Track 10 · Comparing Groups and Categorical Data · Lesson 8 of 11
Mann–Whitney U test
Compare two independent groups with the Mann–Whitney U test, compute U from ranks, and state correctly what the test does — and does not — show.
Flight delays are mostly a few minutes, with a long tail of flights held for hours. Comparing mean delays in bad weather and good weather lets a handful of extreme flights dominate. A rank-based test asks a sturdier question: do flights in bad weather tend to be more delayed?
The Mann–Whitney U test (also called the Wilcoxon rank-sum test) compares two independent samples using only the order of the values. Pool both samples, rank them from smallest (rank 1) to largest, and see whether one group's ranks are systematically higher. Because only ranks are used, a 300-minute delay counts no more than a 60-minute one if both are the largest values — the test is resistant to outliers and needs no normality assumption.
Included with a Formula Quest membership
It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Compute rank sums and U, and interpret U as a count of pairs
- Choose between the exact distribution and the tie-corrected normal approximation
- State the conclusion as stochastic dominance (“tend to be larger”), not as a difference in medians, unless the shapes match
- Report the probability of superiority P(X > Y) or the rank-biserial correlation as an effect size