The Choice Between Pearson's χ2 Test and Fisher's Exact Test for 2 × 2 Tables

Abstract

Pearson's asymptotic χ2 test is often used to compare binary data between two groups. However, when the sample sizes or expected frequencies are small, the test is usually replaced by Fisher's exact test. Several alternative rules of thumb exist for defining “small” in this context. Replacing one test with another based on the obtained data is unusual in statistical practice. Moreover, this commonly-used switch is unnecessary because Pearson's χ2 test can easily be carried out as an exact test for any sample sizes. Therefore, we recommend routinely using an exact test regardless of the obtained data. This change of approach allows prespecifying a particular test and a much less ambiguous and more reliable analysis.