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The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power of α , and then used as the prior distribution in the analysis of the replication data. Posterior distribution and Bayes factor hypothesis tests related to the power parameter α quantify the degree of compatibility between the original and replication study. Inferences for other parameters, such as effect sizes, dynamically borrow information from the original study. The degree of borrowing depends on the conflict between the two studies. The practical value of the approach is illustrated on data from three replication studies, and the connection to hierarchical modeling approaches explored. We generalize the known connection between normal power priors and normal hierarchical models for fixed parameters and show that normal power prior inferences with a beta prior on the power parameter α align with normal hierarchical model inferences using a generalized beta prior on the relative heterogeneity variance I 2 . The connection illustrates that power prior modeling is unnatural from the perspective of hierarchical modeling since it corresponds to specifying priors on a relative rather than an absolute heterogeneity scale. [ABSTRACT FROM AUTHOR]

Researchers conduct meta-analyses in order to synthesize information across different studies. Compared to standard meta-analytic methods, Bayesian model-averaged meta-analysis offers several practical advantages including the ability to quantify evidence in favor of the absence of an effect, the ability to monitor evidence as individual studies accumulate indefinitely, and the ability to draw inferences based on multiple models simultaneously. This tutorial introduces the concepts and logic underlying Bayesian model-averaged meta-analysis and illustrates its application using the open-source software JASP. As a running example, we perform a Bayesian meta-analysis on language development in children. We show how to conduct a Bayesian model-averaged meta-analysis and how to interpret the results. [ABSTRACT FROM AUTHOR]

Huisman (Psychonomic Bulletin & Review, 1–10. 2022) argued that a valid measure of evidence should indicate more support in favor of a true alternative hypothesis when sample size is large than when it is small. Bayes factors may violate this pattern and hence Huisman concluded that Bayes factors are invalid as a measure of evidence. In this brief comment we call attention to the following: (1) Huisman's purported anomaly is in fact dictated by probability theory; (2) Huisman's anomaly has been discussed and explained in the statistical literature since 1939; the anomaly was also highlighted in the Psychonomic Bulletin & Review article by Rouder et al. (2009), who interpreted the anomaly as "ideal": an interpretation diametrically opposed to that of Huisman. We conclude that when intuition clashes with probability theory, chances are that it is intuition that needs schooling. [ABSTRACT FROM AUTHOR]

The multibridgeR package allows a Bayesian evaluation of informed hypotheses H r applied to frequency data from an independent binomial or multinomial distribution. multibridge uses bridge sampling to efficiently compute Bayes factors for the following hypotheses concerning the latent category proportions 휃: (a) hypotheses that postulate equality constraints (e.g., 휃1 = 휃2 = 휃3); (b) hypotheses that postulate inequality constraints (e.g., 휃1 < 휃2 < 휃3 or 휃1 > 휃2 > 휃3); (c) hypotheses that postulate combinations of inequality constraints and equality constraints (e.g., 휃1 < 휃2 = 휃3); and (d) hypotheses that postulate combinations of (a)–(c) (e.g., 휃1 < (휃2 = 휃3),휃4). Any informed hypothesis H r may be compared against the encompassing hypothesis H e that all category proportions vary freely, or against the null hypothesis H 0 that all category proportions are equal. multibridge facilitates the fast and accurate comparison of large models with many constraints and models for which relatively little posterior mass falls in the restricted parameter space. This paper describes the underlying methodology and illustrates the use of multibridge through fully reproducible examples. [ABSTRACT FROM AUTHOR]

This Editorial reports an exchange in form of a comment and reply on the article "History and Nature of the Jeffreys–Lindley Paradox" (Arch Hist Exact Sci 77:25, 2023) by Eric-Jan Wagenmakers and Alexander Ly. [ABSTRACT FROM AUTHOR]

The current practice of reliability analysis is both uniform and troublesome: most reports consider only Cronbach's α, and almost all reports focus exclusively on a point estimate, disregarding the impact of sampling error. In an attempt to improve the status quo we have implemented Bayesian estimation routines for five popular single-test reliability coefficients in the open-source statistical software program JASP. Using JASP, researchers can easily obtain Bayesian credible intervals to indicate a range of plausible values and thereby quantify the precision of the point estimate. In addition, researchers may use the posterior distribution of the reliability coefficients to address practically relevant questions such as "What is the probability that the reliability of my test is larger than a threshold value of.80?". In this tutorial article, we outline how to conduct a Bayesian reliability analysis in JASP and correctly interpret the results. By making available a computationally complex procedure in an easy-to-use software package, we hope to motivate researchers to include uncertainty estimates whenever reporting the results of a single-test reliability analysis. [ABSTRACT FROM AUTHOR]

