Stochastic dominance and Wilcoxon’s Two Sample Test
Usually, when a client wants to know whether a new treatment or process is better than the current one, they are asking about stochastic dominance. In the first session I will define stochastic dominance, and state and prove the Coupling Theorem, which is the key representation theorem. I will go on to define a significance procedure (the grown-up definition), and an unbiased significance procedure, and explain how we can use stochastic dominance to choose unbiased significance procedures.
In the second session I will introduce Wilcoxon’s Two Sample Test for the equality of two distributions. The key result (not well-known) is that the associated significance procedure is unbiased for the alternative hypothesis that one distribution stochastically dominates the other. I will work through an application about donkeys, also showing my preferred client-friendly visualisation. I will outline generalisations from one- to two-tailed tests, and for more than two distributions.
Note that this Compass Special Lecture will be delivered over two sessions:
09:40-10:20 Stochastic Dominance
— break —
12:30-13:10 Wilcoxon’s two-sample test