If you want to prove that there are differences between two groups with quantitative variables with non-normal distribution, the Mann-Whitney U test is used. This test is opposite of the Student t test that uses quantitative variables with a normal distribution. If you want to compare three or more nonrelated groups, the Kruskal-Wallis test is applied. When two related samples are compared, the Wilcoxon test is the best option (a before and after maneuver comparison); when three related samples are compared, the Friedman test is used. These tests correspond to the parametric opposing paired t test and ANOVA, respectively.