Bayesian Reanalyses From Summary Statistics: A Guide for Academic Consumers

Abstract

Across the social sciences, researchers have overwhelmingly used the classical statistical paradigm to draw conclusions from data, often focusing heavily on a single number: p. Recent years, however, have witnessed a surge of interest in an alternative statistical paradigm: Bayesian inference, in which probabilities are attached to parameters and models. We feel it is informative to provide statistical conclusions that go beyond a single number, and—regardless of one’s statistical preference—it can be prudent to report the results from both the classical and the Bayesian paradigms. In order to promote a more inclusive and insightful approach to statistical inference, we show how the Summary Stats module in the open-source software program JASP ( https://jasp-stats.org ) can provide comprehensive Bayesian reanalyses from just a few commonly reported summary statistics, such as t and N. These Bayesian reanalyses allow researchers—and also editors, reviewers, readers, and reporters—to (a) quantify evidence on a continuous scale using Bayes factors, (b) assess the robustness of that evidence to changes in the prior distribution, and (c) gauge which posterior parameter ranges are more credible than others by examining the posterior distribution of the effect size. The procedure is illustrated using Festinger and Carlsmith’s (1959) seminal study on cognitive dissonance.