Standardized Effect Size for Single-Case Research
Also known as: Single-Case d, Within-Case Standardized Mean Difference, Design-Comparable Effect Size, Single-Case Standardized Mean Difference
A standardized effect size for single-case research expresses the difference between treatment and baseline phases in standard-deviation units so that it can be placed on the same scale as the familiar between-groups Cohen's d and combined across studies in a meta-analysis. The design-comparable estimator of Hedges, Pustejovsky, and Shadish (2012) explicitly models within-case and between-case variation and applies a small-sample correction, addressing the long-standing problem that nonoverlap indices and naive single-case d statistics are not comparable to the effect sizes used in group-design research.
Key highlights
- Places single-case effects on the same standardized metric as between-groups Cohen's d, enabling cross-design comparison and synthesis.
- Built on an explicit hierarchical model that separates within-case from between-case variation rather than ignoring the distinction.
- Includes a principled small-sample bias correction and a variance estimate, supporting confidence intervals and meta-analytic weighting.
- Grounded in mainstream meta-analytic theory, lending single-case synthesis the same statistical footing as group-design synthesis.
Intuition
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How it works
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When to use it
Use a design-comparable standardized effect size when you need a single-case effect on the same scale as group-design research — most importantly when synthesizing single-case studies in a meta-analysis or comparing them with randomized-trial effects. It requires replication across cases (ideally several) so the between-case variance can be estimated, and reasonably modeled autocorrelation. It is less suitable for a one-off single case with no replication (where the between-case variance is unidentifiable and nonoverlap indices are more honest), or when the outcome scale is so idiosyncratic that a standardized mean difference is hard to interpret.
Strengths & limitations
- Places single-case effects on the same standardized metric as between-groups Cohen's d, enabling cross-design comparison and synthesis.
- Built on an explicit hierarchical model that separates within-case from between-case variation rather than ignoring the distinction.
- Includes a principled small-sample bias correction and a variance estimate, supporting confidence intervals and meta-analytic weighting.
- Grounded in mainstream meta-analytic theory, lending single-case synthesis the same statistical footing as group-design synthesis.
- Requires replication across multiple cases to estimate the between-case variance; it is not well defined for an isolated single case.
- Depends on correctly modeling autocorrelation and the variance structure, and is sensitive to misspecification.
- More computationally and conceptually demanding than nonoverlap indices, raising the barrier for routine practitioner use.
- Like all standardized mean differences it can be unstable or hard to interpret when baselines have floor/ceiling effects or strong trend.
Common pitfalls
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Applications
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Frequently asked
How is this different from just computing Cohen's d on one person's data?
Computing d by dividing a single person's phase difference by their own within-session standard deviation gives a within-case effect that is not on the same scale as a between-groups d, because the group-design denominator is the between-person standard deviation. The design-comparable estimator models both within-case and between-case variance and standardizes by their total, so the resulting d answers the question 'what between-subjects effect would this correspond to?' and can be meta-analyzed with group studies.
Why does the method need several cases?
The denominator requires an estimate of how much people differ from one another — the between-case variance. With only one case there is no information about between-case variation, so that component cannot be identified and a truly group-comparable standardized effect cannot be computed. Designs that replicate the effect across multiple cases (multiple-baseline-across-participants, for instance) supply the needed information; for a lone case, nonoverlap indices are the more honest summary.
Does it handle autocorrelation?
Yes — the estimator is derived within a hierarchical model that can represent serial dependence in the within-case observations, and the variance estimates and bias correction account for it. This is an advantage over nonoverlap indices, which ignore autocorrelation entirely. The trade-off is that results depend on the assumed correlation structure, so misspecifying it can bias the effect size and its standard error.
Sources
- 1.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.
- 2.Shadish, W. R., Hedges, L. V., & Pustejovsky, J. E. (2014). Analysis and meta-analysis of single-case designs with a standardized mean difference statistic: A primer and applications. Journal of School Psychology, 52(2), 123–147.
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Cite this page
ScholarGate. (2026, June 22). Standardized Effect Size for Single-Case Research. ScholarGate. https://scholargate.app/social-work/standardized-effect-size-single-case