MANOVA: unequal group numbers and inverse transformation

Hi! :wave:

I'm helping my wife with stats for her dissertation. The basic setup:

DVs: 15 response items on a personality test
IV: 5 levels (different types of trauma) with hugely different ns for each level; n1=16, n2=13, n3=34, n4=21, n5=101

Straight MANOVA in SPSS was showing big failure for Levene's test, most DVs p<0.05; I tried a 1/x transformation on the data and they all passed.

Skewness values for some, but not all of the DVs at the various levels were within +/-1 before transformation (though a few were >1); after much more were within +/-1, even more like +/-0.5

Kurtosis values for the DVs at the various levels were within +/-2.5 (some DVs at a couple IV levels were 3 or 4) before transformation; after the transformation most were within +/-2, though a few were at 4-5.

Histograms after transformation look much more normal.

DVs at most of the levels fail the Shapiro-Wilk (p<0.05) before and after transformation.

I also tried log10, ln, and squareroot transformations, and none fixed the unequal variance problem like the 1/x did.

Is the MANOVA going to be workable in this scenario? Would Kruskal-Wallis be better? Any suggestions or ideas or insight would be so appreciated!


Doesn't actually exist
a few things (which i believe have been brought forward before in other thread questions but i might be wrong). the assumption of (multivariate) normality is not on the variables themselves but on the residuals, have you had a look at those? now, although n1-n4 should not be too bad for the unequal sample-size MANOVA, n5 is definitely a problem, especially if the variance of n5 is also the group with the largest variance...
now, Kurskal-Wallis is a univariate technique, and multivariate extensions of non-parametric analyses of variance are not particualrly straightforward.... i'd be very interested in understanding how you'd jump from a MANOVA to a Kruskal-Wallis without changing the research hypothesis (or are you planning to change it?).