= Exact power of Fisher's exact test
{title2=$\sum_{(b,c)\in\mathcal R}\operatorname{Bin}_{n,p_0}(b)\operatorname{Bin}_{n,p_1}(c)$}
For two independent binomial counts, form the <Fisher exact test> rejection region from their conditional null <hypergeometric distribution>. Summing alternative joint binomial <probabilities> over that region gives its exact power. For equal group sizes, the null allocation is symmetric, so the two-sided <probability>-ordering test agrees with doubled lower-tail <probabilities>. Conservative test discreteness can make a normal-approximation <sample size> underpowered even when both samples are large but event counts are low.
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