|Two trends in data analysis converge on Bayesian estimation. (NHST = null hypothesis significance testing. MLE = maximum likelihood estimate.)|
Abstract: There have been two historical shifts in the practice of data analysis. One shift is from hypothesis testing to estimation with uncertainty and meta-analysis, which among frequentists in psychology has recently been dubbed “the New Statistics” (Cumming, 2014). A second shift is from frequentist methods to Bayesian methods. We explain and applaud both of these shifts. Our main goal in this article is to explain how Bayesian methods achieve the goals of the New Statistics better than frequentist methods. The two historical trends converge in Bayesian methods for estimation with uncertainty and meta-analysis.
Excerpt: Our main goal in this article is to explain how Bayesian methods achieve the goals of the New Statistics better than frequentist methods. We will recapitulate the goals of the New Statistics and the frequentist methods for addressing them, and we will describe Bayesian methods for achieving those goals. We will cover hypothesis testing, estimation of magnitude (e.g., of effect size), assessment of uncertainty (with confidence intervals or posterior distributions), meta-analysis, and power analysis. We hope to convince you that Bayesian approaches to all these goals are more direct, more intuitive, and more informative than frequentist approaches. We believe that the goals of the New Statistics, including meta-analytic thinking engendered by an estimation approach, are better realized by Bayesian methods.
The manuscript is available at this link (via SSRN).