A Bayesian bird's eye view of 'Replications of important results in social psychology'

R Soc Open Sci. 2017 Jan 18;4(1):160426. doi: 10.1098/rsos.160426. eCollection 2017 Jan.

Abstract

We applied three Bayesian methods to reanalyse the preregistered contributions to the Social Psychology special issue 'Replications of Important Results in Social Psychology' (Nosek & Lakens. 2014 Registered reports: a method to increase the credibility of published results. Soc. Psychol.45, 137-141. (doi:10.1027/1864-9335/a000192)). First, individual-experiment Bayesian parameter estimation revealed that for directed effect size measures, only three out of 44 central 95% credible intervals did not overlap with zero and fell in the expected direction. For undirected effect size measures, only four out of 59 credible intervals contained values greater than [Formula: see text] (10% of variance explained) and only 19 intervals contained values larger than [Formula: see text]. Second, a Bayesian random-effects meta-analysis for all 38 t-tests showed that only one out of the 38 hierarchically estimated credible intervals did not overlap with zero and fell in the expected direction. Third, a Bayes factor hypothesis test was used to quantify the evidence for the null hypothesis against a default one-sided alternative. Only seven out of 60 Bayes factors indicated non-anecdotal support in favour of the alternative hypothesis ([Formula: see text]), whereas 51 Bayes factors indicated at least some support for the null hypothesis. We hope that future analyses of replication success will embrace a more inclusive statistical approach by adopting a wider range of complementary techniques.

Keywords: Bayes factor; credible interval; evidence; preregistration; reproducibility.