A non-parametric maximum test for the Behrens–Fisher problem

Anke Welz, Graeme D. Ruxton, Markus Neuhäuser

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


Non-normality and heteroscedasticity are common in applications. For the comparison of two samples in the non-parametric Behrens-Fisher problem, different tests have been proposed, but no single test can be recommended for all situations. Here, we propose combining two tests, the Welch t test based on ranks and the Brunner-Munzel test, within a maximum test. Simulation studies indicate that this maximum test, performed as a permutation test, controls the type I error rate and stabilizes the power. That is, it has good power characteristics for a variety of distributions, and also for unbalanced sample sizes. Compared to the single tests, the maximum test shows acceptable type I error control.
Original languageEnglish
Pages (from-to)1336-1347
Number of pages12
JournalJournal of Statistical Computation and Simulation
Issue number7
Early online date31 Jan 2018
Publication statusPublished - Mar 2018


  • Behrens-Fisher problem
  • Brunner-Munzel test
  • Maximum test
  • Welch t test


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