Bayes factors functions based on test statistics and non-local moment prior densities

Abstract

We describe Bayes factors based on z, t, ${\chi }^2$, and F statistics when non-local moment prior distributions are used to define alternative hypotheses. The non-local alternative prior distributions are centered on standardized effects. The prior densities include a dispersion parameter that can be used to model prior precision and the variation of effect sizes across replicated experiments. We examine the convergence rates of Bayes factors under true null and true alternative hypotheses and show how these Bayes factors can be used to construct Bayes factor functions. Examples illustrate the application of resulting Bayes factors functions to psychological experiments.