Resurrecting the One-Sided P-value as a Likelihood Ratio

TL;DR

This paper re-establishes the one-sided P-value as a likelihood ratio, providing a new interpretation that addresses criticisms and enhances its evidential value in statistical testing.

Contribution

It demonstrates a bijective relationship between the one-sided P-value and likelihood ratio, reviving its theoretical and practical significance.

Findings

A bijective link between one-sided P-value and likelihood ratio

Criticisms of P-values are mitigated under likelihood interpretation

Likelihood ratio conversion enhances evidential interpretation

Abstract

The one-sided P-value has a long history stretching at least as far back as Laplace (1812) but has in recent times been mostly supplanted by the two-sided P-value. We present justification for a bijective relationship between the one-sided P-value and a likelihood ratio based on maximum likelihood, a relationship that cannot be demonstrated for the two-sided P-value. A number of criticisms of P-values are discussed and it is shown that many of these criticisms are not justified when a likelihood ratio interpretation of a one-sided P-value is employed. Converting a one-sided P-value to a likelihood ratio provides the advantages of the likelihood evidential paradigm.