Fisher's exact test

Fisher's exact test (also Fisher-Irwin test) is a statistical significance test used in the analysis of contingency tables.^[1][2][3] Although in practice it is employed when sample sizes are small, it is valid for all sample sizes. The test assumes that all row and column sums of the contingency table were fixed by design and tends to be conservative and underpowered outside of this setting.^[4] It is one of a class of exact tests, so called because the significance of the deviation from a null hypothesis (e.g., p-value) can be calculated exactly, rather than relying on an approximation that becomes exact in the limit as the sample size grows to infinity, as with many statistical tests.

The test is named after its inventor, Ronald Fisher, who is said to have devised the test following a comment from Muriel Bristol, who claimed to be able to detect whether the tea or the milk was added first to her cup. He tested her claim in the "lady tasting tea" experiment.^[5]