Tang Liansheng Larry, Balakrishnan N
Department of Statistics, George Mason University, Fairfax, VA 22030, USA.
J Stat Plan Inference. 2011 Jan 1;141(1):335-344. doi: 10.1016/j.jspi.2010.06.011. Epub 2010 Jun 12.
The Wilcoxon-Mann-Whitney statistic is commonly used for a distribution-free comparison of two groups. One requirement for its use is that the sample sizes of the two groups are fixed. This is violated in some of the applications such as medical imaging studies and diagnostic marker studies; in the former, the violation occurs since the number of correctly localized abnormal images is random, while in the latter the violation is due to some subjects not having observable measurements. For this reason, we propose here a random-sum Wilcoxon statistic for comparing two groups in the presence of ties, and derive its variance as well as its asymptotic distribution for large sample sizes. The proposed statistic includes the regular Wilcoxon rank-sum statistic. Finally, we apply the proposed statistic for summarizing location response operating characteristic data from a liver computed tomography study, and also for summarizing diagnostic accuracy of biomarker data.
威尔科克森-曼-惠特尼统计量通常用于两组的无分布比较。使用该统计量的一个要求是两组的样本量固定。在一些应用中，如医学成像研究和诊断标志物研究，这一要求会被违反；在前者中，违反是因为正确定位的异常图像数量是随机的，而在后者中，违反是由于一些受试者没有可观测的测量值。因此，我们在此提出一种随机和威尔科克森统计量，用于在存在 ties 的情况下比较两组，并推导其方差以及大样本量时的渐近分布。所提出的统计量包括常规的威尔科克森秩和统计量。最后，我们将所提出的统计量应用于总结肝脏计算机断层扫描研究中的位置响应操作特征数据，以及总结生物标志物数据的诊断准确性。
