Examining the normality assumption of a design-comparable effect size in single-case designs

What Works Clearinghouse (WWC, 2022) recommends a design-comparable effect size (D-CES; i.e., g_AB) to gauge an intervention in single-case experimental design (SCED) studies, or to synthesize findings in meta-analysis. So far, no research has examined g_AB's performance under non-normal distributions. This study expanded Pustejovsky et al. (2014) to investigate the impact of data distributions, number of cases (m), number of measurements (N), within-case reliability or intra-class correlation (ρ), ratio of variance components (λ), and autocorrelation (ϕ) on g_AB in multiple-baseline (MB) design. The performance of g_AB was assessed by relative bias (RB), relative bias of variance (RBV), MSE, and coverage rate of 95% CIs (CR). Findings revealed that g_AB was unbiased even under non-normal distributions. g_AB's variance was generally overestimated, and its 95% CI was over-covered, especially when distributions were normal or nearly normal combined with small m and N. Large imprecision of g_AB occurred when m was small and ρ was large. According to the ANOVA results, data distributions contributed to approximately 49% of variance in RB and 25% of variance in both RBV and CR. m and ρ each contributed to 34% of variance in MSE. We recommend g_AB for MB studies and meta-analysis with N ≥ 16 and when either (1) data distributions are normal or nearly normal, m = 6, and ρ = 0.6 or 0.8, or (2) data distributions are mildly or moderately non-normal, m ≥ 4, and ρ = 0.2, 0.4, or 0.6. The paper concludes with a discussion of g_AB's applicability and design-comparability, and sound reporting practices of ES indices.