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There are some cases where I would like to correct for multiple comparisons where the null hypotheses vary.

For example, if I am performing a chi-squared test or a fisher's exact test on multiple contingency tables of different sizes, the null hypotheses vary from table to table. Can I still apply the Benjamini-Hochberg procedure for multiple comparisons using the p-values from these tests? If not, what should be done in this situation?

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No, there is no such restriction. The only restriction is whether the tests themselves are independent or not, and there is even some wiggle room there: if the tests are positively correlated, you can pretend they are independent. See e.g False Discovery Rate or the references from Qvalue.

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