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

Area of Science:

• Statistics
• Bayesian Inference

Background:

• Classical statistics links null hypothesis significance testing (NHST) with confidence intervals.
• The Bayesian counterpart, linking null hypothesis Bayesian testing (NHBT) with posterior distributions, is less direct but established.
• A spike-and-slab prior is key to connecting NHBT and Bayesian estimation.

Purpose of the Study:

• To explain the spike-and-slab prior and derive related results.
• To approximate the spike-and-slab prior with a continuous probability density function.
• To demonstrate how NHBT can be approximated by Bayesian estimation with a peaked prior.

Main Methods:

• Detailed explanation of the spike-and-slab prior definition.
• Approximation of the spike-and-slab prior using a probability density function with a rectangular peak ('hill-and-chimney' prior).
• Further approximation of the 'hill-and-chimney' prior using fully continuous priors.

Main Results:

• The spike-and-slab prior facilitates a link between NHBT and Bayesian estimation.
• The 'hill-and-chimney' prior serves as an effective approximation for the spike-and-slab prior.
• Bayesian estimation with a strongly peaked prior approximates NHBT results.

Conclusions:

• NHBT results can be well-approximated by Bayesian estimation using a strongly peaked prior.
• Bayesian estimation offers more than posterior odds, including effect size information, aligning with APA standards.
• This approach provides a transparent view of NHBT using priors peaked at the point null hypothesis.