Confidences in Hypotheses

TL;DR

This paper extends hypotheses assessment methods to two simple hypotheses, clarifying their benefits in classical statistics and addressing how to condition on data for relevant, powerful inferences.

Contribution

It introduces an extended assessment method for two simple hypotheses, emphasizing relevance, admissibility, and the relationship with Bayesian probabilities.

Findings

Provides minimum and maximum confidences for hypotheses

Addresses conditioning to ensure relevant inferences

Discusses symmetric and asymmetric experiment assessments

Abstract

This article extends the hypotheses assessment method to the case with two competing simple hypotheses. In doing so we further clarify the benefits that hypotheses assessments can bring to classical statistical analyses. Given that confidences in hypotheses are based on conditional probabilities, we address the issue of what to condition on in order to avoid poor conditional properties. This step is essential if the resulting inferences are to be relevant to the data at hand. Admissibility is addressed within a framework of seeking confidences that are relevant to the data at hand and are as powerful as the application allows. Confidence procedures are said to be consistent if they are free of super-relevant betting strategies. For simple hypotheses, the assessment method produces minimum and maximum confidences in each hypothesis. Assessments for both symmetric and asymmetric experiments are included, and the relationship with Bayesian posterior probabilities discussed.