Statistical Methods & Applications

, Volume 20, Issue 4, pp 409–422 | Cite as

Robust nonparametric tests for the two-sample location problem

  • Roland FriedEmail author
  • Herold Dehling


We construct and investigate robust nonparametric tests for the two-sample location problem. A test based on a suitable scaling of the median of the set of differences between the two samples, which is the Hodges-Lehmann shift estimator corresponding to the Wilcoxon two-sample rank test, leads to higher robustness against outliers than the Wilcoxon test itself, while preserving its efficiency under a broad range of distributions. The good performance of the constructed test is investigated under different distributions and outlier configurations and compared to alternatives like the two-sample t-, the Wilcoxon and the median test, as well as to tests based on the difference of the sample medians or the one-sample Hodges-Lehmann estimators.


Distribution-free tests Wilcoxon test Outliers Heavy tails Skewed distributions 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of StatisticsTU Dortmund UniversityDortmundGermany
  2. 2.Department of MathematicsRuhr-University of BochumBochumGermany

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