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      bayestestR: Describing Effects and their Uncertainty, Existence and Significance within the Bayesian Framework

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          The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective.

          In the practice of data analysis, there is a conceptual distinction between hypothesis testing, on the one hand, and estimation with quantified uncertainty on the other. Among frequentists in psychology, a shift of emphasis from hypothesis testing to estimation has been dubbed "the New Statistics" (Cumming 2014). A second conceptual distinction is between frequentist methods and Bayesian methods. Our main goal in this article is to explain how Bayesian methods achieve the goals of the New Statistics better than frequentist methods. The article reviews frequentist and Bayesian approaches to hypothesis testing and to estimation with confidence or credible intervals. The article also describes Bayesian approaches to meta-analysis, randomized controlled trials, and power analysis.
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            Bayesian hypothesis testing for psychologists: a tutorial on the Savage-Dickey method.

            In the field of cognitive psychology, the p-value hypothesis test has established a stranglehold on statistical reporting. This is unfortunate, as the p-value provides at best a rough estimate of the evidence that the data provide for the presence of an experimental effect. An alternative and arguably more appropriate measure of evidence is conveyed by a Bayesian hypothesis test, which prefers the model with the highest average likelihood. One of the main problems with this Bayesian hypothesis test, however, is that it often requires relatively sophisticated numerical methods for its computation. Here we draw attention to the Savage-Dickey density ratio method, a method that can be used to compute the result of a Bayesian hypothesis test for nested models and under certain plausible restrictions on the parameter priors. Practical examples demonstrate the method's validity, generality, and flexibility. Copyright 2009 Elsevier Inc. All rights reserved.
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              Rejecting or Accepting Parameter Values in Bayesian Estimation

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                Author and article information

                Journal
                Journal of Open Source Software
                JOSS
                The Open Journal
                2475-9066
                August 2019
                August 13 2019
                : 4
                : 40
                : 1541
                Article
                10.21105/joss.01541
                19323591
                32cce5ef-54b1-473a-92e9-542db8d105b7
                © 2019

                http://creativecommons.org/licenses/by/4.0/

                http://creativecommons.org/licenses/by/4.0/

                http://creativecommons.org/licenses/by/4.0/

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