Rank test

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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.


[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:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098