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A generalization of the Wilcoxon signed-rank test and its applications

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  • S. Taheri
  • G. Hesamian

Abstract

This paper extends the Wilcoxon signed-rank test to the case where the available observations are imprecise quantities, rather than crisp. To do this, the associated test statistic is extended, using the α-cuts approach. In addition, the concept of critical value is generalized to the case when the significance level is given by a fuzzy number. Finally, to accept or reject the null hypothesis of interest, a preference degree between two fuzzy sets is employed for comparing the observed fuzzy test statistic and fuzzy critical value. Copyright Springer-Verlag 2013

Suggested Citation

  • S. Taheri & G. Hesamian, 2013. "A generalization of the Wilcoxon signed-rank test and its applications," Statistical Papers, Springer, vol. 54(2), pages 457-470, May.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:2:p:457-470
    DOI: 10.1007/s00362-012-0443-4
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    References listed on IDEAS

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    1. P. Filzmoser & R. Viertl, 2004. "Testing hypotheses with fuzzy data: The fuzzy p-value," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(1), pages 21-29, February.
    2. Hryniewicz, Olgierd, 2006. "Goodman-Kruskal [gamma] measure of dependence for fuzzy ordered categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 323-334, November.
    3. Abbas Parchami & S. Taheri & Mashaallah Mashinchi, 2012. "Testing fuzzy hypotheses based on vague observations: a p-value approach," Statistical Papers, Springer, vol. 53(2), pages 469-484, May.
    4. Abbas Parchami & S. Taheri & Mashaallah Mashinchi, 2010. "Fuzzy p-value in testing fuzzy hypotheses with crisp data," Statistical Papers, Springer, vol. 51(1), pages 209-226, January.
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