A note on p-values interpreted as plausibilities

Abstract

P-values are a mainstay in statistics but are often misinterpreted. We propose a new interpretation of p-value as a meaningful plausibility, where this is to be interpreted formally within the inferential model framework. We show that, for most practical hypothesis testing problems, there exists an inferential model such that the corresponding plausibility function, evaluated at the null hypothesis, is exactly the p-value. The advantages of this representation are that the notion of plausibility is consistent with the way practitioners use and interpret p-values, and the plausibility calculation avoids the troublesome conditioning on the truthfulness of the null. This connection with plausibilities also reveals a shortcoming of standard p-values in problems with non-trivial parameter constraints.

13 pages, 1 figure

References in corpus (8)

• The formal definition of reference priors
• Inferential models: A framework for prior-free posterior probabilistic inference
• Objective Priors: An Introduction for Frequentists
• Marginal inferential models: prior-free probabilistic inference on interest parameters
• Conditional inferential models: combining information for prior-free probabilistic inference
• Plausibility functions and exact frequentist inference
• Discussion: Foundations of Statistical Inference, Revisited
• Optimal inferential models for a Poisson mean

Cited by in corpus (11)

• Marginal inferential models: prior-free probabilistic inference on interest parameters
• False confidence, non-additive beliefs, and valid statistical inference
• Plausibility functions and exact frequentist inference
• Frameworks for prior-free posterior probabilistic inference
• Discussion: Foundations of Statistical Inference, Revisited
• Inferential models and possibility measures
• A mathematical characterization of confidence as valid belief
• Possibilistic inferential models: a review
• Valid uncertainty quantification about the model in a linear regression setting
• Partial Conditioning for Inference of Many-Normal-Means with Hölder Constraints
• p-Value as the Strength of Evidence Measured by Confidence Distribution