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This may be a lame question, but I got stuck and can't get my head around it. I am running a gene expression analysis, comparing $\sim 10,000$ genes between two groups, $n=6$ samples per group. My pipeline goes like this:

  1. I check whether the two groups have equal variances using Levene's test for each gene.
  2. For those genes that do have equal variances, I run a moderated t-test (as in limma), as it assumes equal variances.
  3. For the rest of the genes I run Mann-Whitney U.

(Before you tell me about multiple test correction, I do calculate FDR later on by permuting the population labels on samples and re-running the above tests).

Now, I want to calculate effect size for all the genes. I am using Cohen's d with pooled variance (see Wikipedia), but I wonder whether I can do it for both groups of genes (ie ones with and without equal variance between groups). I think I can't, but it's a guess really (I think I can only run it for the equal variance genes). If I can't, is there a more appropriate way to do this?

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