a multifactorial ANOVA design. A multifactorial ANOVA allows a researcher to test multiple IVs on a single DV and observe any interactions between the IVs as well. For a multifactorial ANOVA, a researcher tests multiple main effects (one for each IV) and an interaction between all combinations of the IVs. When referring to an ANOVA as a two-way or three-way, the number two or three refers to the number of factors or IVs being used in the analysis. The use of a single DV makes ANOVA a univariate test. The IV in an ANOVA should be a nominal-level variable and the DV (also called response variables) should be interval or ratio-level.
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