Evidence and experimental design in sequential trials

Abstract

To what extent does the design of statistical experiments, in particular sequential trials, affect their interpretation? Should postexperimental decisions depend on the observed data alone, or should they account for the used stopping rule? Bayesians and frequentists are apparently deadlocked in their controversy over these questions. To resolve the deadlock, I suggest a three-part strategy that combines conceptual, methodological, and decision-theoretic arguments. This approach maintains the pre-experimental relevance of experimental design and stopping rules but vindicates their evidential, post- experimental irrelevance.