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Statistical evidence in experimental psychology: An empirical comparison using 855 t tests
 Perspectives on Psychological Science
, 2011
"... Statistical inference in psychology has traditionally relied heavily on pvalue 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 me ..."
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Cited by 27 (4 self)
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Statistical inference in psychology has traditionally relied heavily on pvalue 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. Keywords
Default Bayes factors for ANOVA designs.
 Journal of Mathematical Psychology,
, 2012
"... Abstract Bayes factors have been advocated as superior to pvalues for assessing statistical evidence in data. Despite the advantages of Bayes factors and the drawbacks of pvalues, inference by pvalues is still nearly ubiquitous. One impediment to adoption of Bayes factors is a lack of practical ..."
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Cited by 25 (4 self)
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Abstract Bayes factors have been advocated as superior to pvalues for assessing statistical evidence in data. Despite the advantages of Bayes factors and the drawbacks of pvalues, inference by pvalues is still nearly ubiquitous. One impediment to adoption of Bayes factors is a lack of practical development, particularly a lack of readytouse formulas and algorithms. In this paper, we discuss and expand a set of default Bayes factor tests for ANOVA designs. These tests are based on multivariate generalizations of Cauchy priors on standardized effects, and have the desirable properties of being invariant with respect to linear transformations of measurement units. Moreover, these Bayes factors are computationally convenient, and straightforward sampling algorithms are provided. We cover models with fixed, random, and mixed effects, including random interactions, and do so for withinsubject, betweensubject, and mixed designs. We extend the discussion to regression models with continuous covariates. We also discuss how these Bayes factors may be applied in nonlinear settings, and show how they are useful in differentiating between the power law and the exponential law of skill acquisition. In sum, the current development makes the computation of Bayes factors straightforward for the vast majority of designs in experimental psychology. * Correspondence: 210 McAlester Hall, Columbia, MO 65203, rouderj@missouri.edu. We thank Brandon Turner and EricJan Wagenmakers for detailed and constructive comments. This research is supported by NSF SES 1024080.
Bayesian Estimation Supersedes the t Test
"... This document is copyrighted by the American Psychological Association or one of its allied publishers. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. Bayesian estimation for 2 groups provides complete distributions of credible valu ..."
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Cited by 12 (2 self)
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This document is copyrighted by the American Psychological Association or one of its allied publishers. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. Bayesian estimation for 2 groups provides complete distributions of credible values for the effect size, group means and their difference, standard deviations and their difference, and the normality of the data. The method handles outliers. The decision rule can accept the null value (unlike traditional t tests) when certainty in the estimate is high (unlike Bayesian model comparison using Bayes factors). The method also yields precise estimates of statistical power for various research goals. The software and programs are free and run on Macintosh, Windows, and Linux platforms.
Introduction to special section on Bayesian data analysis
 Perspectives on Psychological Science
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The Ising Decision Maker: A Binary Stochastic Network for Choice Response Time
"... The Ising Decision Maker (IDM) is a new formal model for speeded twochoice decision making derived from the stochastic Hopfield network or dynamic Ising model. On a microscopic level, it consists of 2 pools of binary stochastic neurons with pairwise interactions. Inside each pool, neurons excite ea ..."
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The Ising Decision Maker (IDM) is a new formal model for speeded twochoice decision making derived from the stochastic Hopfield network or dynamic Ising model. On a microscopic level, it consists of 2 pools of binary stochastic neurons with pairwise interactions. Inside each pool, neurons excite each other, whereas between pools, neurons inhibit each other. The perceptual input is represented by an external excitatory field. Using methods from statistical mechanics, the highdimensional network of neurons (microscopic level) is reduced to a twodimensional stochastic process, describing the evolution of the mean neural activity per pool (macroscopic level). The IDM can be seen as an abstract, analytically tractable multiple attractor network model of information accumulation. In this article, the properties of the IDM are studied, the relations to existing models are discussed, and it is shown that the most important basic aspects of twochoice response time data can be reproduced. In addition, the IDM is shown to predict a variety of observed psychophysical relations such as Piéron’s law, the van der MolenKeuss effect, and Weber’s law. Using Bayesian methods, the model is fitted to both simulated and real data, and its performance is compared to the Ratcliff diffusion model.
