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Two sample tests for the nonparametric Behrens–Fisher problem with clustered data

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  • Denis Larocque
  • Riina Haataja
  • Jaakko Nevalainen
  • Hannu Oja

Abstract

In this paper, we consider the nonparametric Behrens–Fisher problem with cluster-correlated data. A class of weighted Mann–Whitney test statistics is introduced and studied. In particular, a comparison with other recent testing procedures for related problems is provided. The new tests are valid when the distributions do not have the same scales and/or shapes under the null hypothesis. A general class of weighted U-statistics for clustered data, encompassing the Mann–Whitney statistic, is also introduced. A simulation studies the type I error robustness and the power of the new and of some recently proposed procedures. This study shows that the incorporation of appropriate weights can greatly improve the power of the test. A real data example illustrates the use of the tests.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:6:p:755-771
    DOI: 10.1080/10485250903469728
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Mei‐Ling Ting Lee & Herold G. Dehling, 2005. "Generalized two‐sample U‐statistics for clustered data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(3), pages 313-323, August.
    4. 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.
    5. 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.
    6. Bernard Rosner & Robert J. Glynn & Mei-Ling T. Lee, 2006. "Extension of the Rank Sum Test for Clustered Data: Two-Group Comparisons with Group Membership Defined at the Subunit Level," Biometrics, The International Biometric Society, vol. 62(4), pages 1251-1259, December.
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    Cited by:

    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.

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