# Rank test

From Encyclopedia of Mathematics

A statistical test based on a rank statistic. The Wilcoxon and Mann–Whitney tests (cf. Mann–Whitney test; Wilcoxon test) are examples of rank tests. Rank tests are invariant with respect to groups of transformations defined by continuous strictly-increasing functions. Hence they are invariant with respect to variations of the shift and scaling parameters. Moreover, in many problems of hypotheses testing the most-powerful invariant tests can be well approximated by rank tests.

#### References

[1] | J. Hájek, Z. Sidák, "Theory of rank tests" , Acad. Press (1967) |

[2] | E.L. Lehmann, "Testing statistical hypotheses" , Wiley (1986) |

**How to Cite This Entry:**

Rank test. M.S. Nikulin (originator),

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Rank_test&oldid=18520

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098