The Wilcoxon–Mann–Whitney Procedure Fails as a Test of Medians

Figures & data

Figure 1. Emergency department visits in 12 months for the Puff City study.

Figure 2. Changes in postoperative nausea after aromatherapy.

Figure 3. No difference in WMW test, but very different medians.

Figure 4. A difference by WMW test, but very different medians. But in wrong direction!

Figure 5. A global inconsistency.

Figure 6. Bubble plot representing the estimate of p″ = Pr(X₁<X₂) + Pr(X₁ = X₂)/2 for toy example.

Figure 7. ROC curve area representing the estimate of p″ = Pr(X₁<X₂) + Pr(X₁ = X₂)/2 for toy example.

Figure 8. Dominance diagram representing the estimate of p″ = Pr(X₁<X₂) + Pr(X₁ = X₂)/2 for toy example.