# Rank test

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{{Short description|Type of statistical test}}
In [statistics](/source/statistics), a '''rank test''' is any [test](/source/Statistical_hypothesis_testing) involving [rank](/source/ranking)s. Rank tests are related to [permutation test](/source/permutation_test)s.

The motivation to test differences between samples is that ranks are in some sense maximally [invariant](/source/Invariant_(mathematics)) to monotone transformations.
This may be important when there is [outlier](/source/outlier)s or when dealing with [ordinal data](/source/ordinal_data).

==Examples of rank tests==
*[Wilcoxon signed-rank test](/source/Wilcoxon_signed-rank_test)
*[Kruskal–Wallis test](/source/Kruskal%E2%80%93Wallis_test)
**[Mann–Whitney ''U'' test](/source/Mann%E2%80%93Whitney_U_test) (special case)
*[Page's trend test](/source/Page's_trend_test)
*[Friedman test](/source/Friedman_test)
*[Rank product](/source/Rank_product)s
*[Cucconi test](/source/Cucconi_test)
*[Lepage test](/source/Lepage_test)

== References ==
* Boos, D.D., Stefanski, L.A. (2013). Permutation and Rank Tests. In: Essential Statistical Inference. Springer Texts in Statistics, vol 120. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4818-1_12

Category:Statistical tests

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