Friday, December 16, 2016

The Bayesian New Statistics: Hypothesis Testing, Estimation, Meta-Analysis, and Power Analysis from a Bayesian Perspective

UPDATE: Now published, see this post.

Two conceptual distinctions in the practice of data analysis. Rows show point-value hypothesis testing versus estimating magnitude with uncertainty. Columns show frequentist versus Bayesian methods. Cells indicate the typical information provided by each approach. [Figure 1 of Kruschke & Liddell (in press), The Bayesian new statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective. Psychonomic Bulletin & Review.]
Many people have found the table above to be useful for understanding two conceptual distinctions in the practice of data analysis. The article that discusses the table, and many other issues, is now in press. (It was submitted in mid May, 2015, and was just accepted; a blog post announcing its original version is here, along with many comments.) The in-press version can be found at OSF and at SSRN.

Abstract: 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 hand. 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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