Design-Comparable Effect Sizes in Multiple Baseline Designs: A General Modeling Framework

In single-case research, the multiple baseline design is a widely used approach for evaluating the effects of interventions on individuals. Multiple baseline designs involve repeated measurement of outcomes over time and the controlled introduction of a treatment at different times for different individuals. This article outlines a general framework for defining effect sizes in multiple baseline designs that are directly comparable to the standardized mean difference from a between-subjects randomized experiment. The target, design-comparable effect size parameter can be estimated using restricted maximum likelihood together with a small sample correction analogous to Hedges's g. The approach is demonstrated using hierarchical linear models that include baseline time trends and treatment-by-time interactions. A simulation compares the performance of the proposed estimator to that of an alternative, and an application illustrates the model-fitting process.