IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v66y2025i3d10.1007_s00362-025-01692-z.html
   My bibliography  Save this article

The two-sample Mood statistic for clustered data

Author

Listed:
  • Akira Suzuki

    (Tokyo University of Science)

  • Hidetoshi Murakami

    (Tokyo University of Science)

Abstract

The classical Mood statistic is frequently used to test the equality of scale parameters in two-sample problems. However, its application requires the assumption of independent observations. In many practical situations, correlated observations often arise due to clustered data. To address this issue, we develop a test for clustered data under the assumption of homoscedasticity. This study derives the asymptotic distribution of the proposed statistic under the null hypothesis. Simulations are performed to investigate the robustness and power performance of the proposed statistics in various situations. The simulation results demonstrate that the proposed statistic is a strong competitor to existing statistics and offers advantages in certain cases. Two illustrations using oribatid mite data and BMI data are provided. Finally, the concluding remarks are presented.

Suggested Citation

  • Akira Suzuki & Hidetoshi Murakami, 2025. "The two-sample Mood statistic for clustered data," Statistical Papers, Springer, vol. 66(3), pages 1-33, April.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:3:d:10.1007_s00362-025-01692-z
    DOI: 10.1007/s00362-025-01692-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-025-01692-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-025-01692-z?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Somnath Datta & Jaakko Nevalainen & Hannu Oja, 2012. "A general class of signed-rank tests for clustered data when the cluster size is potentially informative," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 797-808.
    2. Datta, Somnath & Satten, Glen A., 2005. "Rank-Sum Tests for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 908-915, September.
    3. Haataja, Riina & Larocque, Denis & Nevalainen, Jaakko & Oja, Hannu, 2009. "A weighted multivariate signed-rank test for cluster-correlated data," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1107-1119, July.
    4. Denis Larocque & Riina Haataja & Jaakko Nevalainen & Hannu Oja, 2010. "Two sample tests for the nonparametric Behrens–Fisher problem with clustered data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(6), pages 755-771.
    5. Riina Lemponen & Denis Larocque & Jaakko Nevalainen & Hannu Oja, 2012. "Weighted rank tests and Hodges-Lehmann estimates for the multivariate two-sample location problem with clustered data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 977-991, December.
    6. Denis Larocque & Jaakko Nevalainen & Hannu Oja, 2007. "A weighted multivariate sign test for cluster-correlated data," Biometrika, Biometrika Trust, vol. 94(2), pages 267-283.
    7. Sandipan Dutta & Somnath Datta, 2016. "A rank-sum test for clustered data when the number of subjects in a group within a cluster is informative," Biometrics, The International Biometric Society, vol. 72(2), pages 432-440, June.
    8. Nevalainen, Jaakko & Larocque, Denis & Oja, Hannu & Pörsti, Ilkka, 2010. "Nonparametric Analysis of Clustered Multivariate Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 864-872.
    9. Somnath Datta & Glen A. Satten, 2008. "A Signed-Rank Test for Clustered Data," Biometrics, The International Biometric Society, vol. 64(2), pages 501-507, June.
    10. Jiahua Chen & Pengfei Li & Yukun Liu & James V. Zidek, 2021. "Composite empirical likelihood for multisample clustered data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 33(1), pages 60-81, January.
    11. Bernard Rosner & Robert J. Glynn & Mei-Ling Ting Lee, 2003. "Incorporation of Clustering Effects for the Wilcoxon Rank Sum Test: A Large-Sample Approach," Biometrics, The International Biometric Society, vol. 59(4), pages 1089-1098, December.
    12. Marozzi, Marco, 2004. "A bi-aspect nonparametric test for the two-sample location problem," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 639-648, January.
    Full references (including those not matched with items on IDEAS)

    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. Riina Lemponen & Denis Larocque & Jaakko Nevalainen & Hannu Oja, 2012. "Weighted rank tests and Hodges-Lehmann estimates for the multivariate two-sample location problem with clustered data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 977-991, December.
    2. Omer Ozturk & Asuman Turkmen, 2016. "Quantile inference based on clustered data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(7), pages 867-893, October.
    3. Sandipan Dutta, 2022. "Robust Testing of Paired Outcomes Incorporating Covariate Effects in Clustered Data with Informative Cluster Size," Stats, MDPI, vol. 5(4), pages 1-13, December.
    4. Somnath Datta & Jaakko Nevalainen & Hannu Oja, 2012. "A general class of signed-rank tests for clustered data when the cluster size is potentially informative," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 797-808.
    5. Denis Larocque & Riina Haataja & Jaakko Nevalainen & Hannu Oja, 2010. "Two sample tests for the nonparametric Behrens–Fisher problem with clustered data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(6), pages 755-771.
    6. Liya Fu & You-Gan Wang, 2012. "Efficient Estimation for Rank-Based Regression with Clustered Data," Biometrics, The International Biometric Society, vol. 68(4), pages 1074-1082, December.
    7. Haataja, Riina & Larocque, Denis & Nevalainen, Jaakko & Oja, Hannu, 2009. "A weighted multivariate signed-rank test for cluster-correlated data," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1107-1119, July.
    8. Jaakko Nevalainen & Somnath Datta & Hannu Oja, 2014. "Inference on the marginal distribution of clustered data with informative cluster size," Statistical Papers, Springer, vol. 55(1), pages 71-92, February.
    9. Jaakko Nevalainen & Denis Larocque & Hannu Oja, 2007. "A weighted spatial median for clustered data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 355-379, February.
    10. Hasika K. Wickrama Senevirathne & Sandipan Dutta, 2024. "Testing Informativeness of Covariate-Induced Group Sizes in Clustered Data," Mathematics, MDPI, vol. 12(11), pages 1-15, May.
    11. Jaakko Nevalainen & Denis Larocque & Hannu Oja, 2007. "A weighted spatial median for clustered data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 355-379, February.
    12. Lea Cassar, 2014. "Job mission as a substitute for monetary incentives: experimental evidence," ECON - Working Papers 177, Department of Economics - University of Zurich.
    13. Philippe Aghion & Stefan Bechtold & Lea Cassar & Holger Herz, 2018. "The Causal Effects of Competition on Innovation: Experimental Evidence," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 34(2), pages 162-195.
    14. Gelder, Alan & Kovenock, Dan, 2017. "Dynamic behavior and player types in majoritarian multi-battle contests," Games and Economic Behavior, Elsevier, vol. 104(C), pages 444-455.
    15. Maul, D. & Schiereck, D., 2017. "The bond event study methodology since 1974," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 80723, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    16. You-Gan Wang & Yudong Zhao, 2008. "Weighted Rank Regression for Clustered Data Analysis," Biometrics, The International Biometric Society, vol. 64(1), pages 39-45, March.
    17. Werner, Carola & Brunner, Edgar, 2007. "Rank methods for the analysis of clustered data in diagnostic trials," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5041-5054, June.
    18. Paindaveine, Davy, 2009. "On Multivariate Runs Tests for Randomness," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1525-1538.
    19. Feng, Jun & Ho, Chun-Yu & Qin, Xiangdong, 2022. "Internal and external reference dependence of incomplete contracts: Experimental evidences," Journal of Economic Behavior & Organization, Elsevier, vol. 203(C), pages 189-209.
    20. Bernard Rosner & Robert J. Glynn, 2011. "Power and Sample Size Estimation for the Clustered Wilcoxon Test," Biometrics, The International Biometric Society, vol. 67(2), pages 646-653, June.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:66:y:2025:i:3:d:10.1007_s00362-025-01692-z. 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.