Fisher's exact test is a statistical significance test widely used to analyze 2x2 contingency tables, particularly in situations where sample sizes are small. Unlike the chi-squared test, which approximates P-values and assumes minimum expected frequencies of at least five in each cell, Fisher's exact test calculates the exact probability (P-value) of observing the data or more extreme results under the null hypothesis. This feature makes it especially valuable when the assumptions of the chi-squared test are not met due to low expected frequencies.

This test is non-parametric, meaning it does not rely on the data following any specific distribution. Its exactness ensures accurate results, even in cases with sparse data. As a result, Fisher's exact test is often preferred in scenarios involving small sample sizes or low cell counts, where other methods may fail or provide unreliable outcomes.

Fisher's exact test is applicable when data can be represented in a 2x2 contingency table and one or both variables are categorical. It is particularly useful when expected cell counts are low, such as fewer than five observations in any cell of the table. Its ability to handle small datasets and its precision make it a robust alternative to the chi-squared test, especially in studies where obtaining large sample sizes is not feasible.

The test is used in various fields, including biology, medicine, and social sciences. For example, in medical research, it is commonly employed in small clinical trials to evaluate treatment effects. In biology, it is used to analyze genetic associations or experimental outcomes, while in social sciences, it helps examine relationships between categorical variables. Fisher's exact test is highly versatile, offering a reliable method to assess statistical significance when other tests might be unsuitable due to the limitations of sample size or data distribution.

In summary, Fisher's exact test is a precise and reliable tool for analyzing associations between categorical variables in small datasets. Its exact nature and robustness make it an essential method for researchers working with contingency tables where traditional approaches like the chi-squared test may falter.