Publication bias is a ubiquitous threat to the validity of meta-analysis and the accumulation of scientific evidence. In order to estimate and counteract the impact of publication bias, multiple methods have been developed; however, recent simulation studies have shown the methods' performance to depend on the true data generating process, and no…

Sir Ronald Fisher's venerable experiment "The Lady Tasting Tea" is revisited from a Bayesian perspective. We demonstrate how a similar tasting experiment, conducted in a classroom setting, can familiarize students with several key concepts of Bayesian inference, such as the prior distribution, the posterior distribution, the Bayes…

Uncertainty is ubiquitous in science, but scientific knowledge is often represented to the public and in educational contexts as certain and immutable. This contrast can foster distrust when scientific knowledge develops in a way that people perceive as a reversals, as we have observed during the ongoing COVID-19 pandemic. Drawing on research in…

P values have been critiqued on several grounds but remain entrenched as the dominant inferential method in the empirical sciences. In this article, we elaborate on the fact that in many statistical models, the one-sided "P" value has a direct Bayesian interpretation as the approximate posterior mass for values lower than zero. The…

Current developments in the statistics community suggest that modern statistics education should be structured holistically, that is, by allowing students to work with real data and to answer concrete statistical questions, but also by educating them about alternative frameworks, such as Bayesian inference. In this article, we describe how we…

In 1881, Donald MacAlister posed a problem in the "Educational Times" that remains relevant today. The problem centers on the statistical evidence for the effectiveness of a treatment based on a comparison between two proportions. A brief historical sketch is followed by a discussion of two default Bayesian solutions, one based on a…

Many theories of human cognition postulate that people are equipped with a repertoire of strategies to solve the tasks they face. This theoretical framework of a cognitive toolbox provides a plausible account of intra- and interindividual differences in human behavior. Unfortunately, it is often unclear how to rigorously test the toolbox…

In their influential "Psychological Review" article, Bogacz, Brown, Moehlis, Holmes, and Cohen (2006) discussed optimal decision making as accomplished by the drift diffusion model (DDM). The authors showed that neural inhibition models, such as the leaky competing accumulator model (LCA) and the feedforward inhibition model (FFI), can mimic the…

For decisions between many alternatives, the benchmark result is Hick's Law: that response time increases log-linearly with the number of choice alternatives. Even when Hick's Law is observed for response times, divergent results have been observed for error rates--sometimes error rates increase with the number of choice alternatives, and…

The purpose of the recently proposed "p[subscript rep]" statistic is to estimate the probability of concurrence, that is, the probability that a replicate experiment yields an effect of the same sign (Killeen, 2005a). The influential journal "Psychological Science" endorses "p[subscript rep]" and recommends its use…

This article reviews current methods for evaluating models in the cognitive sciences, including theoretically based approaches, such as Bayes factors and minimum description length measures; simulation approaches, including model mimicry evaluations; and practical approaches, such as validation and generalization measures. This article argues…

D. Trafimow presented an analysis of null hypothesis significance testing (NHST) using Bayes's theorem. Among other points, he concluded that NHST is logically invalid, but that logically valid Bayesian analyses are often not possible. The latter conclusion reflects a fundamental misunderstanding of the nature of Bayesian inference. This view…

This paper comments on the response offered by Trafimow on Lee and Wagenmakers comments on Trafimow's original article. It seems our comment should have made it clear that the objective Bayesian approach we advocate views probabilities neither as relative frequencies nor as belief states, but as degrees of plausibility assigned to propositions in…