反正弦分布下Wilcoxon和Student两样本检验样本量的实验比较

F. M. Al-athari
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引用次数: 0

摘要

当进行统计实验时,应该以某种最佳方式选择样本量,这样我们就应该使用不超过必要的样本量。本文比较了正弦分布下两样本t检验和Wilcoxon秩和检验的最小样本量,基于它们的幂[1,2]。为了完成这项任务,作者推导了一些在Wilcoxon秩和检验的幂和样本量确定中有用的基本概率,用于计算Lehmann[2]给出的近似公式。使用复合数值积分算法来计算这些概率,这些概率与反正弦分布有关。在这项研究中,作者建立了一个计算机程序,通过对n进行迭代,找到任何有效水平和幂的精确(模拟)最小样本量n,n的起始点由[2,3]的近似公式提供。这篇研究论文的科学新颖性在于,通过考虑一组新的正弦分布移位替代方案来确定最小样本量,该替代方案将位移分布的左端作为第二分布的p阶分位数,0本文章由计算机程序翻译,如有差异,请以英文原文为准。
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Experimental Comparison of the Sample Sizes of the Two-Sample Tests of Wilcoxon and Student under the Arcsine Distribution
When statistical experiments are performed, a sample size should be chosen in some optimum way so that we should use a sample size no larger than necessary. This paper compares the minimum sample sizes of two-sample t-test and the Wilcoxon rank-sum test under the arcsine distribution, based on their power [1, 2]. To accomplish this task, some essential probabilities that are useful in the power and sample size determination of the Wilcoxon rank-sum test were derived by the author for computing the approximated formula given by Lehmann [2]. The composite numerical integration algorithm is used to compute these probabilities, which are related to the arcsine distribution. In this study, a computer program was built by the author to find the exact (simulated) minimum sample sizes n for any significant level and power by iterating on n with starting points for n provided by the approximated formulas of [2, 3]. The scientific novelty of this research paper is determining the minimum sample sizes by considering a new set of the arcsine distribution shift alternatives of the forms giving the left-hand endpoint of the displaced distribution as the quantile of order p, 0 < p < 1, of the second distribution rather than using alternatives that specify as the quantile of order p, p < 0.5. As considered by [1], a choice that prevents losing some important alternative hypotheses is an extension to the set of alternative hypotheses considered by Guenther [1]. The exact (simulated) minimum sample sizes were computed and compared with each other and with the corresponding approximated formulas given by Lehmann [2] and Guenther [3]. Numerical results showed that the approximated formulas are very accurate and the Wilcoxon rank-sum test is more efficient when the sample size is more than 45. Otherwise, the Student two-sample t-test is better.
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湖南大学学报(自然科学版)
CiteScore
1.30
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0.00%
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7139
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