A d-statistic for single-case designs that is equivalent to the usual between-groups d-statistic

Abstract

We describe a standardised mean difference statistic (d) for single-case designs that is equivalent to the usual d in between-groups experiments. We show how it can be used to summarise treatment effects over cases within a study, to do power analyses in planning new studies and grant proposals, and to meta-analyse effects across studies of the same question. We discuss limitations of this d-statistic, and possible remedies to them. Even so, this d-statistic is better founded statistically than other effect size measures for single-case design, and unlike many general linear model approaches such as multilevel modelling or generalised additive models, it produces a standardised effect size that can be integrated over studies with different outcome measures. SPSS macros for both effect size computation and power analysis are available.

Keywords:

• Single-case designs
• Analysis
• Meta-analysis
• Standardised mean difference
• d-Statistic

This research was supported in part by grant R305D100046 from the Institute for Educational Sciences, US Department of Education, and by a grant from the University of California Office of the President to the University of California Educational Evaluation Consortium.