Replacing P values with frequentist posterior probabilities - as possible parameter values must have uniform base-rate prior probabilities by definition in a random sampling model

TL;DR

This paper proposes replacing P-values with frequentist posterior probabilities derived from uniform prior assumptions, offering a potentially clearer interpretation of statistical evidence and replication likelihood.

Contribution

It introduces a method to compute frequentist posterior probabilities that align with P-values under certain conditions, enhancing interpretability and combining Bayesian and frequentist approaches.

Findings

Frequentist posterior probabilities can replace P-values in hypothesis testing.

Symmetrical likelihood functions make P-values equal to posterior probabilities.

An idealistic replication probability provides an upper bound for real-world scenarios.

Abstract

Possible parameter values in a random sampling model are shown by definition to have uniform base-rate prior probabilities. This allows a frequentist posterior probability distribution to be calculated for such possible parameter values conditional solely on actual study observations. If the likelihood probability distribution of a random selection is modelled with a symmetrical continuous function then the frequentist posterior probability of something equal to or more extreme than the null hypothesis will be equal to the P-value; otherwise the P value would be an approximation. An idealistic probability of replication based on an assumption of perfect study methodological reproducibility can be used as the upper bound of a realistic probability of replication that may be affected by various confounding factors. Bayesian distributions can be combined with these frequentist distributions. The idealistic frequentist posterior probability of replication may be easier than the P-value for non-statisticians to understand and to interpret.