The Full Bayesian Significance Test and the e-value -- Foundations, theory and application in the cognitive sciences

TL;DR

This paper introduces the Full Bayesian Significance Test (FBST) and e-value as a Bayesian alternative to p-value-based significance testing, demonstrating its application and advantages in psychological research.

Contribution

It provides a comprehensive tutorial on FBST, including practical examples, guidelines, and R code, highlighting its potential benefits over traditional significance tests.

Findings

FBST performs better than frequentist significance testing.

The method is applicable to common psychological research methods.

FBST has not been widely used in psychological sciences before.

Abstract

Hypothesis testing is a central statistical method in psychological research and the cognitive sciences. While the problems of null hypothesis significance testing (NHST) have been debated widely, few attractive alternatives exist. In this paper, we provide a tutorial on the Full Bayesian Significance Test (FBST) and the e-value, which is a fully Bayesian alternative to traditional significance tests which rely on p-values. The FBST is an advanced methodological procedure which can be applied to several areas. In this tutorial, we showcase with two examples of widely used statistical methods in psychological research how the FBST can be used in practice, provide researchers with explicit guidelines on how to conduct it and make available R-code to reproduce all results. The FBST is an innovative method which has clearly demonstrated to perform better than frequentist significance testing. However, to our best knowledge, it has not been used so far in the psychological sciences and should be of wide interest to a broad range of researchers in psychology and the cognitive sciences.