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Advanced Proof

The Subplots: Deep Dive into Non-Parametric Tests

Students often assume non-parametric tests compare 'medians.' However, the Wilcoxon test only tests for medians if you assume the distributions have identical shapes (location shift only). If shapes differ, the test strictly evaluates stochastic dominance: P(X>Y)0.5 P(X > Y) \neq 0.5 .
Institutional Reference: Applied Statistics
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