With Bayesian estimation one can get all that Bayes factors offer, and more

In classical statistics, there is a close link between null hypothesis significance testing (NHST) and parameter estimation via confidence intervals. However, for the Bayesian counterpart, a link between null hypothesis Bayesian testing (NHBT) and Bayesian estimation via a posterior distribution is less straightforward, but does exist, and has recently been reiterated by Rouder, Haaf, and Vandekerckhove (2018). It hinges on a combination of a point mass probability and a probability density function as prior (denoted as the spike-and-slab prior). In the present paper, it is first carefully explained how the spike-and-slab prior is defined, and how results can be derived for which proofs were not given in Rouder, Haaf, and Vandekerckhove (2018). Next, it is shown that this spike-and-slab prior can be approximated by a pure probability density function with a rectangular peak around the center towering highly above the remainder of the density function. Finally, we will indicate how this ‘hill-and-chimney’ prior may in turn be approximated by fully continuous priors. In this way, it is shown that NHBT results can be approximated well by results from estimation using a strongly peaked prior, and it is noted that the estimation itself offers more than merely the posterior odds on which NHBT is based. Thus, it complies with the strong APA requirement of not just mentioning testing results but also offering effect size information. It also offers a transparent perspective on the NHBT approach employing a prior with a strong peak around the chosen point null hypothesis value.