Editing Fisher's exact test (section)

{{Short description|Statistical significance test}}
{{Use dmy dates|date=August 2021}}
'''Fisher's exact test''' (also '''Fisher-Irwin test''') is a [[statistical significance]] test used in the analysis of [[contingency table]]s.<ref>{{Cite journal| last=Fisher | first=R. A. | author-link= Ronald Fisher | year=1922 | title=On the interpretation of χ<sup>2</sup> from contingency tables, and the calculation of P |journal=[[Journal of the Royal Statistical Society]] | volume=85 | issue=1 | pages=87–94 | doi=10.2307/2340521| jstor=2340521| url=https://zenodo.org/record/1449484 }}</ref><ref>{{Cite book| last1=Fisher | first1=R.A. | year= 1954 | title=Statistical Methods for Research Workers | publisher=Oliver and Boyd| isbn=0-05-002170-2| title-link=Statistical Methods for Research Workers }}</ref><ref>{{Cite journal| last=Agresti | first=Alan | year=1992 | title=A Survey of Exact Inference for Contingency Tables |journal =Statistical Science | volume=7 | number=1 | pages=131–153 | doi=10.1214/ss/1177011454 | jstor = 2246001| citeseerx=10.1.1.296.874 }}</ref> Although in practice it is employed when [[sample (statistics)|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 [[Power (statistics)|underpowered]] outside of this setting.<ref name="campbell2007">{{cite journal | last=Campbell | first=Ian | title=Chi-squared and Fisher–Irwin tests of two-by-two tables with small sample recommendations | journal=Statistics in Medicine | volume=26 | issue=19 | date=2007-08-30 | issn=0277-6715 | doi=10.1002/sim.2832 | pages=3661–3675| pmid=17315184 }}</ref> It is one of a class of [[exact test]]s, so called because the significance of the deviation from a [[null hypothesis]] (e.g., [[p-value|''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.<ref name=newman>{{Cite book
|first=Sir Ronald A.
|last=Fisher
|author-link=Ronald Fisher
|chapter=Mathematics of a Lady Tasting Tea
|orig-year=''[[The Design of Experiments]]'' (1935)
|year=1956
|title=The World of Mathematics, volume 3
|editor=James Roy Newman
|chapter-url=https://books.google.com/books?id=oKZwtLQTmNAC&q=%22mathematics+of+a+lady+tasting+tea%22&pg=PA1512
|publisher=Courier Dover Publications
|isbn=978-0-486-41151-4
}}</ref>