On unbiasedness and biasedness of the Wilcoxon and some nonparametric tests

Abstract

In several fields of applications, the underlying theoretical distribution is unknown and cannot be assumed to have a specific parametric distribution such as a normal distribution. Nonparametric statistical methods are preferable in these cases. Nonparametric testing hypotheses have been one of the primarily used statistical procedures for nearly a century, and the power of the test is an important property in nonparametric testing procedures. This review discusses the unbiasedness of nonparametric tests. In nonparametric hypothesis, the best‐known Wilcoxon–Mann–Whitney (WMW) test has both robustness and power performance. Therefore, the WMW test is widely used to determine the location parameter. In this review, the unbiasedness and biasedness of the WMW test for the location parameter family of the distribution is mainly investigated. An overview of historical developments, detailed discussions, and works on the unbiasedness/biasedness of several nonparametric tests are presented with references to numerous studies. Finally, we conclude this review with a discussion on the unbiasedness/biasedness of nonparametric test procedures. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Nonparametric Methods.