Editing Fisher's exact test (section)

==Alternatives==
An alternative exact test, [[Barnard's exact test]], has been developed and proponents<ref>{{cite journal | author = Lydersen, S., Fagerland, M. W., and Laake, P. | year = 2009 | title = Recommended tests for association in 2× 2 tables | journal = Statistics in Medicine | volume = 28 | issue = 7 | pages = 1159–1175 | doi= 10.1002/sim.3531| pmid = 19170020 | s2cid = 3900997 }}</ref> of it suggest that this method is more powerful, particularly in 2×2 tables.<ref>{{cite journal | author = Berger R.L. | year = 1994 | title = Power comparison of exact unconditional tests for comparing two binomial proportions | journal = Institute of Statistics Mimeo Series No. 2266 | pages = 1–19 }}</ref> Furthermore, [[Boschloo's test]] is an exact test that is uniformly more powerful than Fisher's exact test by construction.<ref name="Boschloo">{{cite journal | author = Boschloo R.D. | year = 1970 | title = Raised Conditional Level of Significance for the ''2''x''2''-table when Testing the Equality of Two Probabilities | journal = Statistica Neerlandica | volume = 24 | pages = 1–35 | doi = 10.1111/j.1467-9574.1970.tb00104.x}}</ref>

Most modern [[statistical package]]s will calculate the significance of Fisher tests, in some cases even where the chi-squared approximation would also be acceptable. The actual computations as performed by statistical software packages will as a rule differ from those described above, because numerical difficulties may result from the large values taken by the factorials. A simple, somewhat better computational approach relies on a [[gamma function]] or log-gamma function, but methods for accurate computation of hypergeometric and binomial probabilities remains an active research area.

For stratified categorical data the [[Cochran–Mantel–Haenszel test]] must be used instead of Fisher's test.

Choi et al.<ref name="Choi2015" /> propose a ''p''-value derived from the likelihood ratio test based on the conditional distribution of the [[odds ratio]] given the marginal success rate. This ''p''-value is inferentially consistent with classical tests of normally distributed data as well as with likelihood ratios and support intervals based on this conditional likelihood function. It is also readily computable.<ref name="Choi2011">{{Cite web
 | last = Choi
 | first = Leena
 | year = 2011
 | title = ProfileLikelihood: profile likelihood for a parameter in commonly used statistical models; 2011. R package version 1.1.
 | url = https://cran.r-project.org/web/packages/ProfileLikelihood/index.html
 }}
See also: [http://statcomp2.vanderbilt.edu:37212/dalep/ProfileLikelihood/ Likelihood Ratio Statistics for 2 x 2 Tables] {{Webarchive|url=https://web.archive.org/web/20160604023208/http://statcomp2.vanderbilt.edu:37212/dalep/ProfileLikelihood/ |date=4 June 2016 }} (Online calculator).</ref>