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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.
Fisher's exact test, based on the work of Ronald Fisher and E. J. G. Pitman in the 1930s, is exact because the sampling distribution (conditional on the marginals) is known exactly. This should be compared with Pearson's chi-squared test , which (although it tests the same null) is not exact because the distribution of the test statistic is ...
Fisher, R. A. 1954. Statistical Methods for Research Workers. Oliver and Boyd. Mehta, C. R. 1995. SPSS 6.1 Exact test for Windows. Prentice Hall. Mehta CR and Patel NR. 1983. A network algorithm for performing Fisher's exact test in rxc contingency tables. Journal of the American Statistical Association, 78(382): 427–434. Mehta CR and Patel ...
A test that relies on different assumptions is Fisher's exact test; if its assumption of fixed marginal distributions is met it is substantially more accurate in obtaining a significance level, especially with few observations. In the vast majority of applications this assumption will not be met, and Fisher's exact test will be over ...
The ANOVA F-test can be used to assess whether any of the treatments are on average superior, or inferior, to the others versus the null hypothesis that all four treatments yield the same mean response. This is an example of an "omnibus" test, meaning that a single test is performed to detect any of several possible differences.
[50] [61] In this book Fisher also outlined the Lady tasting tea, now a famous design of a statistical randomized experiment which uses Fisher's exact test and is the original exposition of Fisher's notion of a null hypothesis. [62] [63]
Fisher's description is less than 10 pages in length and is notable for its simplicity and completeness regarding terminology, calculations and design of the experiment. [5] The test used was Fisher's exact test.
Fisher's approach had certain philosophical advantages, while Neyman and Pearson emphasized rigorous mathematics. Hypothesis testing remains a subject of controversy for some users, but the most widely accepted alternative method, confidence intervals, is based on the same mathematical principles.