New Procedure in Testing Differences between Two Groups

TL;DR: In this paper, the pseudo-median was proposed as the location measure of interest for the one-sample nonparametric Wilcoxon procedure in a two-group setting.

Abstract: Despite the theoretical correctness of the t-test in testing differences between two groups and the existence of the nonparametric backup, i.e. Mann-Whitney-Wilcoxon test, these test fail to simultaneously control Type I error and maintain adequate power under certain condition. This study intends to alleviate this problem by a pplying the pseudo-median as the location measure of interest into the one-sample nonparametric Wilcoxon procedure in a two group setting. Pseudo-median is the median of all possible differences of observations from the two groups. Since the sampling distribution of this procedure is intractable, the bootstrap method was used to achieve the significance level. The finding shows that the new p rocedure has the ability to control Type I error rates and maintaining high power rates regardless of distributional shape whether symmetrical or asymmetrical. The performance of the new procedure is compatible to t-test and Mann-Whitney-Wilcoxon test.