A default Bayesian hypothesis test for mediation.

In order to quantify the relationship between multiple variables, researchers often carry out a mediation analysis. In such an analysis, a mediator (e.g., knowledge of a healthy diet) transmits the effect from an independent variable (e.g., classroom instruction on a healthy diet) to a dependent variable (e.g., consumption of fruits and vegetables). Almost all mediation analyses in psychology use frequentist estimation and hypothesis-testing techniques. A recent exception is Yuan and MacKinnon (Psychological Methods, 14, 301-322, 2009), who outlined a Bayesian parameter estimation procedure for mediation analysis. Here we complete the Bayesian alternative to frequentist mediation analysis by specifying a default Bayesian hypothesis test based on the Jeffreys-Zellner-Siow approach. We further extend this default Bayesian test by allowing a comparison to directional or one-sided alternatives, using Markov chain Monte Carlo techniques implemented in JAGS. All Bayesian tests are implemented in the R package BayesMed (Nuijten, Wetzels, Matzke, Dolan, & Wagenmakers, 2014).

Is the unconscious, if it exists, a superior decision maker?

Newell & Shanks (N&S) show that there is no convincing evidence that processes assumed to be unconscious and superior are indeed unconscious. We take their argument one step further by showing that there is also no convincing evidence that these processes are superior. We review alternative paradigms that may provide more convincing tests of the superiority of (presumed) unconscious processes.

Bayesian inference using WBDev: a tutorial for social scientists.

Over the last decade, the popularity of Bayesian data analysis in the empirical sciences has greatly increased. This is partly due to the availability of WinBUGS, a free and flexible statistical software package that comes with an array of predefined functions and distributions, allowing users to build complex models with ease. For many applications in the psychological sciences, however, it is highly desirable to be able to define one's own distributions and functions. This functionality is available through the WinBUGS Development Interface (WBDev). This tutorial illustrates the use of WBDev by means of concrete examples, featuring the expectancy-valence model for risky behavior in decision making, and the shifted Wald distribution of response times in speeded choice.

How to quantify support for and against the null hypothesis: a flexible WinBUGS implementation of a default Bayesian t test.

We propose a sampling-based Bayesian t test that allows researchers to quantify the statistical evidence in favor of the null hypothesis. This Savage-Dickey (SD) t test is inspired by the Jeffreys-Zellner-Siow (JZS) t test recently proposed by Rouder, Speckman, Sun, Morey, and Iverson (2009). The SD test retains the key concepts of the JZS test but is applicable to a wider range of statistical problems. The SD test allows researchers to test order restrictions and applies to two-sample situations in which the different groups do not share the same variance.

Hidden multiplicity in exploratory multiway ANOVA: Prevalence and remedies.

Many psychologists do not realize that exploratory use of the popular multiway analysis of variance harbors a multiple-comparison problem. In the case of two factors, three separate null hypotheses are subject to test (i.e., two main effects and one interaction). Consequently, the probability of at least one Type I error (if all null hypotheses are true) is 14 % rather than 5 %, if the three tests are independent. We explain the multiple-comparison problem and demonstrate that researchers almost never correct for it. To mitigate the problem, we describe four remedies: the omnibus F test, control of the familywise error rate, control of the false discovery rate, and preregistration of the hypotheses.

Validating the PVL-Delta model for the Iowa gambling task.

Decision-making deficits in clinical populations are often assessed with the Iowa gambling task (IGT). Performance on this task is driven by latent psychological processes, the assessment of which requires an analysis using cognitive models. Two popular examples of such models are the Expectancy Valence (EV) and Prospect Valence Learning (PVL) models. These models have recently been subjected to sophisticated procedures of model checking, spawning a hybrid version of the EV and PVL models-the PVL-Delta model. In order to test the validity of the PVL-Delta model we present a parameter space partitioning (PSP) study and a test of selective influence. The PSP study allows one to assess the choice patterns that the PVL-Delta model generates across its entire parameter space. The PSP study revealed that the model accounts for empirical choice patterns featuring a preference for the good decks or the decks with infrequent losses; however, the model fails to account for empirical choice patterns featuring a preference for the bad decks. The test of selective influence investigates the effectiveness of experimental manipulations designed to target only a single model parameter. This test showed that the manipulations were successful for all but one parameter. To conclude, despite a few shortcomings, the PVL-Delta model seems to be a better IGT model than the popular EV and PVL models.

Performance of healthy participants on the Iowa Gambling Task.

