# How to deal with a non-gaussian distribution & heteroscedasticity

I am working on my thesis project and have come across a problem with the statistics which I am looking for a bit of guidance.

I am running ANOVA tests to determine significance between groups but i have come across a problem with a couple of the results which do not have equal variance (p<0.05 & p<0.001). This alone wasn't particularly a problem (Welch correction and unequal variance post-tests)

But one of my assays shows non-normal distribution & unequal variance:

• I ran D’Agostino-Pearson omnibus test with P<0.05 in one of the groups (however my sample sizes are small 3 datasets with n=7,15,&16).
• In the literature it appears there is some skew in this distribution from the 'healthy' adult population so it is reasonable to assume it is not normal in my groups.
• Bartletts test for homogeneity of variance has p>0.01.

It was recommended I run Kruskal-Wallis ANOVA, but: - This test assumes equal variance, which is not the case. - Also my sample size is a bit small in the first patient group (n=7), which to my understanding is that Kruskal-Wallis has little power in this case as well?

I essentially do not know what to do with this data set! Any help would me most appreciated!

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Kruskal-Wallis... assumes equal variance This is incorrect statement. If you've picked this from Wikipedia please know that the article is inaccurate. See Discussion sheet there. –  ttnphns Nov 5 '11 at 8:37