Editing Hypergeometric distribution (section)

== Statistical Inference ==
=== Hypergeometric test ===
{{see also|Fisher's noncentral hypergeometric distribution}}

The '''hypergeometric test''' uses the hypergeometric distribution to measure the statistical significance of having drawn a sample consisting of a specific number of <math>k</math> successes (out of <math>n</math> total draws) from a population of size <math>N</math> containing <math>K</math> successes. In a test for over-representation of successes in the sample, the hypergeometric p-value is calculated as the probability of randomly drawing <math>k</math> or more successes from the population in <math>n</math> total draws. In a test for under-representation, the p-value is the probability of randomly drawing <math>k</math> or fewer successes.

[[File:Youngronaldfisher2.JPG|thumb|right|200px|Biologist and statistician [[Ronald Fisher]]]]

The test based on the hypergeometric distribution (hypergeometric test) is identical to the corresponding one-tailed version of [[Fisher's exact test]].<ref>{{cite journal| first1=I.|last1= Rivals|first2= L. |last2=Personnaz | first3= L. |last3=Taing |first4= M.-C |last4=Potier| title=Enrichment or depletion of a GO category within a class of genes: which test? |volume= 23|journal= Bioinformatics |year=2007 |pages= 401–407|pmid=17182697| doi=10.1093/bioinformatics/btl633| issue=4|url=https://hal-espci.archives-ouvertes.fr/hal-00801557/document|doi-access=free}}</ref> Reciprocally, the p-value of a two-sided Fisher's exact test can be calculated as the sum of two appropriate hypergeometric tests (for more information see<ref>{{cite web| author=K. Preacher and N. Briggs| title=Calculation for Fisher's Exact Test: An interactive calculation tool for Fisher's exact probability test for 2 x 2 tables (interactive page) | url=http://quantpsy.org/fisher/fisher.htm}}</ref>).

The test is often used to identify which sub-populations are over- or under-represented in a sample. This test has a wide range of applications. For example, a marketing group could use the test to understand their customer base by testing a set of known customers for over-representation of various demographic subgroups (e.g., women, people under 30).