Dora Matzke

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.

Psychological interpretation of the ex-Gaussian and shifted Wald parameters: A diffusion model analysis

A growing number of researchers use descriptive distributions such as the ex-Gaussian and the shifted Wald to summarize response time data for speeded two-choice tasks. Some of these researchers also assume that the parameters of these distributions uniquely correspond to specific cognitive processes. We studied the validity of this cognitive interpretation by relating the parameters of the ex-Gaussian and shifted Wald distributions to those of the Ratcliff diffusion model, a successful model whose parameters have well-established cognitive interpretations. In a simulation study, we fitted the ex-Gaussian and shifted Wald distributions to data generated from the diffusion model by systematically varying its parameters across a wide range of plausible values. In an empirical study, the two descriptive distributions were fitted to published data that featured manipulations of task difficulty, response caution, and a priori bias. The results clearly demonstrate that the ex-Gaussian and shifted Wald parameters do not correspond uniquely to parameters of the diffusion model. We conclude that researchers should resist the temptation to interpret changes in the ex-Gaussian and shifted Wald parameters in terms of cognitive processes. Supporting materials may be downloaded from http://pbr.psychonomic-journals .org/content/supplemental.

Bayesian inference for psychology. Part II: Example applications with JASP

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.

Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications

Bayesian parameter estimation and Bayesian hypothesis testing present attractive alternatives to classical inference using confidence intervals and p values. In part I of this series we outline ten prominent advantages of the Bayesian approach. Many of these advantages translate to concrete opportunities for pragmatic researchers. For instance, Bayesian hypothesis testing allows researchers to quantify evidence and monitor its progression as data come in, without needing to know the intention with which the data were collected. We end by countering several objections to Bayesian hypothesis testing. Part II of this series discusses JASP, a free and open source software program that makes it easy to conduct Bayesian estimation and testing for a range of popular statistical scenarios (Wagenmakers et al. this issue).

Meta-analyses are no substitute for registered replications: a skeptical perspective on religious priming

According to a recent meta-analysis, religious priming has a positive effect on prosocial behavior (Shariff et al., 2015). We first argue that this meta-analysis suffers from a number of methodological shortcomings that limit the conclusions that can be drawn about the potential benefits of religious priming. Next we present a re-analysis of the religious priming data using two different meta-analytic techniques. A Precision-Effect Testing–Precision-Effect-Estimate with Standard Error (PET-PEESE) meta-analysis suggests that the effect of religious priming is driven solely by publication bias. In contrast, an analysis using Bayesian bias correction suggests the presence of a religious priming effect, even after controlling for publication bias. These contradictory statistical results demonstrate that meta-analytic techniques alone may not be sufficiently robust to firmly establish the presence or absence of an effect. We argue that a conclusive resolution of the debate about the effect of religious priming on prosocial behavior – and about theoretically disputed effects more generally – requires a large-scale, preregistered replication project, which we consider to be the sole remedy for the adverse effects of experimenter bias and publication bias.

Bayesian parametric estimation of stop-signal reaction time distributions

The cognitive concept of response inhibition can be measured with the stop-signal paradigm. In this paradigm, participants perform a 2-choice response time (RT) task where, on some of the trials, the primary task is interrupted by a stop signal that prompts participants to withhold their response. The dependent variable of interest is the latency of the unobservable stop response (stop-signal reaction time, or SSRT). Based on the horse race model (Logan & Cowan, 1984), several methods have been developed to estimate SSRTs. None of these approaches allow for the accurate estimation of the entire distribution of SSRTs. Here we introduce a Bayesian parametric approach that addresses this limitation. Our method is based on the assumptions of the horse race model and rests on the concept of censored distributions. We treat response inhibition as a censoring mechanism, where the distribution of RTs on the primary task (go RTs) is censored by the distribution of SSRTs. The method assumes that go RTs and SSRTs are ex-Gaussian distributed and uses Markov chain Monte Carlo sampling to obtain posterior distributions for the model parameters. The method can be applied to individual as well as hierarchical data structures. We present the results of a number of parameter recovery and robustness studies and apply our approach to published data from a stop-signal experiment.

Bayesian Estimation of Multinomial Processing Tree Models with Heterogeneity in Participants and Items

Multinomial processing tree (MPT) models are theoretically motivated stochastic models for the analysis of categorical data. Here we focus on a crossed-random effects extension of the Bayesian latent-trait pair-clustering MPT model. Our approach assumes that participant and item effects combine additively on the probit scale and postulates (multivariate) normal distributions for the random effects. We provide a WinBUGS implementation of the crossed-random effects pair-clustering model and an application to novel experimental data. The present approach may be adapted to handle other MPT models.

A power fallacy

The power fallacy refers to the misconception that what holds on average –across an ensemble of hypothetical experiments– also holds for each case individually. According to the fallacy, high-power experiments always yield more informative data than do low-power experiments. Here we expose the fallacy with concrete examples, demonstrating that a particular outcome from a high-power experiment can be completely uninformative, whereas a particular outcome from a low-power experiment can be highly informative. Although power is useful in planning an experiment, it is less useful—and sometimes even misleading—for making inferences from observed data. To make inferences from data, we recommend the use of likelihood ratios or Bayes factors, which are the extension of likelihood ratios beyond point hypotheses. These methods of inference do not average over hypothetical replications of an experiment, but instead condition on the data that have actually been observed. In this way, likelihood ratios and Bayes factors rationally quantify the evidence that a particular data set provides for or against the null or any other hypothesis.

The Effect of Horizontal Eye Movements on Free Recall: A Preregistered Adversarial Collaboration

A growing body of research has suggested that horizontal saccadic eye movements facilitate the retrieval of episodic memories in free recall and recognition memory tasks. Nevertheless, a minority of studies have failed to replicate this effect. This article attempts to resolve the inconsistent results by introducing a novel variant of proponent-skeptic collaboration. The proposed approach combines the features of adversarial collaboration and purely confirmatory preregistered research. Prior to data collection, the adversaries reached consensus on an optimal research design, formulated their expectations, and agreed to submit the findings to an academic journal regardless of the outcome. To increase transparency and secure the purely confirmatory nature of the investigation, the 2 parties set up a publicly available adversarial collaboration agreement that detailed the proposed design and all foreseeable aspects of the data analysis. As anticipated by the skeptics, a series of Bayesian hypothesis tests indicated that horizontal eye movements did not improve free recall performance. The skeptics suggested that the nonreplication may partly reflect the use of suboptimal and questionable research practices in earlier eye movement studies. The proponents countered this suggestion and used a p curve analysis to argue that the effect of horizontal eye movements on explicit memory did not merely reflect selective reporting.

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).