“…In addition, we found that the WMW test is not unbiased against the shifted location parameter given by the counter-examples. Furthermore, we reviewed the studies on the unbiasedness of tests in various other nonparametric research fields, including permutation tests (Pesarin & De Martini, 2002;Pesarin & Salmaso, 2010), counter-example studies of one-sample location test (Amrhein, 1995;Kitani & Murakami, 2022), the goodness of fit test (Frey, 2009;Hanyuda & Murakami, 2021;Massey, 1950;Thompson, 1966), scale test (Lee et al, 2005), multivariate test (Jurečkov a & Kalina, 2012). In future research, we recommend developing the bias correction methods for biased test statistics, such as the WMW location test and other nonparametric tests like the goodness of fit test, scale test, and multivariate test.…”