A tradition that goes back to Sir Karl R. Popper assesses the value of a statistical test primarily by its severity: was there an honest and stringent attempt to prove the tested hypothesis wrong? For "error statisticians" such as Mayo (1996, 2018), and frequentists more generally, severity is a key virtue in hypothesis tests. Conversely, failure to incorporate severity into statistical inference, as allegedly happens in Bayesian inference, counts as a major methodological shortcoming. Our paper pursues a double goal: First, we argue that the error-statistical explication of severity has substantive drawbacks; specifically, the neglect of research context and the specificity of the predictions of the hypothesis. Second, we argue that severity matters for Bayesian inference via the value of specific, risky predictions: severity boosts the expected evidential value of a Bayesian hypothesis test. We illustrate severity-based reasoning in Bayesian statistics by means of a practical example and discuss its advantages and potential drawbacks. [ABSTRACT FROM AUTHOR]

The Jeffreys–Lindley paradox exposes a rift between Bayesian and frequentist hypothesis testing that strikes at the heart of statistical inference. Contrary to what most current literature suggests, the paradox was central to the Bayesian testing methodology developed by Sir Harold Jeffreys in the late 1930s. Jeffreys showed that the evidence for a point-null hypothesis H 0 scales with n and repeatedly argued that it would, therefore, be mistaken to set a threshold for rejecting H 0 at a constant multiple of the standard error. Here, we summarize Jeffreys's early work on the paradox and clarify his reasons for including the n term. The prior distribution is seen to play a crucial role; by implicitly correcting for selection, small parameter values are identified as relatively surprising under H 1 . We highlight the general nature of the paradox by presenting both a fully frequentist and a fully Bayesian version. We also demonstrate that the paradox does not depend on assigning prior mass to a point hypothesis, as is commonly believed. [ABSTRACT FROM AUTHOR]

A perennial objection against Bayes factor point-null hypothesis tests is that the point-null hypothesis is known to be false from the outset. We examine the consequences of approximating the sharp point-null hypothesis by a hazy 'peri-null' hypothesis instantiated as a narrow prior distribution centered on the point of interest. The peri-null Bayes factor then equals the point-null Bayes factor multiplied by a correction term which is itself a Bayes factor. For moderate sample sizes, the correction term is relatively inconsequential; however, for large sample sizes, the correction term becomes influential and causes the peri-null Bayes factor to be inconsistent and approach a limit that depends on the ratio of prior ordinates evaluated at the maximum likelihood estimate. We characterize the asymptotic behavior of the peri-null Bayes factor and briefly discuss suggestions on how to construct peri-null Bayes factor hypothesis tests that are also consistent. [ABSTRACT FROM AUTHOR]

In a sequential hypothesis test, the analyst checks at multiple steps during data collection whether sufficient evidence has accrued to make a decision about the tested hypotheses. As soon as sufficient information has been obtained, data collection is terminated. Here, we compare two sequential hypothesis testing procedures that have recently been proposed for use in psychological research: Sequential Probability Ratio Test (SPRT; Psychological Methods, 25(2), 206–226, 2020) and the Sequential Bayes Factor Test (SBFT; Psychological Methods, 22(2), 322–339, 2017). We show that although the two methods have different philosophical roots, they share many similarities and can even be mathematically regarded as two instances of an overarching hypothesis testing framework. We demonstrate that the two methods use the same mechanisms for evidence monitoring and error control, and that differences in efficiency between the methods depend on the exact specification of the statistical models involved, as well as on the population truth. Our simulations indicate that when deciding on a sequential design within a unified sequential testing framework, researchers need to balance the needs of test efficiency, robustness against model misspecification, and appropriate uncertainty quantification. We provide guidance for navigating these design decisions based on individual preferences and simulation-based design analyses. [ABSTRACT FROM AUTHOR]

