Before/after Bayes: A comparison of frequentist and Bayesian mixed-effects models in applied psychological research

Bayesian methods are becoming increasingly used in applied psychological research. Previous researchers have thoroughly written about much of the details already, including the philosophy underlying Bayesian methods, computational issues associated with Bayesian model estimation, Bayesian model development and summary, and the role of Bayesian methods in the so-called replication crisis. In this paper, we seek to provide case studies comparing the use of frequentist methods to the use of Bayesian methods in applied psychological research. These case studies are intended to 'illustrate by example' the ways that Bayesian modelling differs from frequentist modelling and the differing conclusions that one may arrive at using the two methods. The intended audience is applied psychological researchers who have been trained in the traditional frequentist framework, who are familiar with mixed-effects models and who are curious about how statistical results might look in a Bayesian context. Along with our case studies, we provide general opinions and guidance on the use of Bayesian methods in applied psychological research.