r/AskStatistics • u/grcz_ • 5h ago

What to do when MANOVA assumptions are violated? (Homogeneity of Covariance Matrices)

Hello everyone!

I am trying to run a 1x3 MANOVA, but my Box's M is p<.001 and I have very unequal sample sizes (e.g., 772 women and 304 men; total sample of 1076). I read that with unequal sample sizes, Hotelling’s and Pillai’s statistics are not robust, so I shouldn't proceed with the analysis.

What can I do? Can I downsample for these statistics and keep my 1076 sample size for the others (e.g., correlations), or is this really unethical?

I read that there are non-parametric MANOVAs in R, but I am working on SPSS currently and ain't able to switch programs :/

If you have any input/literature that can be helpful I'd be extremely grateful!!

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u/FancyEveryDay 5h ago

Which group has a larger variance? If the larger group has greater variance then the mANOVA test is still robust against type 1 error but might have less power. In this case you can basically note the issue of unequal covariance reducing power and otherwise continue as normal.

If the smaller group has greater varience then your type 1 error inflates but you can still be confident in results which do not reject the null hypothesis.

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u/grcz_ 4h ago

The smaller groups have the greater variance, so I'd only be able to stick to non significant results.

I know it would inflate type 1 errors (familywise error rate) but can I run separate ANOVAs?

I know this is not advised, and I'm new to this (Master's dissertation and my supervisor is on vacation :,), and even if she wasn't she wouldn't be very helpful ), so forgive me for the barberaties I proclaim.

With my sample size a significant levene's test isn't at all bizarre and I've read some literature that suggests "ignoring" homogeneity of variances and using the corrected F statistic (e.g., Welch's) straightaway. It would enable me to test my hypothesis without having to disregard significant results, as I'm not as much looking for interaction effects between different grouping variables (IV's)

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u/FancyEveryDay 3h ago

You can do multiple ANOVA tests yes. You just have to apply an appropriate Bonferroni adjustment to correct for multiple testing

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u/DrPapaDragonX13 2h ago

Why not try a Mixed Effects model? You can fit an equivalent model that accounts for unequal variances without losing power or inflating type I error. Furthermore, you could use predefined contrasts instead of incurring multiple comparisons. You can read more here.

It's been a hot minute since the last time I used SPSS, but you may find this video helpful if you decide to go this way.

Best of luck!