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

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.