论文标题
Wilcoxon-Mann-Whitney-Test的最佳设计
Optimal design of the Wilcoxon-Mann-Whitney-test
论文作者
论文摘要
在科学研究中，许多假设与两个独立群体的比较有关。通常，使用设计（即，固定$ n = m + n $的样本尺寸$ m $ and $ n $的分配）是很感兴趣的，从而最大程度地利用了应用统计测试的功率。众所周知，当差异不等式但使用同样大样本时，用于均质和异质差异的两样本t检验可能会失去实质性的功率。我们证明，非参数Wilcoxon-Mann-Whitney-Test并非如此，其在生物识别研究领域的应用是由癌症研究的两个例子激励的。在对称和形状相同形状的分布情况下，我们证明了设计的最佳性，使用正常近似值，并表明该设计通常只能可忽略的功率比广泛的分布范围的最佳设计可忽略不计。请引用本文发表在《生物识别杂志》（https://doi.org/10.1002/bimj.201600022）中。
In scientific research, many hypotheses relate to the comparison of two independent groups. Usually, it is of interest to use a design (i.e., the allocation of sample sizes $m$ and $n$ for fixed $N = m + n$) that maximizes the power of the applied statistical test. It is known that the two-sample t-tests for homogeneous and heterogeneous variances may lose substantial power when variances are unequal but equally large samples are used. We demonstrate that this is not the case for the non-parametric Wilcoxon-Mann-Whitney-test, whose application in biometrical research fields is motivated by two examples from cancer research. We prove the optimality of the design $m = n$ in case of symmetric and identically shaped distributions using normal approximations and show that this design generally offers power only negligibly lower than the optimal design for a wide range of distributions. Please cite this paper as published in the Biometrical Journal (https://doi.org/10.1002/bimj.201600022).
