Research Design and Statistical Consulting

George M. Diekhoff, Ph.D.

Some of the best advice I received as a grad student learning multivariate statistics was this: If there’s any alternative to using multivariate analysis of variance (MANOVA), use it!

MANOVA is a widely used, but unwieldy statistical procedure. In comparisons of two or more groups that are defined by a single independent variable or factor (as in a one-way MANOVA), a significant multivariate effect will tell you that you have a reliable, replicable treatment effect, that is, at least the largest between-group difference is statistically significant. But different in what way? Ah, there’s the rub! MANOVA creates a new dependent variate from the multiple dependent variables that were entered into the analysis, and the groups differ on this variate. But what does that variate measure? MANOVA doesn’t tell you. It might be 2 parts of DV1, 4 parts of DV2, 3 parts of DV3, etc., but nothing in the output tells you. All you know, then, is that some unknown combination of your dependent variables has been created on which your groups differ significantly. Really, what point is there in knowing that the groups differ if you can’t describe HOW they differ? That’s when people resort to comparing the groups on each of the original dependent variables. But wasn’t the point of the MANOVA to avoid those univariate tests in the first place?

And what about factorial MANOVA? Things get even more delicious here! In a two-factor MANOVA, there will be tests of two main effects and the interaction effect. Each of these tests uses a DIFFERENT VARIATE, i.e., a different combination of the original dependent variables. So the main effect of Factor A might be tested on a variate that consists of 2 parts DV1, 4 parts DV2, 8 parts DV3…. and the main effect of Factor B might be tested using a variate that is 1 part of DV1, 9 parts of DV2, 5 parts of DV3…. and the interaction effect is probably tested using yet some other combination of the original dependent variables. Again, you’ll know if your independent variables (factors) had a significant effect, but you won’t be able to describe the nature of that effect! What are the alternatives? Instead of the one-way MANOVA, try discriminant analysis. This procedure will tell you if there is a significant effect of a single independent variable, AND it’ll tell you how the variate was constructed that produced this significant effect. So you’ll know not only that the groups differ, you’ll also know in what way the groups differ.

Unfortunately, there are no discriminant analysis alternatives to the within-subjects (“repeated measures”) one-way MANOVA. Discriminant analysis is just a between-subjects test. Also, there is no factorial version of the discriminant analysis, so you can’t use it to look for interaction effects. But if you want a multivariate form of one-way between-subjects ANOVA, try the discriminant analysis.