Editing Chi-squared test (section)

== Other examples of chi-squared tests ==

One [[test statistic]] that follows a [[chi-squared distribution]] exactly is the test that the variance of a normally distributed population has a given value based on a [[sample variance]]. Such tests are uncommon in practice because the true variance of the population is usually unknown. However, there are several statistical tests where the [[chi-squared distribution]] is approximately valid:

=== Fisher's exact test ===
For an [[exact test]] used in place of the 2 × 2 chi-squared test for independence when all the row and column totals were fixed by design, see [[Fisher's exact test]]. When the row or column margins (or both) are random variables (as in most common research designs) this tends to be overly conservative and [[Power (statistics)|underpowered]].<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>

=== Binomial test ===
For an exact test used in place of the 2 × 1 chi-squared test for goodness of fit, see [[binomial test]].

=== Other chi-squared tests ===
* [[Cochran–Mantel–Haenszel statistics|Cochran–Mantel–Haenszel chi-squared test]].
* [[McNemar's test]], used in certain {{nowrap|2 × 2}} tables with pairing
* [[Tukey's test of additivity]]
* The [[portmanteau test]] in [[time-series analysis]], testing for the presence of [[autocorrelation]]
* [[Likelihood-ratio test]]s in general [[statistical model]]ling, for testing whether there is evidence of the need to move from a simple model to a more complicated one (where the simple model is nested within the complicated one).