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 statistics, child development, and several studies in science education, we argue that a Bayesian approach can support science learners to make sense of uncertainty. We provide a brief primer on Bayes' theorem and then describe three ways to make Bayesian reasoning practical in K-12 science education contexts. There are a) using principles informed by Bayes' theorem that relate to the nature of knowing and knowledge, b) interacting with a web-based application (or widget—Confidence Updater) that makes the calculations needed to apply Bayes' theorem more practical, and c) adopting strategies for supporting even young learners to engage in Bayesian reasoning. We conclude with directions for future research and sum up how viewing science and scientific knowledge from a Bayesian perspective can build trust in science. [ABSTRACT FROM AUTHOR]

Bayesian inference requires the specification of prior distributions that quantify the pre-data uncertainty about parameter values. One way to specify prior distributions is through prior elicitation, an interview method guiding field experts through the process of expressing their knowledge in the form of a probability distribution. However, prior distributions elicited from experts can be subject to idiosyncrasies of experts and elicitation procedures, raising the spectre of subjectivity and prejudice. Here, we investigate the effect of interpersonal variation in elicited prior distributions on the Bayes factor hypothesis test. We elicited prior distributions from six academic experts with a background in different fields of psychology and applied the elicited prior distributions as well as commonly used default priors in a re-analysis of 1710 studies in psychology. The degree to which the Bayes factors vary as a function of the different prior distributions is quantified by three measures of concordance of evidence: We assess whether the prior distributions change the Bayes factor direction, whether they cause a switch in the category of evidence strength, and how much influence they have on the value of the Bayes factor. Our results show that although the Bayes factor is sensitive to changes in the prior distribution, these changes do not necessarily affect the qualitative conclusions of a hypothesis test. We hope that these results help researchers gauge the influence of interpersonal variation in elicited prior distributions in future psychological studies. Additionally, our sensitivity analyses can be used as a template for Bayesian robustness analyses that involve prior elicitation from multiple experts. [ABSTRACT FROM AUTHOR]

Many studies report atypical responses to sensory information in autistic individuals, yet it is not clear which stages of processing are affected, with little consideration given to decision-making processes. We combined diffusion modelling with high-density EEG to identify which processing stages differ between 50 autistic and 50 typically developing children aged 6–14 years during two visual motion tasks. Our pre-registered hypotheses were that autistic children would show task-dependent differences in sensory evidence accumulation, alongside a more cautious decision-making style and longer non-decision time across tasks. We tested these hypotheses using hierarchical Bayesian diffusion models with a rigorous blind modelling approach, finding no conclusive evidence for our hypotheses. Using a data-driven method, we identified a response-locked centro-parietal component previously linked to the decision-making process. The build-up in this component did not consistently relate to evidence accumulation in autistic children. This suggests that the relationship between the EEG measure and diffusion-modelling is not straightforward in autistic children. Compared to a related study of children with dyslexia, motion processing differences appear less pronounced in autistic children. Exploratory analyses also suggest weak evidence that ADHD symptoms moderate perceptual decision-making in autistic children. [ABSTRACT FROM AUTHOR]

A frequentist confidence interval can be constructed by inverting a hypothesis test, such that the interval contains only parameter values that would not have been rejected by the test. We show how a similar definition can be employed to construct a Bayesian support interval. Consistent with Carnap's theory of corroboration, the support interval contains only parameter values that receive at least some minimum amount of support from the data. The support interval is not subject to Lindley's paradox and provides an evidence-based perspective on inference that differs from the belief-based perspective that forms the basis of the standard Bayesian credible interval. [ABSTRACT FROM AUTHOR]

Linear regression analyses commonly involve two consecutive stages of statistical inquiry. In the first stage, a single 'best' model is defined by a specific selection of relevant predictors; in the second stage, the regression coefficients of the winning model are used for prediction and for inference concerning the importance of the predictors. However, such second-stage inference ignores the model uncertainty from the first stage, resulting in overconfident parameter estimates that generalize poorly. These drawbacks can be overcome by model averaging, a technique that retains all models for inference, weighting each model's contribution by its posterior probability. Although conceptually straightforward, model averaging is rarely used in applied research, possibly due to the lack of easily accessible software. To bridge the gap between theory and practice, we provide a tutorial on linear regression using Bayesian model averaging in JASP, based on the BAS package in R. Firstly, we provide theoretical background on linear regression, Bayesian inference, and Bayesian model averaging. Secondly, we demonstrate the method on an example data set from the World Happiness Report. Lastly, we discuss limitations of model averaging and directions for dealing with violations of model assumptions. [ABSTRACT FROM AUTHOR]

