Standardized Mean Difference for Single-Case Designs
The between-case standardized mean difference is an effect-size measure that puts the result of a single-case experiment on the same numerical scale as Cohen's d from a conventional between-groups study, so that single-case and group findings can be combined in the same meta-analysis. Developed by Larry Hedges, James Pustejovsky, and William Shadish in 2012, it solves a long-standing problem: the many ad hoc nonoverlap indices used in single-case research (PND, PAND, IRD, Tau-U) are not comparable in scale to the standardized mean differences that dominate the broader evidence-synthesis literature. Their estimator models the single-case data with a hierarchical model that separates within-case variation from between-case variation, then standardizes the estimated treatment effect by the total standard deviation — the same denominator a between-subjects d would use. A 2013 extension specialized the estimator to multiple-baseline designs across individuals. The result is a design-comparable effect size with a known variance, suitable for disability and special-education research where single-case studies are abundant.
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- Hedges, L. V., Pustejovsky, J. E., & Shadish, W. R. (2012). A standardized mean difference effect size for single case designs. Research Synthesis Methods, 3(3), 224-239. · DOI 10.1002/jrsm.1052
- Hedges, L. V., Pustejovsky, J. E., & Shadish, W. R. (2013). A standardized mean difference effect size for multiple baseline designs across individuals. Research Synthesis Methods, 4(4), 324-341. · DOI 10.1002/jrsm.1086
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