Combinatorics, computer algebra and Wilcoxon-Mann-Whitney test

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    Abstract

    We show the combinatorics behind the Wilcoxon-??Mann-??Whitney two-??sample test.?? This yields new combinatorial proofs of recurrences for its null distribution given recently by Brus and Chang??, as well as new recurrences.?? It is shown how to convert these recurrences into generating functions.?? These generating functions are used to obtain closed expressions for the null distribution when one of the sample sizes is fixed and to compute moments??. We also show how to perform these calculations with the aid of the computer algebra system Mathematica??. Keywords: Wilcoxon??-Mann-??Whitney two-??sample test,?? partitions,?? Gaussian binomial coefficients,?? computer algebra,?? generating functions,?? recurrences.
    Original languageEnglish
    Place of PublicationEindhoven
    PublisherTechnische Universiteit Eindhoven
    Number of pages16
    Publication statusPublished - 1996

    Publication series

    NameMemorandum COSOR
    Volume9624
    ISSN (Print)0926-4493

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