Mann-Whitney U Test: Rank-Based Group Comparison

This simulator builds the Mann-Whitney U test (the workhorse nonparametric alternative to the two-sample t-test) from the ground up: two samples are drawn from a chosen distribution shape, pooled and ranked jointly, and the U statistic is computed directly from those ranks rather than from means and variances. A 3D rank track shows every point at its rank position with its real value as height, making visible exactly how much the two groups interleave. Beside it, 2,000 label-shuffling permutations build the true null distribution of U live, and the bins at least as extreme as the observed split light up red — that fraction is the permutation p-value, computed the same way a nonparametric test earns significance without ever assuming normality.