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Assessing the statistical significance of an observed 2x2 contingency tablecan easily be accomplished using Fisher's exact test (FET). However, if thecell entries are continuous or represent values inferred from a continuousparametric model, then FET cannot be applied. Such tables arise frequently inareas of biostatistical research including population genetics and evolutionarygenomics, where cell entries are estimated by computational methods and resultin cell entries drawn from the non-negative real line R+. Simply rounding cellentries to conform to the assumptions of FET is an ill-suited approach that weshow creates problems related to both type-I and type-II errors. Pearson'schi^2 test for independence, while technically applicable, is not ofteneffective for these tables, as the test has several limiting assumptions thatmake application of this method inadvisable in many common instances(particularly with small cell entries). Here we develop a novel method fortables with continuous entries, which we term continuous Fisher's Exact Test(cFET). Through simulations, we show that cFET has a close-to-uniformdistribution of p-values under the null hypothesis of independence, and morepower when applied to tables where the null hypothesis is false (compared toFET applied to rounded cell entries). We apply cFET to an example fromcomparative genomics to confirm an overall increased evolutionary rate amongprimates compared to rodents, and identify several genes that show particularlyelevated evolutionary rates in primates. Some of these genes exhibit signaturesof continued positive selection along the human lineage since our divergencewith chimpanzee 5-7 million years ago, as well as ongoing selection in modernhumans.

Comparing Evolutionary Rates Using An Exact Test for 2x2 Tables with Continuous Cell Entries