Given an urn with N genes, ugh - I mean with N balls, B of which are white, I can calculate the probability of randomly drawing b or more white balls in a sample of n using hypergeometric test. This gives me a p-value I can use to reject H0.

However, I'd like to use an estimate of the effect size. I use (b/n)/(B/N) ("relative enrichment") but it seems sometimes to be very misleading. Is there a better option?

  • $\begingroup$ "Effect sizes" are measures of something. What are you trying to measure? $\endgroup$ – Glen_b Nov 11 '14 at 22:48
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    $\begingroup$ Ultimately, I'm trying to measure the effect of a treatment on gene expression, the extent to which a particular treatment affects the immune response. I do this by looking on how many genes that seem to be affected by treatment belong into a particular category. However, the numbers are relative, they depend on the category, so "number of affected genes" is not a good estimate. The "enrichment" defined above is not bad, but as I know that there are many ways to skin a microarray, I wonder whether there are alternatives. $\endgroup$ – January Nov 12 '14 at 7:37
  • $\begingroup$ Can you explain how the things in your real problem relate to the variables in the toy problem (i.e. what's N,B,n,b ?) $\endgroup$ – Glen_b Nov 12 '14 at 8:34
  • $\begingroup$ N is the total number of genes, and B is the number of genes in the given category (say, "immune response genes"). n is the total number of genes that appear to be affected, and b is the number of genes in that category which are among the n affected genes. $\endgroup$ – January Nov 12 '14 at 10:31
  • $\begingroup$ You'd have to bound $n$ away from $0$ or the expectation of the ratio would be undefined. $\endgroup$ – Glen_b Nov 12 '14 at 12:32

Instead of the hypergeometric test, use the chi-square test. (Chi-square test on the table would be a continuous approximation to the discrete distribution). The effect size is then given using the Cramer's V.

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