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I am reading from this where they mention running 500K fisher exact test to find significant associations between different DNA changes and a phenotype.

They also mention that Bonferroni, Benjamini, and FDR can be used to set a significance threshold, which I think I understand.

What I don't get is that they say permutation can also be used to set a significance threshold. How can you use permutation on fisher exact test output to set a significance threshold?

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It's difficult to speculate they mean without giving a citation or reference, but they may be referring to the Westfall-Young method which is a permutation based method. I did just answer a question at CV where I suggested using permutation testing (empirical p-value testing), which is here.

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