{{Short description, Type of statistical test In

statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

, a rank test is any

test Test(s), testing, or TEST may refer to: * Test (assessment), an educational assessment intended to measure the respondents' knowledge or other abilities Arts and entertainment * ''Test'' (2013 film), an American film * ''Test'' (2014 film) ...

involving

rank A rank is a position in a hierarchy. It can be formally recognized—for example, cardinal, chief executive officer, general, professor—or unofficial. People Formal ranks * Academic rank * Corporate title * Diplomatic rank * Hierarchy ...

s. Rank tests are related to

permutation test A permutation test (also called re-randomization test or shuffle test) is an exact statistical hypothesis test. A permutation test involves two or more samples. The (possibly counterfactual) null hypothesis is that all samples come from the same ...

Motivation

The motivation to test differences between samples is that ranks are in some sense maximally invariant to monotone transformations. This may be important when there is

outlier In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are ...

s or when dealing with

ordinal data Ordinal data is a categorical, statistical data type where the variables have natural, ordered categories and the distances between the categories are not known. These data exist on an ordinal scale, one of four Level of measurement, levels of m ...

Examples

* Wilcoxon signed-rank test * Kruskal–Wallis one-way analysis of variance ** Mann–Whitney U (special case) * Page's trend test *

Friedman test The Friedman test is a non-parametric statistical test developed by Milton Friedman. Similar to the parametric repeated measures ANOVA, it is used to detect differences in treatments across multiple test attempts. The procedure involves ranking ...

* Rank products * Cucconi test * Lepage test

Literature

* 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 Statistical tests