FisherExact

Fisher's Exact Test is a statistical significance test used in the analysis of categorical data. It is most commonly applied to 2x2 contingency tables, which are used to display the frequency distribution of two categorical variables. Unlike the chi-squared test, Fisher's Exact Test does not rely on any assumptions about the distribution of the data, making it particularly useful for small sample sizes.

The test calculates the exact probability of observing the data, or more extreme data, given the marginal totals of the contingency table. This probability is determined by enumerating all possible tables with the same marginal totals and calculating the probability of each table under the null hypothesis of independence between the two variables. The p-value is then the sum of the probabilities of tables that are as extreme or more extreme than the observed table.

Fisher's Exact Test is particularly valuable when sample sizes are small, or when expected cell counts are low, as the chi-squared approximation may not be accurate in such cases. While computationally more intensive than the chi-squared test, its exactness makes it the preferred method for small sample contingency table analysis. It is widely used in fields such as biology, medicine, and social sciences to assess associations between categorical variables.