The replicability of findings in experimental psychology can be improved by distinguishing sharply between hypothesis-generating research and hypothesis-testing research. This distinction can be achieved by preregistration, a method that has recently attracted widespread attention. Although preregistration is fair in the sense that it inoculates researchers against hindsight bias and confirmation bias, preregistration does not allow researchers to analyze the data flexibly without the analysis being demoted to exploratory. To alleviate this concern we discuss how researchers may conduct blinded analyses (MacCoun and Perlmutter in Nature 526:187–189, 2015). As with preregistration, blinded analyses break the feedback loop between the analysis plan and analysis outcome, thereby preventing cherry-picking and significance seeking. However, blinded analyses retain the flexibility to account for unexpected peculiarities in the data. We discuss different methods of blinding, offer recommendations for blinding of popular experimental designs, and introduce the design for an online blinding protocol. [ABSTRACT FROM AUTHOR]

The shifted-Wald model is a popular analysis tool for one-choice reaction-time tasks. In its simplest version, the shifted-Wald model assumes a constant trial-independent drift rate parameter. However, the presence of endogenous processes—fluctuation in attention and motivation, fatigue and boredom—suggest that drift rate might vary across experimental trials. Here we show how across-trial variability in drift rate can be accounted for by assuming a trial-specific drift rate parameter that is governed by a positive-valued distribution. We consider two candidate distributions: the truncated normal distribution and the gamma distribution. For the resulting distributions of first-arrival times, we derive analytical and sampling-based solutions, and implement the models in a Bayesian framework. Recovery studies and an application to a data set comprised of 1469 participants suggest that (1) both mixture distributions yield similar results; (2) all model parameters can be recovered accurately except for the drift variance parameter; (3) despite poor recovery, the presence of the drift variance parameter facilitates accurate recovery of the remaining parameters; (4) shift, threshold, and drift mean parameters are correlated. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Any single analysis hides an iceberg of uncertainty. Multi-team analysis can reveal it. [ABSTRACT FROM AUTHOR]

A standard assumption of most sequential sampling models is that decision-makers rely on a decision criterion that remains constant throughout the decision process. However, several authors have recently suggested that, in order to maximize reward rates in dynamic environments, decision-makers need to rely on a decision criterion that changes over the course of the decision process. We used dynamic programming and simulation methods to quantify the reward rates obtained by constant and dynamic decision criteria in different environments. We further investigated what influence a decision-maker's uncertainty about the stochastic structure of the environment has on reward rates. Our results show that in most dynamic environments, both types of decision criteria yield similar reward rates, across different levels of uncertainty. This suggests that a static decision criterion might provide a robust default setting. [ABSTRACT FROM AUTHOR]

We describe a general method that allows experimenters to quantify the evidence from the data of a direct replication attempt given data already acquired from an original study. These so-called replication Bayes factors are a reconceptualization of the ones introduced by Verhagen and Wagenmakers (Journal of Experimental Psychology: General, 143(4), 1457–1475 2014) for the common t test. This reconceptualization is computationally simpler and generalizes easily to most common experimental designs for which Bayes factors are available. [ABSTRACT FROM AUTHOR]

Signal detection theory (SDT) is used to quantify people's ability and bias in discriminating stimuli. The ability to detect a stimulus is often measured through confidence ratings. In SDT models, the use of confidence ratings necessitates the estimation of confidence category thresholds, a requirement that can easily result in models that are overly complex. As a parsimonious alternative, we propose a threshold SDT model that estimates these category thresholds using only two parameters. We fit the model to data from Pratte et al. (Journal of Experimental Psychology: Learning, Memory, and Cognition, 36, 224–232 2010) and illustrate its benefits over previous threshold SDT models. [ABSTRACT FROM AUTHOR]

Data torturing, cherry-picking, P-hacking and the invention of tools such as ChatGPT — when it comes to assisting the spread of disinformation science is its own worst enemy, argues a new book. [ABSTRACT FROM AUTHOR]