Neuroscience, and Nature Neuroscience frequently publish
"... Over the last two decades, the appeal and prevalence of shortandfast publications in our field have increased dramatically. ..."
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Over the last two decades, the appeal and prevalence of shortandfast publications in our field have increased dramatically.
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"... Reasoning effectively about magnitude is central to informationbased decision making in all aspects of life. People process information involving numerical stimuli every day, with examples as diverse as prices, distances, weights, amounts, times, and ratings. Such information is represented as a m ..."
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Reasoning effectively about magnitude is central to informationbased decision making in all aspects of life. People process information involving numerical stimuli every day, with examples as diverse as prices, distances, weights, amounts, times, and ratings. Such information is represented as a magnitude holding no meaning on its own and a unit of measurement denoting a meaningful standard quantity. The judgment of such information should be based on a multiplication of the magnitude and the unit. For the most commonly encountered units (e.g., inches), the standard quantity represented is well known. However, in many cases, people encounter units representing poorly known quantities (e.g., megapixels; Hsee, Yang, Gu, & Chen, 2009). How do people make judgments about quantities described with numerical information, such as the aptitude of a student who has a score of 21 points on the American College Test, the size of a 3acre property, the performance of a 24mm camera lens, the hearing risk of a 110dB rock concert, the power of a 150horsepower (hp) engine, or the price of a hotel room costing 138 Brazilian real? Specifically, how does the numerical component of the information (the magnitude) affect people’s judgments when they have limited knowledge about the standard quantity represented by the accompanying unit? Previous research on numerical reasoning suggests contradictory answers to this question. Research on the money illu
To appear in Perspectives on Psychological Science. Bayesian assessment of null values via parameter estimation and
, 2011
"... Psychologists have been trained to do data analysis by asking whether null values can be rejected. Is the difference between groups nonzero? Is choice accuracy not at chance level? These questions have been addressed, traditionally, by null hypothesis significance testing (NHST). NHST has deep pro ..."
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Psychologists have been trained to do data analysis by asking whether null values can be rejected. Is the difference between groups nonzero? Is choice accuracy not at chance level? These questions have been addressed, traditionally, by null hypothesis significance testing (NHST). NHST has deep problems that are solved by Bayesian data analysis. As psychologists transition to Bayesian data analysis, it is natural to ask how Bayesian analysis assesses null values. The article explains and evaluates two different Bayesian approaches. One method involves Bayesian model comparison (and uses “Bayes factors”). The second method involves Bayesian parameter estimation and assesses whether the null value falls among the most credible values. Which method to use depends on the specific question that the analyst wants to answer, but typically the estimation approach (not using Bayes factors) provides richer information than the model comparison approach. Psychologists are routinely trained to frame their research design and analysis in terms of rejecting null values. For example, when studying the influence of distraction on response time, we might ask whether the change in response
Reprints and permission:
"... Reasoning effectively about magnitude is central to informationbased decision making in all aspects of life. People process information involving numerical stimuli every day, with examples as diverse as prices, distances, weights, amounts, times, and ratings. Such information is represented as a m ..."
Abstract
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Reasoning effectively about magnitude is central to informationbased decision making in all aspects of life. People process information involving numerical stimuli every day, with examples as diverse as prices, distances, weights, amounts, times, and ratings. Such information is represented as a magnitude holding no meaning on its own and a unit of measurement denoting a meaningful standard quantity. The judgment of such information should be based on a multiplication of the magnitude and the unit. For the most commonly encountered units (e.g., inches), the standard quantity represented is well known. However, in many cases, people encounter units representing poorly known quantities (e.g., megapixels; Hsee, Yang, Gu, & Chen, 2009). How do people make judgments about quantities described with numerical information, such as the aptitude of a student who has a score of 21 points on the American College Test, the size of a 3acre property, the performance of a 24mm camera lens, the hearing risk of a 110dB rock concert, the power of a 150horsepower (hp) engine, or the price of a hotel room costing 138 Brazilian real? Specifically, how does the numerical component of the information (the magnitude) affect people’s judgments when they have limited knowledge about the standard quantity represented by the accompanying unit? Previous research on numerical reasoning suggests contradictory answers to this question. Research on the money illusion (e.g., Fehr & Tyran, 2001; Raghubir & Srivastava, 2002;