We propose new smoothed median and the Wilcoxon's rank sum test. As is
pointed out by Maesono et al.(2016), some nonparametric discrete tests have a
problem with their significance probability. Because of this problem, the
selection of the median and the Wilcoxon's test can be biased too, however, we
show new smoothed tests are free from the problem. Significance probabilities
and local asymptotic powers of the new tests are studied, and we show that they
inherit good properties of the discrete tests
