How to deal with a non-gaussian distribution & heteroscedasticity

Question

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!

Answer 1

You can use bootstrap methods to assess whether the group means are different. Bootstrap methods do not have any specific distributional assumptions and may be an appropriate tool to use.

See the wiki for an explanation of case resampling which is one of the simplest bootstrap methods. You can extend the idea to the case of multiple groups and estimate p-values.