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

• Published in: Journal of educational and behavioral statistics Vol. 39; no. 5; pp. 368 - 393
• Main Authors: Pustejovsky, James E., Hedges, Larry V., Shadish, William R.
• Format: Journal Article
• Language: English
• Published: Los Angeles, CA SAGE Publications 01.10.2014; American Educational Research Association
• Subjects: Comparative Analysis; Computation; Covariance matrices; Effect Size; Estimation bias; Estimation methods; Estimators; Experiment design; Goodness of Fit; Hierarchical Linear Modeling; Intervention; Maximum Likelihood Statistics; Measurement; Meta Analysis; Modeling; Outcome Measures; Parametric models; Point estimators; Research Design; Simulation; Statistical Analysis; Statistical variance; effect size; Single-case research; hierarchical linear model
• ISSN: 1076-9986; 1935-1054
• DOI: 10.3102/1076998614547577

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.