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The procedure tests the null hypothesis , where  denotes the Mann\u2013Whitney effect. Apart from the trivial case of one\u2010point distributions, no restrictions are imposed on the underlying data distribution. The test is derived by evaluating the ratio of the true variance  of the Mann\u2013Whitney effect estimator  to its theoretical maximum, as derived from the Birnbaum\u2013Klose inequality. Through simulations, we demonstrate that the proposed test effectively controls the type\u2010I error rate under various conditions, including small and unbalanced sample sizes, and different data\u2010generating mechanisms. Notably, it provides better control of the type\u2010I error rate than the widely used Brunner\u2013Munzel test, particularly at small significance levels such as . We further construct range\u2010preserving compatible confidence intervals and show that they exhibit improved coverage compared to the confidence intervals compatible to the Brunner\u2013Munzel test. Finally, we illustrate the application of the method in a clinical trial\u00a0example.<\/jats:p>","DOI":"10.1002\/bimj.70096","type":"journal-article","created":{"date-parts":[[2025,11,10]],"date-time":"2025-11-10T06:03:21Z","timestamp":1762754601000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A New Approach to the Nonparametric Behrens\u2013Fisher Problem With Compatible Confidence Intervals"],"prefix":"10.1002","volume":"67","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-3124-6056","authenticated-orcid":false,"given":"Stephen","family":"Sch\u00fc\u00fcrhuis","sequence":"first","affiliation":[{"name":"Institute of Biometry and Clinical Epidemiology Charit\u2010Universit\u00e4tsmedizin Berlin Freie Universit\u00e4t Berlin and Humboldt\u2010Universit\u00e4t zu Berlin Berlin Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5674-2076","authenticated-orcid":false,"given":"Frank","family":"Konietschke","sequence":"additional","affiliation":[{"name":"Institute of Biometry and Clinical Epidemiology Charit\u2010Universit\u00e4tsmedizin Berlin Freie Universit\u00e4t Berlin and Humboldt\u2010Universit\u00e4t zu Berlin Berlin Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Edgar","family":"Brunner","sequence":"additional","affiliation":[{"name":"Department of Medical Statistics Universit\u00e4tsmedizin G\u00f6ttingen G\u00f6ttingen Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2025,11,9]]},"reference":[{"key":"e_1_2_13_2_1","unstructured":"Ara T.2022.brunnermunzel: (Permuted) Brunner\u2013Munzel Test.https:\/\/cran.r\u2010project.org\/web\/packages\/brunnermunzel\/index.html."},{"key":"e_1_2_13_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-2496(75)90001-2"},{"key":"e_1_2_13_4_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41562-017-0189-z"},{"key":"e_1_2_13_5_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177706794"},{"key":"e_1_2_13_6_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2044-8317.1978.tb00581.x"},{"key":"e_1_2_13_7_1","volume-title":"Rank and Pseudo\u2010Rank Procedures for Independent Observations in Factorial Designs, Using R and SAS","author":"Brunner E.","year":"2019"},{"key":"e_1_2_13_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00362-024-01635-0"},{"key":"e_1_2_13_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1521-4036(200001)42:1<17::AID-BIMJ17>3.0.CO;2-U"},{"key":"e_1_2_13_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.8967"},{"key":"e_1_2_13_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.3923"},{"key":"e_1_2_13_12_1","doi-asserted-by":"publisher","DOI":"10.2307\/2531595"},{"key":"e_1_2_13_13_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1981.10477623"},{"key":"e_1_2_13_14_1","doi-asserted-by":"publisher","DOI":"10.1080\/10543406.2022.2152831"},{"key":"e_1_2_13_15_1","unstructured":"Gastwirth J. 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