Suppose that I perform two different comparisons on the same genomic dataset (with say 1000 genes, and three conditions).
For each comparison, I adjust the pvalues using Benjamini Hochberg, controlling the FDR. So, in each comparison, I would have say, 0.1 false positives on expectation.
Suppose that I do not control in any way for the fact that I perform two comparisons and not just one.
What would be the False Discovery Rate for the whole list of significantly changed genes for the two comparisons?
I think that if I set the threshold to be 0.1 then (for a single comparisons)
P(false positive) = 0.1
P(true positive) = 1 - 0.1
For two comparisons:
P(true positive) = (1 - 0.1)^2
P(false positive) = 1 - (1-0.1)^2
And thus the the FDR would be 1-(1-alpha)^n
But I would like some verification of that.