Track 10 · Comparing Groups and Categorical Data · Lesson 9 of 11
Wilcoxon signed-rank test
Analyse paired data without assuming normal differences using the Wilcoxon signed-rank test, handle zeros and ties, and choose between it, the sign test and the paired t-test.
A courier company measured the same 60 routes before and after introducing route-optimisation software. A paired t-test is the natural analysis — but if the route-level changes were skewed or contained a few wild values, a rank-based paired test would give a more trustworthy answer.
With paired data (the same unit measured twice, or matched pairs) the analysis works on the differences . The paired t-test asks whether their mean is zero and relies on the differences being roughly normal. The Wilcoxon signed-rank test uses the signs of the differences and the ranks of their sizes.
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It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Compute W⁺ and W⁻ from the signed ranks of paired differences, handling zeros and ties
- Choose the exact distribution or the tie-corrected normal approximation
- Explain the symmetry assumption and when the sign test is the safer choice
- Report a paired comparison with its effect size and the limits of a before/after design