Navigating the Bayes maze: The psychologist's guide to Bayesian statistics, a hands-on tutorial with R code

Abstract

Bayesian statistics has gained substantial popularity in the social sciences, particularly in psychology. Despite its growing prominence in the psychological literature, many researchers remain unacquainted with Bayesian methods and their advantages. This tutorial addresses the needs of curious applied psychology researchers and introduces Bayesian analysis as an accessible and powerful tool. We begin by comparing Bayesian and frequentist approaches, redefining fundamental terms from both perspectives with practical illustrations. Our exploration of Bayesian statistics includes Bayes's Theorem, likelihood, prior and posterior distributions, various prior types, and Markov-Chain Monte Carlo (MCMC) methods, supplemented by graphical aids for clarity. To bridge theory and practice, we employ a psychological research example with real, open data. We analyse the data using both frequentist and Bayesian approaches, providing R code and comprehensive supporting information, and emphasising best practices for interpretation and reporting. We discuss and demonstrate how to interpret parameter estimates and credible intervals, among other essential topics. Throughout, we maintain an accessible and user-friendly language, focusing on practical implications, intuitive examples, and actionable recommendations.