The t-test is already pretty good because it relies on the t distribution that is leptokurtic with fatter tails (similar to your stock returns distribution). The Welch's test is essentially a t-test accommodating for two samples of different size and with different variance. The Mann-Whitney test is even more distribution independent than the My question is: how does one tune wilcox.test in R to compare means instead of medians? Background. According to this site by Laerd Statistics one can use a Wilcoxon Rank-Sum / Mann-Whitney U test for determining if there is a statistically significant difference in the center of two continuous distributions. Specifically, the default behavior of the test is to compare the medians. The t-test and the Wilcoxon ranked-sum differ in that the t-test is comparing the means of the two distributions, while the Wilcoxon is comparing the 'locations' by looking at how the values of the two distributions compare when ranked. When your entire ratings distribution has only two values, one group has only ratings of 4 and your sample In general, the t t -test is very robust. Three assumptions are typically listed: independence, homoscedasticity, and normality. The assumption that the residuals are normally distributed comes last and is least important. If those two qq-plots are for the two groups that you want to compare, you probably have enough data and the data are The Mann-Whitney U test is used to compare differences between two independent groups when the dependent variable is either ordinal or continuous, but not normally distributed. For example, you could use the Mann-Whitney U test to understand whether attitudes towards pay discrimination, where attitudes are measured on an ordinal scale, differ 1 Answer. Mann-Whitney's U U is not equal to ROC AUC, it is proportional to the area under the ROC curve: where n0 n 0 is the number of negative examples and n1 n 1 is the number of positive examples and U U is the Mann-Whitney U U statistic. From this expression, it should be clear that even U U must be bounded, because AUROC ∈ [0, 1] AUROC In my textbook (the one that my teachers drafted), it is said that "The Wilcoxon,Mann-Whitney test does not allow testing the two-sided alternative hypothesis". But it is weird to me because in R, we can see the option "alternative=two.sided" in the command wilcox.test. And I also see many sources on the Internet that show how to build this Wilcoxon rank sum test. The Wilcoxon rank sum test is a non-parametric alternative to the independent two samples t-test for comparing two independent groups of samples, in the situation where the data are not normally distributed. Synonymous: Mann-Whitney test, Mann-Whitney U test, Wilcoxon-Mann-Whitney test and two-sample Wilcoxon test. The Mann-Whitney statistic W XY (and the Wilcoxon rank sum W s, up to an additive constant) measures the number of (control, treatment) pairs for which the treatment response is at least as large as the control response. The larger the positive effect of treatment, the larger the Mann-Whitney and Wilcoxon rank sum statistics tend to be. The values will be paired (on user), not independent, so no, you would not normally consider the Wilcoxon-Mann-Whitney. You would use a paired analysis (e.g. paired-t, Wilcoxon signed rank, sign test etc). 2UvvN.