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The two-sample Mood statistic for clustered data

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  • 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
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    References listed on IDEAS

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    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.
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