The Mann-Whitney Test is a non-parametric test that compares the population means between two independent groups. If a data fails a “test for normality” (i.e., W-test or the Kolmogorov-Smirnov test) you cannot use the t-test and must use the Mann-Whitney Test. The Mann-Whitney Test is also known as the U-test, the Mann-Whitney U Test, or the Wilcoxon rank sum test.
- H0: μ1 = μ2 (there is no difference between the two means)
- H1: μ1 ≠ μ2 (there is a difference between the two means)
Example: You might use the Mann-Whitney to compare mean morphine consumption between total knee replacement patients that received a femoral nerve block and those that did not if the data is not normally distributed.