A gentle introduction to Bayesian statistics, with applications to bilingualism research

Bayesian statistics have been increasingly adopted as a replacement for traditional (frequentist) methods, particularly since recent computational advances have made it possible to fit Bayesian models quickly and easily. However, Bayesian methods have not yet gained wide acceptance in bilingualism and second language research, possibly because existing introductions have not been directed at our field, and because these methods are perceived as having a steep learning curve. The current paper aims to fill these gaps. It provides a gentle introduction to Bayesian statistics, while highlighting its advantages for the bilingualism researcher. We present a theoretical introduction to the foundational principles of Bayesian statistics and a practical tutorial on estimation and hypothesis testing using the brms R package. The examples build up from simple linear regression to more advanced mixed-effects models, and showcase the different aspects of a Bayesian workflow. All data and code are publicly available at https://osf.io/n3jgm/.