# ANOVAs and MANOVAs

Quantitative Results
Statistical Analysis

An ANOVA is used to assess differences on time and/or group for one continuous variable and a MANOVA is used to assess differences on time and/or group for multiple continuous variables, but what other factors go into the decision to conduct multiple ANOVAs or a single MANOVA?  MANOVAs are best conducted when the dependent variables used in the analysis are highly negatively correlated and are also acceptable if the dependent variables are found to be correlated around .60, either positive or negative.  The use of MANOVA is discouraged when the dependent variables are not related or highly positively correlated.

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MANOVA is discouraged with highly positively correlated variables because, although the overall multivariate analysis works well, once the highest priority dependent variables has been assessed, the tests conducted and results presented on the remaining dependent variables will be vague.  The reason for this is because once the highest priority dependent variable becomes a covariate, the variance that remains for the lower priority dependent variables is not enough to be significantly related to the main effects or interactions.  Additionally, the univariate ANOVA results are misleading.

MANOVA is also discouraged when the dependent variables are not significantly related.  A multivariate analysis has lower power than univariate analyses, therefore the difference between univariate and step-down analysis is small.  In this instance the only benefit to conducting a MANOVA over univariate ANOVAs is a reduction in the likelihood of Type I error.  If multiple ANOVAs are the more appropriate analysis, Type I error can be controlled for with the use of the Bonferroni correction, α = 1 – (1 – α1)(1 – α2)…(1 – αn).

In the case where some the dependent variables are correlated in different sets, it may be more appropriate to run two separate MANVOAs; one with each set of correlated variables.