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Mathematics
Set Theory, Logic, Probability, Statistics
Can MANOVA still be used with violated assumptions?
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[QUOTE="micromass, post: 5484600, member: 205308"] It is very rare that all assumptions of MANOVA are satisfied. It is therefore good that MANOVA is robust under certain deviations of the assumptions. As for multivariate normality, as long as your number of observations are much (and they are), the central limit theorem will apply and your MANOVA result will be robust under violation of normality. Note however that the stronger your deviation for normality, the more the size of your population matters. In either case, you could always try a multivariate Box-Cox transformation to make things more normal. As for equality of the covariance matrices, this is a bigger issue. Usually it is not a problem when the sample sizes are equal. But this is not the case with you, so it is doubtful that your MANOVA will be good. If you can take care that the sample sizes are equal, then your MANOVA should be good and you should use the Pillai trace as that is most stable under robustness. While the Levene test is good for departures against normality, I would also suggest the Brown-Forsythe test since it is even more robust against departure from normality. In either case, you will want a multivariate version of the test since you're dealing with MANOVA. [/QUOTE]
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Can MANOVA still be used with violated assumptions?
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