Editing Mathematical statistics (section)

===Nonparametric statistics===
{{main|Nonparametric statistics}}
'''Nonparametric statistics''' are values calculated from data in a way that is not based on [[Statistical parameter|parameterized]] families of [[probability distribution]]s. They include both [[descriptive statistics|descriptive]] and [[statistical inference|inferential]] statistics. The typical parameters are the expectations, variance, etc. Unlike [[parametric statistics]], nonparametric statistics make no assumptions about the [[probability distribution]]s of the variables being assessed.<ref>{{Cite web |title=Research Nonparametric Methods |url=https://d8.stat.cmu.edu/research-areas/nonparametric-methods |access-date=August 30, 2022 |website=Carnegie Mellon University}}</ref>

Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars).  The use of non-parametric methods may be necessary when data have a [[ranking]] but no clear numerical interpretation, such as when assessing [[preferences]]. In terms of [[level of measurement|levels of measurement]], non-parametric methods result in "ordinal" data.

As non-parametric methods make fewer assumptions, their applicability is much wider than the corresponding parametric methods.  In particular, they may be applied in situations where less is known about the application in question.  Also, due to the reliance on fewer assumptions, non-parametric methods are more [[Robust statistics#Introduction|robust]].

One drawback of non-parametric methods is that since they do not rely on assumptions, they are generally less [[Power of a test|powerful]] than their parametric counterparts.<ref name=":0">{{Cite web |title=Nonparametric Tests |url=https://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_Nonparametric/BS704_Nonparametric_print.html |access-date=2022-08-31 |website=sphweb.bumc.bu.edu}}</ref>  Low power non-parametric tests are problematic because a common use of these methods is for when a sample has a low sample size.<ref name=":0" />  Many parametric methods are proven to be the most powerful tests through methods such as the [[Neyman–Pearson lemma]] and the [[Likelihood-ratio test]].

Another justification for the use of non-parametric methods is simplicity.  In certain cases, even when the use of parametric methods is justified, non-parametric methods may be easier to use.  Due both to this simplicity and to their greater robustness, non-parametric methods are seen by some statisticians as leaving less room for improper use and misunderstanding.