Fisher's exact

Fisher's Exact Test is a statistical significance test used in the analysis of contingency tables. Although in practice it is employed when sample sizes are small, it is valid for all sample sizes. It is named after its inventor, Ronald Fisher, and is one of a class of exact tests, so called because the significance of the deviation from a null hypothesis (e.g., P = 0.5) can be calculated exactly, rather than relying on an approximation that becomes exact in the limit as the sample size grows to infinity, as seen in many other statistical tests.

History

Ronald Fisher introduced the exact test in 1922, for the case of a 2x2 contingency table and the null hypothesis of no association between the row and column classifications. The test is exact because its significance level does not depend on an approximation that assumes a fixed sample size or other parameter.

Calculation

The calculation of Fisher's exact test is based on the probabilities of observing the data under the null hypothesis. The test is computed on a 2x2 contingency table, but can be generalized to larger contingency tables.

Application

Fisher's exact test is used when you have two nominal variables and you want to see if there is an association between them. It is often used in scientific studies, for example in medicine and biology, where the sample sizes are typically small.

Limitations

While Fisher's exact test is exact for any given sample size, it becomes conservative as the sample size grows, meaning that it is less likely to reject the null hypothesis when it is false.

See also

• Chi-squared test
• Binomial distribution
• Statistical significance