Editing Pearson's chi-squared test (section)

==Assumptions==
The chi-squared test, when used with the standard approximation that a chi-squared distribution is applicable, has the following assumptions:<ref>{{Cite journal |last=McHugh |first=Mary |date=15 June 2013 |title=The chi-square test of independence. |journal=Biochemia Medica |volume=23 |issue=2 |pages=143–149 |doi=10.11613/BM.2013.018 |pmid=23894860 |pmc=3900058 }}</ref>

; [[Simple random sample]]: The sample data is a random sampling from a fixed distribution or population where every collection of members of the population of the given sample size has an equal probability of selection.  Variants of the test have been developed for complex samples, such as where the data is weighted. Other forms can be used such as [[purposive sampling]].<ref>See {{cite book |title=Discovering Statistics Using SPSS |first=Andy |last=Field }} for assumptions on Chi Square.</ref>
; Sample size (whole table): A sample with a sufficiently large size is assumed. If a chi squared test is conducted on a sample with a smaller size, then the chi squared test will yield an inaccurate inference. The researcher, by using chi squared test on small samples, might end up committing a [[Type II error]]. For small sample sizes the [[Cash test]] is preferred.<ref>{{Cite journal|last=Cash|first=W.|date=1979|title=Parameter estimation in astronomy through application of the likelihood ratio|journal=The Astrophysical Journal|volume=228|pages=939|doi=10.1086/156922|bibcode=1979ApJ...228..939C |issn=0004-637X|doi-access=free}}</ref><ref>{{Cite web|title=The Cash Statistic and Forward Fitting|url=https://hesperia.gsfc.nasa.gov/~schmahl/cash/cash_oddities.html|access-date=2021-10-19|website=hesperia.gsfc.nasa.gov}}</ref>
; Expected cell count: Adequate expected cell counts. Some require 5 or more, and others require 10 or more. A common rule is 5 or more in all cells of a 2-by-2 table, and 5 or more in 80% of cells in larger tables, but no cells with zero expected count. When this assumption is not met, [[Yates's correction for continuity|Yates's correction]] is applied.
; Independence: The observations are always assumed to be independent of each other. This means chi-squared cannot be used to test correlated data (like matched pairs or panel data). In those cases, [[McNemar's test]] may be more appropriate.

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 conservative and not have correct coverage.<ref>{{cite web|title=A Bayesian Formulation for Exploratory Data Analysis and Goodness-of-Fit Testing|url=http://www.stat.columbia.edu/~gelman/research/published/isr.pdf | page=375 |publisher=International Statistical Review}}</ref>