Bayesian hypothesis testing presents an attractive alternative to p value hypothesis testing. Part I of this series outlined several advantages of Bayesian hypothesis testing, including the ability to quantify evidence and the ability to monitor and update this evidence as data come in, without the need to know the intention with which the data were collected. Despite these and other practical advantages, Bayesian hypothesis tests are still reported relatively rarely. An important impediment to the widespread adoption of Bayesian tests is arguably the lack of user-friendly software for the run-of-the-mill statistical problems that confront psychologists for the analysis of almost every experiment: the t-test, ANOVA, correlation, regression, and contingency tables. In Part II of this series we introduce JASP (http://www.jasp-stats.org), an open-source, cross-platform, user-friendly graphical software package that allows users to carry out Bayesian hypothesis tests for standard statistical problems. JASP is based in part on the Bayesian analyses implemented in Morey and Rouder’s BayesFactor package for R. Armed with JASP, the practical advantages of Bayesian hypothesis testing are only a mouse click away.

Many philosophers of science and methodologists have argued that the ability to repeat studies and obtain similar results is an essential component of science. A finding is elevated from single observation to scientific evidence when the procedures that were used to obtain it can be reproduced and the finding itself can be replicated. Recent replication attempts show that some high profile results – most notably in psychology, but in many other disciplines as well – cannot be replicated consistently. These replication attempts have generated a considerable amount of controversy, and the issue of whether direct replications have value has, in particular, proven to be contentious. However, much of this discussion has occurred in published commentaries and social media outlets, resulting in a fragmented discourse. To address the need for an integrative summary, we review various types of replication studies and then discuss the most commonly voiced concerns about direct replication. We provide detailed responses to these concerns and consider different statistical ways to evaluate replications. We conclude there are no theoretical or statistical obstacles to making direct replication a routine aspect of psychological science.

Despite the increasing popularity of Bayesian inference in empirical research, few practical guidelines provide detailed recommendations for how to apply Bayesian procedures and interpret the results. Here we offer specific guidelines for four different stages of Bayesian statistical reasoning in a research setting: planning the analysis, executing the analysis, interpreting the results, and reporting the results. The guidelines for each stage are illustrated with a running example. Although the guidelines are geared towards analyses performed with the open-source statistical software JASP, most guidelines extend to Bayesian inference in general.

We revisit the results of the recent Reproducibility Project: Psychology by the Open Science Collaboration. We compute Bayes factors—a quantity that can be used to express comparative evidence for an hypothesis but also for the null hypothesis—for a large subset (N = 72) of the original papers and their corresponding replication attempts. In our computation, we take into account the likely scenario that publication bias had distorted the originally published results. Overall, 75% of studies gave qualitatively similar results in terms of the amount of evidence provided. However, the evidence was often weak (i.e., Bayes factor < 10). The majority of the studies (64%) did not provide strong evidence for either the null or the alternative hypothesis in either the original or the replication, and no replication attempts provided strong evidence in favor of the null. In all cases where the original paper provided strong evidence but the replication did not (15%), the sample size in the replication was smaller than the original. Where the replication provided strong evidence but the original did not (10%), the replication sample size was larger. We conclude that the apparent failure of the Reproducibility Project to replicate many target effects can be adequately explained by overestimation of effect sizes (or overestimation of evidence against the null hypothesis) due to small sample sizes and publication bias in the psychological literature. We further conclude that traditional sample sizes are insufficient and that a more widespread adoption of Bayesian methods is desirable.

Despite the increasing popularity of Bayesian inference in empirical research, few practical guidelines provide detailed recommendations for how to apply Bayesian procedures and interpret the results. Here we offer specific guidelines for four different stages of Bayesian statistical reasoning in a research setting: planning the analysis, executing the analysis, interpreting the results, and reporting the results. The guidelines for each stage are illustrated with a running example. Although the guidelines are geared toward analyses performed with the open-source statistical software JASP, most guidelines extend to Bayesian inference in general.