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Generalization of Wilcoxon Statistic for the Case of k Samples

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  • Elizabeth H. Yen

Abstract

Doel van het volgende artikel is om aan te tonen, hoe verschillende bekende ranginvariante k‐steekproeven toetsen kunnen worden voortgebracht volgens één zelfdeprincipe. Dit principe is als volgt. Begin met de statistischegrootheden Uij en U0j van WILCOXON te construeren (Uij uit de i‐de enj‐desteekproeven; U0j uit de j‐de steekproefen alle andere tezamen; i, j = 1k). Laat vervolgens het symbool Tij de aanduiding zijn voor de genormaliseerde Uij en T0j voor de genormali‐seerde U0j. Beschouw tenslotte de absolute waardeofhetkwadraatvaneenzodanige lineaire functie van de Tij of de T0j, dat deze absolute waarde ofditkwadraateen zo groot mogelijke waarde heeft (waarbij deze maximalisering plaats vindt over een geschikte verzameling van coëfficienten‐combinaties). Als resultaat verkrijgt men dan de toetsingsgrootheden van TERPSTRA, STEEL, KRUSKAL‐WALLIS, en een nieuwe toetsingsgrootheid.

Suggested Citation

  • Elizabeth H. Yen, 1964. "Generalization of Wilcoxon Statistic for the Case of k Samples," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 18(3), pages 293-302, September.
    • Handle: RePEc:bla:stanee:v:18:y:1964:i:3:p:293-302
    DOI: 10.1111/j.1467-9574.1964.tb00516.x
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