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Difference between revisions of "Rank sum test"

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A test of the homogeneity of two samples <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077520/r0775201.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077520/r0775202.png" /> based on the [[Rank statistic|rank statistic]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077520/r0775203.png" /> — the sum of the ranks <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077520/r0775204.png" /> of the random variables <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077520/r0775205.png" /> in the joint series of order statistics (cf. [[Order statistic|Order statistic]]) of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077520/r0775206.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077520/r0775207.png" /> (the elements of the two samples are mutually independent and come from continuous distributions). It is a variant of the [[Wilcoxon test|Wilcoxon test]].
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A test of the homogeneity of two samples $X_1,\dots, X_n$ and $Y_1,\dots, Y_m$ based on the [[Rank statistic|rank statistic]] $R_1+\dots +R_m$ — the sum of the ranks $R_j$ of the random variables $Y_j$ in the joint series of order statistics (cf. [[Order statistic|Order statistic]]) of $X_i$ and $X_j$ (the elements of the two samples are mutually independent and come from continuous distributions). It is a variant of the [[Wilcoxon test|Wilcoxon test]].

Revision as of 09:54, 11 February 2012

A test of the homogeneity of two samples $X_1,\dots, X_n$ and $Y_1,\dots, Y_m$ based on the rank statistic $R_1+\dots +R_m$ — the sum of the ranks $R_j$ of the random variables $Y_j$ in the joint series of order statistics (cf. Order statistic) of $X_i$ and $X_j$ (the elements of the two samples are mutually independent and come from continuous distributions). It is a variant of the Wilcoxon test.

How to Cite This Entry:
Rank sum test. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Rank_sum_test&oldid=20977
This article was adapted from an original article by A.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article