52% Yes, a signiicant crisis 3% No, there is no crisis 7% Don't know 38% Yes, a slight crisis 38% Yes, a slight crisis 1,576 RESEARCHERS SURVEYED M ore than 70% of researchers have tried and failed to reproduce another scientist's experiments, and more than half have failed to reproduce their own experiments. Those are some of the telling figures that emerged from Nature's survey of 1,576 researchers who took a brief online questionnaire on reproducibility in research. The data reveal sometimes-contradictory attitudes towards reproduc-ibility. Although 52% of those surveyed agree that there is a significant 'crisis' of reproducibility, less than 31% think that failure to reproduce published results means that the result is probably wrong, and most say that they still trust the published literature. Data on how much of the scientific literature is reproducible are rare and generally bleak. The best-known analyses, from psychology 1 and cancer biology 2 , found rates of around 40% and 10%, respectively. Our survey respondents were more optimistic: 73% said that they think that at least half of the papers in their field can be trusted, with physicists and chemists generally showing the most confidence. The results capture a confusing snapshot of attitudes around these issues, says Arturo Casadevall, a microbiologist at the Johns Hopkins Bloomberg School of Public Health in Baltimore, Maryland. "At the current time there is no consensus on what reproducibility is or should be. " But just recognizing that is a step forward, he says. "The next step may be identifying what is the problem and to get a consensus. "

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.

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.

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.

Many statistical scenarios initially involve several candidate models that describe the data-generating process. Analysis often proceeds by first selecting the best model according to some criterion and then learning about the parameters of this selected model. Crucially, however, in this approach the parameter estimates are conditioned on the selected model, and any uncertainty about the model-selection process is ignored. An alternative is to learn the parameters for all candidate models and then combine the estimates according to the posterior probabilities of the associated models. This approach is known as Bayesian model averaging (BMA). BMA has several important advantages over all-or-none selection methods, but has been used only sparingly in the social sciences. In this conceptual introduction, we explain the principles of BMA, describe its advantages over all-or-none model selection, and showcase its utility in three examples: analysis of covariance, meta-analysis, and network analysis.

Author contributions: The 1 st through 4 th and last authors developed the research questions, oversaw the project, and contributed equally. The 1 st through 3 rd authors oversaw the Main Studies and Replication Studies, and the 4 th , 6 th , 7 th , and 8 th authors oversaw the Forecasting Study. The 1 st , 4 th , 5 th , 8 th , and 9 th authors conducted the primary analyses. The 10 th through 15 th authors conducted the Bayesian analyses. The first and 16 th authors conducted the multivariate meta-analysis.

Never use the unfortunate expression "accept the null hypothesis."-Wilkinson and the Task Force on Statistical Inference (1999, p. 599) The interpretation of statistically nonsignificant findings is a vexing point of traditional psychological research. 1 Within the framework of null-hypothesis significance testing (NHST; Fisher, 1925; Neyman & Pearson, 1933), decisions about the null hypothesis are based on the p value. Under NHST logic, one is entitled to reject the null hypothesis whenever the p value is smaller than or equal to a predefined α threshold (typically set at .05; but see Benjamin et al., 2018). In contrast, the p value does not entitle one to claim support in favor of the null hypothesis. According to the common interpretation, any p value higher than α indicates that one has to withhold judgment about the null hypothesis (Cohen, 1994). This asymmetric characteristic of the NHST framework frustrates the interpretation and communication of nonsignificant results (Edwards, Lindman, & Savage, 1963; Nickerson, 2000). It is known that results with a p value greater than .05 are subject to misinterpretation among researchers (Goodman, 2008), 773742A MPXXX10.

Analysis of variance (ANOVA) is the standard procedure for statistical inference in factorial designs. Typically, ANOVAs are executed using frequentist statistics, where p-values determine statistical significance in an all-or-none fashion. In recent years, the Bayesian approach to statistics is increasingly viewed as a legitimate alternative to the p-value. However, the broad adoption of Bayesian statistics –and Bayesian ANOVA in particular– is frustrated by the fact that Bayesian concepts are rarely taught in applied statistics courses. Consequently, practitioners may be unsure how to conduct a Bayesian ANOVA and interpret the results. Herewe provide a guide for executing and interpreting a Bayesian ANOVA with JASP, an open-source statistical software program with a graphical user interface. We explain the key concepts of the Bayesian ANOVA using twoempirical examples.