Mann-Whitney U Test for Non-Parametric Group Comparison

Performs a Mann-Whitney U test (Wilcoxon rank-sum test) to compare two independent groups when data may not be normally distributed. Includes effect size calculation (rank-biserial correlation), Hodges-Lehmann point and interval estimates for median difference, normality diagnostics (Shapiro-Wilk test), and comprehensive visualizations of distributions and ranks. Assumes observations within each group are independent and identically distributed.