A standardized mean difference effect size for multiple baseline designs

Single-case designs are a class of research methods for evaluating treatment effects by measuring outcomes repeatedly over time while systematically introducing different condition (e.g., treatment and control) to the same individual. The designs are used across fields such as behavior analysis, clinical psychology, special education, and medicine. Emerging standards for single-case designs have focused attention on methods for summarizing and meta-analyzing findings and on the need for effect sizes indices that are comparable to those used in between-subjects designs. In the previous work, we discussed how to define and estimate an effect size that is directly comparable to the standardized mean difference often used in between-subjects research based on the data from a particular type of single-case design, the treatment reversal or (AB)k design. This paper extends the effect size measure to another type of single-case study, the multiple baseline design. We propose estimation methods for the effect size and its variance, study the estimators using simulation, and demonstrate the approach in two applications.