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:

09:30-09:40 Introduction

09:40-10:20 Stochastic Dominance

10:20-10:30 Q&A

— break —

12:30-13:10 Wilcoxon’s two-sample test

13:10-13:30 Q&A