MANOVA vs Univariate ANOVAs

A Multivariate Analysis of Variance (MANOVA) takes into account inter-correlations between a group of outcomes. For example we could use a MANOVA if we have two or more highly correlated scores which measure attention and wish to see if these differ en bloc across patient groups.

If these scores were independent OR do not measure the same construct then a series of multiple univariate tests may be more applicable with each score representing a different outcome measure and score means compared across groups using separate anovas.

MANOVA has three advantages over univariate analyses. Firstly, it does not make the strong assumption of sphericity amongst levels of the repeated measures variable. Secondly, it takes into account inter-correlations between sets of outcome variables which are highly correlated. Thirdly it reduces the number of statistical tests by handling multiple outcome variables in the one analysis thus reducing type I error.

MANOVA does assume that variances and covariances in each of the groups are equal. This assumption can be tested by requesting a homogeneity of variance test labelled as Box's M test in the SPSS output.

Jeremy Miles also mentions

Cole et al. (1994) show that the more highly correlated your outcome variables, the higher (i.e.less significant) your multivariate p-values will be, which is kind of the opposite of what you might expect. You get the most power when your outcomes are correlated negatively - but many psychologists (who kind of blindly say "I've got more than one outcome, I'd better do a multivariate test") will have measured two highly correlated outcomes - like anxiety and depression, and then do a multivariate test, because there are two of them, but that guarantees (almost) that you won't get a significant result.

• Understanding and interpreting a MANOVA using ''only'' between subjects differences

• Understanding and interpreting a MANOVA in the SPSS Repeated Measures procedure

• Warning about using MANOVA with covariates

References

Cole DA, Maxwell SE, Arvey R, & Salas E (1994) How the power of MANOVA can both increase and decrease as a function of the intercorrelations among the dependent variables. Psychological Bulletin 115(3) 465-474.

Field A (2005) Discovering statistics using SPSS. 2nd Edition. Sage:London. An excellent primer with worked examples on both MANOVA and ANOVA. (In CBSU library).

Huberty CJ, Morris, JD (1989) Multivariate Analysis Versus Multiple Univariate Analyses. Psychological Bulletin 105(2) 302-308.