Before revision:  Finally the R-test has a greater power than the single-sample Wilcoxon signed-rank test in most cases .
After revision:  Finally the R-test has a greater power than the single-sample Wilcoxon signed-rank statistics as long as the data are not too heavy-tailed. Three two-sample parametric r-statistics are proposed, one with a higher specificity but a smaller sensitivity than Mann-Whitney U-test and the other one a higher sensitivity but a smaller specificity. A nonparametric two-sample r-statistic is introduced, whose power is very close to that of Welch statistic for Gaussian or uniformly distributed variables .