An ANOVAs 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.
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.
