The Three-Level Synthesis of Standardized Single-Subject Experimental Data: A Monte Carlo Simulation Study

Previous research indicates that three-level modeling is a valid statistical method to make inferences from unstandardized data from a set of single-subject experimental studies, especially when a homogeneous set of at least 30 studies are included ( Moeyaert, Ugille, Ferron, Beretvas, & Van den Noortgate, 2013a ). When single-subject data from multiple studies are combined, however, it often occurs that the dependent variable is measured on a different scale, requiring standardization of the data before combining them over studies. One approach is to divide the dependent variable by the residual standard deviation. In this study we use Monte Carlo methods to evaluate this approach. We examine how well the fixed effects (e.g., immediate treatment effect and treatment effect on the time trend) and the variance components (the between- and within-subject variance) are estimated under a number of realistic conditions. The three-level synthesis of standardized single-subject data is found appropriate for the estimation of the treatment effects, especially when many studies (30 or more) and many measurement occasions within subjects (20 or more) are included and when the studies are rather homogeneous (with small between-study variance). The estimates of the variance components are less accurate.