The nonparametric Behrens-Fisher problem with dependent replicates

Akash Roy, Solomon W. Harrar, Frank Konietschke

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Purely nonparametric methods are developed for general two-sample problems in which each experimental unit may have an individual number of possibly correlated replicates. In particular, equality of the variances, or higher moments, of the distributions of the data is not assumed, even under the null hypothesis of no treatment effect. Thus, a solution for the so-called nonparametric Behrens-Fisher problem is proposed for such models. The methods are valid for metric, count, ordered categorical, and even dichotomous data in a unified way. Point estimators of the treatment effects as well as their asymptotic distributions will be studied in detail. For small sample sizes, the distributions of the proposed test statistics are approximated using Satterthwaite-Welch-type t-approximations. Extensive simulation studies show favorable performance of the new methods, in particular, in small sample size situations. A real data set illustrates the application of the proposed methods.

Original languageEnglish
Pages (from-to)4939-4962
Number of pages24
JournalStatistics in Medicine
Issue number25
StatePublished - Nov 10 2019

Bibliographical note

Funding Information:
The authors are grateful to three expert referees, the associate editor, and the joint editor for their helpful comments which led to a considerable improvement of the original version of the paper. We would like to thank Paavo Sattler (Technical University of Dortmund) for valuable discussions. The research is supported by the Deutsche Forschungsgemeinschaft award number DFG KO 4680/3-2. The data that support the findings of this study are openly available in accessed on December 16, 2018.

Publisher Copyright:
© 2019 John Wiley & Sons, Ltd.


  • asymptotics
  • clustered data
  • empirical distribution
  • nonparametric effects
  • ranks
  • two-sample problem

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability


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