From urn models to box models: Making Neyman's (1923) insights accessible

Abstract

Abstract Neyman’s 1923 paper introduced the potential outcomes framework and the foundations of randomization-based inference. We discuss the influence of Neyman’s paper on four introductory to intermediate-level textbooks by Berkeley faculty members (Scheffé; Hodges and Lehmann; Freedman, Pisani, and Purves; and Dunning). These examples illustrate that Neyman’s key insights can be explained in intuitive and interesting ways to audiences at all levels, including undergraduates in introductory statistics courses. We have found Freedman, Pisani, and Purves’s box-of-tickets model to be a valuable expository tool, and we also find their intuitive explanation of Neyman’s variance result helpful: It is a “minor miracle” that in randomized experiments, the two-sample z z -test is conservative because of “two mistakes that cancel.” All four books take a more positive view of Neyman’s results than Neyman himself did. We encourage educators and researchers to explore ways to communicate Neyman’s ideas that are helpful for their own audiences.