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.

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.

Despite an ongoing stream of lamentations, many empirical disciplines still treat the p value as the sole arbiter to separate the scientific wheat from the chaff. The continued reign of the p value is arguably due in part to a perceived lack of workable alternatives. In order to be workable, any alternative methodology must be (1) relevant: it has to address the practitioners' research question, which-for better or for worse-most often concerns the test of a hypothesis, and less often concerns the estimation of a parameter; (2) available: it must have a concrete implementation for practitioners' statistical workhorses such as the t test, regression, and ANOVA; and (3) easy to use: methods that demand practitioners switch to the theoreticians' programming tools will face an uphill struggle for adoption. The above desiderata are fulfilled by Harold Jeffreys's Bayes factor methodology as implemented in the open-source software JASP. We explain Jeffreys's methodology and showcase its practical relevance with two examples.

Dimension reduction is widely used and often necessary to make network analyses and their interpretation tractable by reducing high dimensional data to a small number of underlying variables. Techniques such as Exploratory Factor Analysis (EFA) are used by neuroscientists to reduce measurements from a large number of brain regions to a tractable number of factors. However, dimension reduction often ignores relevant a priori knowledge about the structure of the data. For example, it is well established that the brain is highly symmetric. In this paper, we (a) show the adverse consequences of ignoring a priori structure in factor analysis, (b) propose a technique to accommodate structure in EFA using structured residuals (EFAST), and (c) apply this technique to three large and varied brain imaging network datasets, demonstrating the superior fit and interpretability of our approach. We provide an R software package to enable researchers to apply EFAST to other suitable datasets.

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