A modified mann-whitney-wilcoxon test for the two-sample location problem

Abstract

In the single sample location problem both the sign and signed rank tests can be used to test hypotheses regarding the median. The signed rank test can be considered an improvement on the sign test in the sense that it does not only count the number of values greater than the hypothesized value, but takes their magnitudes into consideration too. The question arose whether an improvement could be obtained in the two-sample case if the Wilcoxon test statistic is modified not only to count the number of observations of one sample exceeding those of the other sample, but by taking the magnitudes of the differences into account also. By means of a sampling study it is shown that in many cases this new test does in fact perform better than the Wilcoxon test, it is more robust to deviations from normality than the t test and it also appears to be more robust against scale differences than both the Wilcoxon and t test.