16. Bayesian statistics

Chapter 16 introduces Bayesian statistics as an alternative to the frequentist perspective commonly used in psychology and other scientific disciplines. The chapter begins by critiquing the dominance of frequentist methods, noting their limitations and the challenges they pose for applied research. Bayesian statistics is presented as a framework that prioritises belief revision and rational decision-making, underpinned by clear probabilistic reasoning. The chapter explains the fundamental principles of Bayesian inference, emphasising how prior beliefs, likelihoods, and observed data interact to update our understanding of hypotheses. Through illustrative examples, such as predicting rainfall based on umbrella usage, the chapter demonstrates the intuitive and flexible nature of Bayesian reasoning, culminating in a clear explanation of Bayes’ rule. This foundational knowledge is then applied to hypothesis testing, showing how Bayesian methods enable researchers to quantify evidence in favour of both null and alternative hypotheses, with Bayes factors serving as a robust measure of evidentiary strength.

In the latter sections, the chapter contrasts Bayesian and frequentist approaches, highlighting the interpretive clarity and evidentiary consistency of Bayesian statistics. Practical examples include Bayesian t-tests, demonstrating how this approach provides more cautious and nuanced interpretations compared to orthodox methods. The chapter also discusses the pitfalls of traditional p-values, particularly in scenarios involving data peeking or optional stopping, and argues for Bayesian methods as a more honest and human-aligned approach to statistical inference. By the end, readers are encouraged to critically evaluate their statistical paradigms, with recommendations for further resources to deepen their understanding of Bayesian analysis.