Bayesian analysis often concerns an evaluation of models with different dimensionality as is necessary in, for example, model selection or mixture models. To facilitate this evaluation, transdimensional Markov chain Monte Carlo (MCMC) relies on sampling a discrete indexing variable to estimate the posterior model probabilities. However, little attention has been paid to the precision of these estimates. If only few switches occur between the models in the transdimensional MCMC output, precision may be low and assessment based on the assumption of independent samples misleading. Here, we propose a new method to estimate the precision based on the observed transition matrix of the model-indexing variable. Assuming a first-order Markov model, the method samples from the posterior of the stationary distribution. This allows assessment of the uncertainty in the estimated posterior model probabilities, model ranks, and Bayes factors. Moreover, the method provides an estimate for the effective sample size of the MCMC output. In two model selection examples, we show that the proposed approach provides a good assessment of the uncertainty associated with the estimated posterior model probabilities. [ABSTRACT FROM AUTHOR]

Well-designed experiments are likely to yield compelling evidence with efficient sample sizes. Bayes Factor Design Analysis (BFDA) is a recently developed methodology that allows researchers to balance the informativeness and efficiency of their experiment (Schönbrodt & Wagenmakers, Psychonomic Bulletin & Review, 25(1), 128–142 2018). With BFDA, researchers can control the rate of misleading evidence but, in addition, they can plan for a target strength of evidence. BFDA can be applied to fixed-N and sequential designs. In this tutorial paper, we provide an introduction to BFDA and analyze how the use of informed prior distributions affects the results of the BFDA. We also present a user-friendly web-based BFDA application that allows researchers to conduct BFDAs with ease. Two practical examples highlight how researchers can use a BFDA to plan for informative and efficient research designs. [ABSTRACT FROM AUTHOR]

Multinomial processing trees (MPTs) are a popular class of cognitive models for categorical data. Typically, researchers compare several MPTs, each equipped with many parameters, especially when the models are implemented in a hierarchical framework. A Bayesian solution is to compute posterior model probabilities and Bayes factors. Both quantities, however, rely on the marginal likelihood, a high-dimensional integral that cannot be evaluated analytically. In this case study, we show how Warp-III bridge sampling can be used to compute the marginal likelihood for hierarchical MPTs. We illustrate the procedure with two published data sets and demonstrate how Warp-III facilitates Bayesian model averaging. [ABSTRACT FROM AUTHOR]

Psychological experiments often yield data that are hierarchically structured. A number of popular shortcut strategies in cognitive modeling do not properly accommodate this structure and can result in biased conclusions. To gauge the severity of these biases, we conducted a simulation study for a two-group experiment. We first considered a modeling strategy that ignores the hierarchical data structure. In line with theoretical results, our simulations showed that Bayesian and frequentist methods that rely on this strategy are biased towards the null hypothesis. Secondly, we considered a modeling strategy that takes a two-step approach by first obtaining participant-level estimates from a hierarchical cognitive model and subsequently using these estimates in a follow-up statistical test. Methods that rely on this strategy are biased towards the alternative hypothesis. Only hierarchical models of the multilevel data lead to correct conclusions. Our results are particularly relevant for the use of hierarchical Bayesian parameter estimates in cognitive modeling. [ABSTRACT FROM AUTHOR]

An important tool in the advancement of cognitive science are quantitative models that represent different cognitive variables in terms of model parameters. To evaluate such models, their parameters are typically tested for relationships with behavioral and physiological variables that are thought to reflect specific cognitive processes. However, many models do not come equipped with the statistical framework needed to relate model parameters to covariates. Instead, researchers often revert to classifying participants into groups depending on their values on the covariates, and subsequently comparing the estimated model parameters between these groups. Here we develop a comprehensive solution to the covariate problem in the form of a Bayesian regression framework. Our framework can be easily added to existing cognitive models and allows researchers to quantify the evidential support for relationships between covariates and model parameters using Bayes factors. Moreover, we present a simulation study that demonstrates the superiority of the Bayesian regression framework to the conventional classification-based approach. [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]

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 userfriendly 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 (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. [ABSTRACT FROM AUTHOR]

