论文标题
Bootstrap P值减少了中值差异差异测试的1型误差
Bootstrap p-values reduce type 1 error of the robust rank-order test of difference in medians
论文作者
论文摘要
强大的排序测试（Fligner and Policello，1981）被设计为改善非参数Wilcoxon-Mann-Whitney U检验，当被比较的样品具有不平等的差异时，更合适。但是，当样品不对称时，它往往过于自由。这很可能是因为假定测试统计量具有样本量> 12的标准正态分布。这项工作提出了一种在线方法，以获取测试统计量的分布，可以从中直接计算关键/p值。可能的最大化方法用于估计要比较样品的父分布的参数。使用这些估计的人群，通过Monte-Carlo方法获得了测试统计量的零分布。进行模拟以将所提出的方法与测试统计量的标准正常近似值进行比较。对于小样本量（<= 20），蒙特 - 卡洛方法的表现优于正常近似方法。对于低显着性水平的低值（<5％）尤其如此。另外，当较小的样品具有较大的标准偏差时，即使对于大样本量，蒙特 - 卡洛方法甚至超过正常近似方法（= 40/60）。两种方法的功率没有差异。最后，发现蒙特卡洛样本大小为10^4足以获得上述性能的相对改善。因此，这项研究的结果为开发工具箱的开发铺平了道路，以无分配方式执行强大的排名测试。
The robust rank-order test (Fligner and Policello, 1981) was designed as an improvement of the non-parametric Wilcoxon-Mann-Whitney U-test to be more appropriate when the samples being compared have unequal variance. However, it tends to be excessively liberal when the samples are asymmetric. This is likely because the test statistic is assumed to have a standard normal distribution for sample sizes > 12. This work proposes an on-the-fly method to obtain the distribution of the test statistic from which the critical/p-value may be computed directly. The method of likelihood maximization is used to estimate the parameters of the parent distributions of the samples being compared. Using these estimated populations, the null distribution of the test statistic is obtained by the Monte-Carlo method. Simulations are performed to compare the proposed method with that of standard normal approximation of the test statistic. For small sample sizes (<= 20), the Monte-Carlo method outperforms the normal approximation method. This is especially true for low values of significance levels (< 5%). Additionally, when the smaller sample has the larger standard deviation, the Monte-Carlo method outperforms the normal approximation method even for large sample sizes (= 40/60). The two methods do not differ in power. Finally, a Monte-Carlo sample size of 10^4 is found to be sufficient to obtain the aforementioned relative improvements in performance. Thus, the results of this study pave the way for development of a toolbox to perform the robust rank-order test in a distribution-free manner.
