IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v54y2013i2p457-470.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-012-0443-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00362-012-0443-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Giacomo Benini & Adam Brandt & Valerio Dotti & Hassan El-Houjeiri, 2023. "The Economic and Environmental Consequences of the Petroleum Industry Extensive Margin," Working Papers 2023:14, Department of Economics, University of Venice "Ca' Foscari".
    2. Ming Shan & Yu-Shan Li & Bon-Gang Hwang & Jia-En Chua, 2021. "Productivity Metrics and Its Implementations in Construction Projects: A Case Study of Singapore," Sustainability, MDPI, vol. 13(21), pages 1-19, November.
    3. Seongmin Kang & Seong-Dong Kim & Eui-Chan Jeon, 2020. "Ammonia Emission Sources Characteristics and Emission Factor Uncertainty at Liquefied Natural Gas Power Plants," IJERPH, MDPI, vol. 17(11), pages 1-10, May.
    4. Abbas Parchami & S. Mahmoud Taheri & Reinhard Viertl & Mashaallah Mashinchi, 2018. "Minimax test for fuzzy hypotheses," Statistical Papers, Springer, vol. 59(4), pages 1623-1648, December.
    5. Antonio Faúndez-Ugalde & Patricia Toledo-Zúñiga & Pedro Castro-Rodríguez, 2022. "Tax Sustainability: Tax Transparency in Latin America and the Chilean Case," Sustainability, MDPI, vol. 14(4), pages 1-17, February.
    6. Gholamreza Hesamian & Jalal Chachi, 2015. "Two-sample Kolmogorov–Smirnov fuzzy test for fuzzy random variables," Statistical Papers, Springer, vol. 56(1), pages 61-82, February.
    7. Johan Cassirame & Antoine Godin & Maxime Chamoux & Gregory Doucende & Laurent Mourot, 2022. "Physiological Implication of Slope Gradient during Incremental Running Test," IJERPH, MDPI, vol. 19(19), pages 1-12, September.
    8. Shima Yosefi & Mohsen Arefi & Mohammad Ghasem Akbari, 2016. "A new approach for testing fuzzy hypotheses based on likelihood ratio statistic," Statistical Papers, Springer, vol. 57(3), pages 665-688, September.
    9. Wei Zhang & Shanshan Yu & Ling Wang & Wei Guo & Man-Fai Leung, 2024. "Constrained Symmetric Non-Negative Matrix Factorization with Deep Autoencoders for Community Detection," Mathematics, MDPI, vol. 12(10), pages 1-17, May.
    10. Emily Tang & Chelsea Jones & Lorraine Smith-MacDonald & Matthew R. G. Brown & Eric H. G. J. M. Vermetten & Suzette Brémault-Phillips, 2021. "Decreased Emotional Dysregulation Following Multi-Modal Motion-Assisted Memory Desensitization and Reconsolidation Therapy (3MDR): Identifying Possible Driving Factors in Remediation of Treatment-Resi," IJERPH, MDPI, vol. 18(22), pages 1-12, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Abbas Parchami & S. Mahmoud Taheri & Reinhard Viertl & Mashaallah Mashinchi, 2018. "Minimax test for fuzzy hypotheses," Statistical Papers, Springer, vol. 59(4), pages 1623-1648, December.
    2. Shima Yosefi & Mohsen Arefi & Mohammad Ghasem Akbari, 2016. "A new approach for testing fuzzy hypotheses based on likelihood ratio statistic," Statistical Papers, Springer, vol. 57(3), pages 665-688, September.
    3. Nataliya Chukhrova & Arne Johannssen, 2020. "Randomized versus non-randomized hypergeometric hypothesis testing with crisp and fuzzy hypotheses," Statistical Papers, Springer, vol. 61(6), pages 2605-2641, December.
    4. Jung-Lin Hung & Cheng-Che Chen & Chun-Mei Lai, 2020. "Possibility Measure of Accepting Statistical Hypothesis," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    5. 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.
    6. Muhammad Aslam, 2022. "Neutrosophic F-Test for Two Counts of Data from the Poisson Distribution with Application in Climatology," Stats, MDPI, vol. 5(3), pages 1-11, August.
    7. Fernando Reche & María Morales & Antonio Salmerón, 2020. "Statistical Parameters Based on Fuzzy Measures," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    8. Gia Sirbiladze & Tariel Khvedelidze, 2023. "Associated Statistical Parameters’ Aggregations in Interactive MADM," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    9. Antonio Calcagnì & Luigi Lombardi & Lorenzo Avanzi & Eduardo Pascali, 2020. "Multiple mediation analysis for interval-valued data," Statistical Papers, Springer, vol. 61(1), pages 347-369, February.
    10. Wu, Chien-Wei, 2009. "Decision-making in testing process performance with fuzzy data," European Journal of Operational Research, Elsevier, vol. 193(2), pages 499-509, March.
    11. 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.
    12. Hsu, Bi-Min & Shu, Ming-Hung, 2008. "Fuzzy inference to assess manufacturing process capability with imprecise data," European Journal of Operational Research, Elsevier, vol. 186(2), pages 652-670, April.
    13. Lubiano, María Asunción & Montenegro, Manuel & Sinova, Beatriz & de la Rosa de Sáa, Sara & Gil, María Ángeles, 2016. "Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications," European Journal of Operational Research, Elsevier, vol. 251(3), pages 918-929.
    14. Coppi, Renato & Gil, Maria A. & Kiers, Henk A.L., 2006. "The fuzzy approach to statistical analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 1-14, November.
    15. Mohammad Ghasem Akbari & Gholamreza Hesamian, 2017. "Record value based on intuitionistic fuzzy random variables," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(15), pages 3305-3315, November.
    16. Viertl, Reinhard, 2006. "Univariate statistical analysis with fuzzy data," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 133-147, November.
    17. Ana Colubi & Renato Coppi & Pierpaolo D’urso & Maria angeles Gil, 2007. "Statistics with fuzzy random variables," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 277-303.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:54:y:2013:i:2:p:457-470. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.