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The traditional frequentist approach is to make use of null hypothesis significance tests which use<jats:italic>p<\/jats:italic>values to reject a null hypothesis. Recently, a lot of research has emerged which proposes Bayesian versions of the most common parametric and nonparametric frequentist two-sample tests. These proposals include Student\u2019s two-sample t-test and its nonparametric counterpart, the Mann\u2013Whitney U test. In this paper, the underlying assumptions, models and their implications for practical research of recently proposed Bayesian two-sample tests are explored and contrasted with the frequentist solutions. An extensive simulation study is provided, the results of which demonstrate that the proposed Bayesian tests achieve better type I error control at slightly increased type II error rates. These results are important, because balancing the type I and II errors is a crucial goal in a variety of research, and shifting towards the Bayesian two-sample tests while simultaneously increasing the sample size yields smaller type I error rates. What is more, the results highlight that the differences in type II error rates between frequentist and Bayesian two-sample tests depend on the magnitude of the underlying effect.<\/jats:p>","DOI":"10.1007\/s00180-020-01034-7","type":"journal-article","created":{"date-parts":[[2020,9,20]],"date-time":"2020-09-20T14:02:30Z","timestamp":1600610550000},"page":"1263-1288","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["Analysis of type I and II error rates of Bayesian and frequentist parametric and nonparametric two-sample hypothesis tests under preliminary assessment of normality"],"prefix":"10.1007","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9068-5696","authenticated-orcid":false,"given":"Riko","family":"Kelter","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,9,20]]},"reference":[{"issue":"4","key":"1034_CR1","doi-asserted-by":"publisher","first-page":"1787","DOI":"10.1214\/aos\/1176348654","volume":"22","author":"J Berger","year":"1994","unstructured":"Berger J, Brown L, Wolpert R (1994) A unified conditional frequentist and Bayesian test for fixed and sequential hypothesis testing. 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