Revisiting the Two Predominant Statistical Problems: The Stopping-rule Problem and the Catch-all Hypothesis Problem

Abstract

The history of statistics is filled with many controversies, in which the prime focus has been the difference in the “interpretation of probability” between Frequentist and Bayesian theories. Many philosophical arguments have been elaborated to examine the problems of both theories based on this dichotomized view of statistics, including the well-known stopping-rule problem and the catch-all hypothesis problem. However, there are also several “hybrid” approaches in theory, practice, and philosophical analysis. This poses many fundamental questions. This paper reviews three cases and argues that the interpretation problem of probability is insufficient to begin a philosophical analysis of the current issues in the field of statistics. A novel viewpoint is proposed to examine the relationship between the stopping-rule problem and the catch-all hypothesis problem.