Hello everyone
When conducting a MANOVA, because we are dealing with several dependent
variables we have to make assumptions about their joint distribution.
Thus in each group, we should have a multivariate normal distribution
and there should be equal variance-covariance matrices. My question
is, what if these assumptions are violated?
In a univariate situation (ANOVA) we could, for example, apply a Box Cox
transformation to the single response variable to improve normality and
stablise variance, but what happens when we have several response
variables as we have in a MANOVA?
If the variables have a MV normal distribution then each variable taken
individually must be normally distributed (however, variables
distributed normally individually will not necessarily have a MV normal
distribution when considered together). Bearing this in mind for our
MANOVA situation, would it be appropriate to consider each dependent
variable separately and identify the most appropriate transformation for
each and apply possibly a different transformation to each dependent
variable before conducting the MANOVA? Perhaps this would not be
sensible.
Many thanks in advance for your suggestions,
Kim.
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