Editing F-test (section)

{{Short description|Statistical hypothesis test, mostly using multiple restrictions}}
{{DISPLAYTITLE:''F''-test}}
[[File:F-test_plot.svg|thumb|An f-test pdf with d1 and d2 = 10, at a significance level of 0.05. (Red shaded region indicates the critical region)]]
An '''F-test''' is a [[statistical test]] that compares variances. It is used to determine if the variances of two samples, or if the ratios of variances among multiple samples, are significantly different. The test calculates a [[Test statistic|statistic]], represented by the random variable F, and checks if it follows an [[F-distribution]]. This check is valid if the [[null hypothesis]] is true and standard assumptions about the errors (ε) in the data hold.<ref name=":0">{{Cite book |last1=Berger |first1=Paul D. |url=http://link.springer.com/10.1007/978-3-319-64583-4 |title=Experimental Design |last2=Maurer |first2=Robert E. |last3=Celli |first3=Giovana B. |date=2018 |publisher=Springer International Publishing |isbn=978-3-319-64582-7 |location=Cham |pages=108 |language=en |doi=10.1007/978-3-319-64583-4}}</ref> 

F-tests are frequently used to compare different statistical models and find the one that best describes the [[population (statistics)|population]] the data came from. When models are created using the [[least squares]] method, the resulting F-tests are often called "exact" F-tests. The F-statistic was developed by [[Ronald Fisher]] in the 1920s as the variance ratio and was later named in his honor by [[George W. Snedecor]].<ref>{{cite book |last=Lomax |first=Richard G. |url=https://archive.org/details/introductiontost0000loma_j6h1 |title=Statistical Concepts: A Second Course |publisher=Lawrence Erlbaum Associates |year=2007 |isbn=978-0-8058-5850-1 |page=[https://archive.org/details/introductiontost0000loma_j6h1/page/10 10] |url-access=registration}}</ref>