A bayesian approach to small samples: Mixed-effects modeling in L2 interventional research

Abstract

Small sample sizes are a common challenge in second language (L2) research, particularly in classroom-based studies or exploratory intervention work. Traditional frequentist approaches often lack the flexibility needed to analyse such data meaningfully. This paper presents a two-study Bayesian tutorial designed to address the small-N problem using logistic mixed-effects models. In Study 1, we analyse pilot data from 27 final-year or postgraduate students across three instructional conditions, using Bayesian mixed-effects modelling with non-informative (uniform) priors to explore effects of instruction, time, conditional type, and proficiency on participants’ binary responses in two language assessment tasks (a processing test and a production test). In Study 2, we build on the pilot by modelling follow-up data from a refined version of the study, focusing on the one treatment group only. Here, we incorporate highly informed priors derived from the posterior estimates of Study 1, demonstrating how prior information can improve estimation and interpretability, even with small datasets. This paper offers practical guidance on specifying priors, modelling binary outcomes, and applying Bayesian reasoning across iterative L2 research designs.