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. The Bayesian New Statistics: Two historical trends converge