A sizeable literature exists on the use of frequentist power analysis in the null-hypothesis significance testing (NHST) paradigm to facilitate the design of informative experiments. In contrast, there is almost no literature that discusses the design of experiments when Bayes factors (BFs) are used as a measure of evidence. Here we explore Bayes Factor Design Analysis (BFDA) as a useful tool to design studies for maximum efficiency and informativeness. We elaborate on three possible BF designs, (a) a fixed-n design, (b) an open-ended Sequential Bayes Factor (SBF) design, where researchers can test after each participant and can stop data collection whenever there is strong evidence for either H1 or H0, and (c) a modified SBF design that defines a maximal sample size where data collection is stopped regardless of the current state of evidence. We demonstrate how the properties of each design (i.e., expected strength of evidence, expected sample size, expected probability of misleading evidence, expected probability of weak evidence) can be evaluated using Monte Carlo simulations and equip researchers with the necessary information to compute their own Bayesian design analyses. [ABSTRACT FROM AUTHOR]

People with higher IQ scores also tend to perform better on elementary cognitive-perceptual tasks, such as deciding quickly whether an arrow points to the left or the right Jensen (2006). The worst performance rule (WPR) finesses this relation by stating that the association between IQ and elementary-task performance is most pronounced when this performance is summarized by people's slowest responses. Previous research has shown that the WPR can be accounted for in the Ratcliff diffusion model by assuming that the same ability parameter-drift rate-mediates performance in both elementary tasks and higher-level cognitive tasks. Here we aim to test four qualitative predictions concerning the WPR and its diffusion model explanation in terms of drift rate. In the first stage, the diffusion model was fit to data from 916 participants completing a perceptual two-choice task; crucially, the fitting happened after randomly shuffling the key variable, i.e., each participant's score on a working memory capacity test. In the second stage, after all modeling decisions were made, the key variable was unshuffled and the adequacy of the predictions was evaluated by means of confirmatory Bayesian hypothesis tests. By temporarily withholding the mapping of the key predictor, we retain flexibility for proper modeling of the data (e.g., outlier exclusion) while preventing biases from unduly influencing the results. Our results provide evidence against the WPR and suggest that it may be less robust and less ubiquitous than is commonly believed. [ABSTRACT FROM AUTHOR]

The analysis of R× C contingency tables usually features a test for independence between row and column counts. Throughout the social sciences, the adequacy of the independence hypothesis is generally evaluated by the outcome of a classical p-value null-hypothesis significance test. Unfortunately, however, the classical p-value comes with a number of well-documented drawbacks. Here we outline an alternative, Bayes factor method to quantify the evidence for and against the hypothesis of independence in R× C contingency tables. First we describe different sampling models for contingency tables and provide the corresponding default Bayes factors as originally developed by Gunel and Dickey ( Biometrika, 61(3):545-557 (1974)). We then illustrate the properties and advantages of a Bayes factor analysis of contingency tables through simulations and practical examples. Computer code is available online and has been incorporated in the 'BayesFactor' R package and the JASP program (). [ABSTRACT FROM AUTHOR]

We present a suite of Bayes factor hypothesis tests that allow researchers to grade the decisiveness of the evidence that the data provide for the presence versus the absence of a correlation between two variables. For concreteness, we apply our methods to the recent work of Donnellan et al. () who conducted nine replication studies with over 3,000 participants and failed to replicate the phenomenon that lonely people compensate for a lack of social warmth by taking warmer baths or showers. We show how the Bayes factor hypothesis test can quantify evidence in favor of the null hypothesis, and how the prior specification for the correlation coefficient can be used to define a broad range of tests that address complementary questions. Specifically, we show how the prior specification can be adjusted to create a two-sided test, a one-sided test, a sensitivity analysis, and a replication test. [ABSTRACT FROM AUTHOR]

For decades sequential sampling models have successfully accounted for human and monkey decision-making, relying on the standard assumption that decision makers maintain a pre-set decision standard throughout the decision process. Based on the theoretical argument of reward rate maximization, some authors have recently suggested that decision makers become increasingly impatient as time passes and therefore lower their decision standard. Indeed, a number of studies show that computational models with an impatience component provide a good fit to human and monkey decision behavior. However, many of these studies lack quantitative model comparisons and systematic manipulations of rewards. Moreover, the often-cited evidence from single-cell recordings is not unequivocal and complimentary data from human subjects is largely missing. We conclude that, despite some enthusiastic calls for the abandonment of the standard model, the idea of an impatience component has yet to be fully established; we suggest a number of recently developed tools that will help bring the debate to a conclusive settlement. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]