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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2504.01796 |
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| author | Schüürhuis, Stephen Konietschke, Frank Brunner, Edgar |
| author_facet | Schüürhuis, Stephen Konietschke, Frank Brunner, Edgar |
| contents | We propose a new test to address the nonparametric Behrens-Fisher problem involving different distribution functions in the two samples. Our procedure tests the null hypothesis $\mathcal{H}_0: θ= \frac{1}{2}$, where $θ= P(X<Y) + \frac{1}{2}P(X=Y)$ denotes the Mann-Whitney effect. No restrictions on the underlying distributions of the data are imposed with the trivial exception of one-point distributions. The method is based on evaluating the ratio of the variance $σ_N^2$ of the Mann-Whitney effect estimator $\widehatθ$ to its theoretical maximum, as derived from the Birnbaum-Klose inequality. Through simulations, we demonstrate that the proposed test effectively controls the type-I error rate under various conditions, including small sample sizes, unbalanced designs, and different data-generating mechanisms. Notably, it provides better control of the type-1 error rate compared to the widely used Brunner-Munzel test, particularly at small significance levels such as $α\in \{0.01, 0.005\}$. Additionally, we derive range-preserving compatible confidence intervals, showing that they offer improved coverage over those compatible to the Brunner-Munzel test. Finally, we illustrate the application of our method in a clinical trial example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01796 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A New Approach to the Nonparametric Behrens-Fisher Problem with Compatible Confidence Intervals Schüürhuis, Stephen Konietschke, Frank Brunner, Edgar Methodology We propose a new test to address the nonparametric Behrens-Fisher problem involving different distribution functions in the two samples. Our procedure tests the null hypothesis $\mathcal{H}_0: θ= \frac{1}{2}$, where $θ= P(X<Y) + \frac{1}{2}P(X=Y)$ denotes the Mann-Whitney effect. No restrictions on the underlying distributions of the data are imposed with the trivial exception of one-point distributions. The method is based on evaluating the ratio of the variance $σ_N^2$ of the Mann-Whitney effect estimator $\widehatθ$ to its theoretical maximum, as derived from the Birnbaum-Klose inequality. Through simulations, we demonstrate that the proposed test effectively controls the type-I error rate under various conditions, including small sample sizes, unbalanced designs, and different data-generating mechanisms. Notably, it provides better control of the type-1 error rate compared to the widely used Brunner-Munzel test, particularly at small significance levels such as $α\in \{0.01, 0.005\}$. Additionally, we derive range-preserving compatible confidence intervals, showing that they offer improved coverage over those compatible to the Brunner-Munzel test. Finally, we illustrate the application of our method in a clinical trial example. |
| title | A New Approach to the Nonparametric Behrens-Fisher Problem with Compatible Confidence Intervals |
| topic | Methodology |
| url | https://arxiv.org/abs/2504.01796 |