The Iowa Gambling Task (IGT; Bechara, Damasio, Damasio, & Anderson, 1994) is often used to assess decision-making deficits in clinical populations. The interpretation of the results hinges on 3 key assumptions: (a) healthy participants learn to prefer the good options over the bad options; (b) healthy participants show homogeneous choice behavior; and (c) healthy participants first explore the different options and then exploit the most profitable ones. Here we test these assumptions using 2 extensive literature reviews and analysis of 8 data sets. The results show that all 3 assumptions may be invalid; that is, (a) healthy participants often prefer decks with infrequent losses; (b) healthy participants show idiosyncratic choice behavior; and (c) healthy participants do not show a systematic decrease in the number of switches across trials. Our findings question the prevailing interpretation of IGT data and suggest that, in future applications of the IGT, key assumptions about performance of healthy participants warrant close scrutiny.

A default Bayesian hypothesis test for correlations and partial correlations.

We propose a default Bayesian hypothesis test for the presence of a correlation or a partial correlation. The test is a direct application of Bayesian techniques for variable selection in regression models. The test is easy to apply and yields practical advantages that the standard frequentist tests lack; in particular, the Bayesian test can quantify evidence in favor of the null hypothesis and allows researchers to monitor the test results as the data come in. We illustrate the use of the Bayesian correlation test with three examples from the psychological literature. Computer code and example data are provided in the journal archives.

An Agenda for Purely Confirmatory Research.

The veracity of substantive research claims hinges on the way experimental data are collected and analyzed. In this article, we discuss an uncomfortable fact that threatens the core of psychology's academic enterprise: almost without exception, psychologists do not commit themselves to a method of data analysis before they see the actual data. It then becomes tempting to fine tune the analysis to the data in order to obtain a desired result-a procedure that invalidates the interpretation of the common statistical tests. The extent of the fine tuning varies widely across experiments and experimenters but is almost impossible for reviewers and readers to gauge. To remedy the situation, we propose that researchers preregister their studies and indicate in advance the analyses they intend to conduct. Only these analyses deserve the label "confirmatory," and only for these analyses are the common statistical tests valid. Other analyses can be carried out but these should be labeled "exploratory." We illustrate our proposal with a confirmatory replication attempt of a study on extrasensory perception.

What's in a Name: A Bayesian Hierarchical Analysis of the Name-Letter Effect.

People generally prefer their initials to the other letters of the alphabet, a phenomenon known as the name-letter effect. This effect, researchers have argued, makes people move to certain cities, buy particular brands of consumer products, and choose particular professions (e.g., Angela moves to Los Angeles, Phil buys a Philips TV, and Dennis becomes a dentist). In order to establish such associations between people's initials and their behavior, researchers typically carry out statistical analyses of large databases. Current methods of analysis ignore the hierarchical structure of the data, do not naturally handle order-restrictions, and are fundamentally incapable of confirming the null hypothesis. Here we outline a Bayesian hierarchical analysis that avoids these limitations and allows coherent inference both on the level of the individual and on the level of the group. To illustrate our method, we re-analyze two data sets that address the question of whether people are disproportionately likely to live in cities that resemble their name.

Why psychologists must change the way they analyze their data: the case of psi: comment on Bem (2011).

Does psi exist? D. J. Bem (2011) conducted 9 studies with over 1,000 participants in an attempt to demonstrate that future events retroactively affect people's responses. Here we discuss several limitations of Bem's experiments on psi; in particular, we show that the data analysis was partly exploratory and that one-sided p values may overstate the statistical evidence against the null hypothesis. We reanalyze Bem's data with a default Bayesian t test and show that the evidence for psi is weak to nonexistent. We argue that in order to convince a skeptical audience of a controversial claim, one needs to conduct strictly confirmatory studies and analyze the results with statistical tests that are conservative rather than liberal. We conclude that Bem's p values do not indicate evidence in favor of precognition; instead, they indicate that experimental psychologists need to change the way they conduct their experiments and analyze their data.

Statistical Evidence in Experimental Psychology: An Empirical Comparison Using 855 t Tests.

Statistical inference in psychology has traditionally relied heavily on p-value significance testing. This approach to drawing conclusions from data, however, has been widely criticized, and two types of remedies have been advocated. The first proposal is to supplement p values with complementary measures of evidence, such as effect sizes. The second is to replace inference with Bayesian measures of evidence, such as the Bayes factor. The authors provide a practical comparison of p values, effect sizes, and default Bayes factors as measures of statistical evidence, using 855 recently published t tests in psychology. The comparison yields two main results. First, although p values and default Bayes factors almost always agree about what hypothesis is better supported by the data, the measures often disagree about the strength of this support; for 70% of the data sets for which the p value falls between .01 and .05, the default Bayes factor indicates that the evidence is only anecdotal. Second, effect sizes can provide additional evidence to p values and default Bayes factors. The authors conclude that the Bayesian approach is comparatively prudent, preventing researchers from overestimating the evidence in favor of an effect.