Bayes factor for single-case ABAB design data

The ABAB design is frequently used among single-case experimental designs (SCED). Bayesian methods have recently received increasing attention for the analysis of SCED data. de Vries and Morey (Psychol Methods 18:165–185, 2013) proposed a method for examining intervention effects using the Bayes factor. However, their method can only be applied to the AB design, which is the simplest, yet has limited applicability. In this study, we extended their method to ensure its application to the ABAB design. Two models were developed: Model A treated the intervention effect by combining two intervention phases, and Model B included three parameters of change in level. Upon applying these models to a real dataset (quoted from Uchida and Tanji, Jpn J Learn Disabil 30:73–84, 2021), both models detected the intervention effect. Model A (a simplified and parsimonious model) was supported by the Bayes factor calculated using the bridge sampling method. In SCED studies, the number of data points, which corresponds to the sample size in other applications, is generally small. Thus, the evaluation of treatment effects based on the Bayes factor has the potential to overcome this shortcoming of SCED data and provide a valid outcome evaluation tool. © 2023, The Behaviormetric Society.