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Previous research indicates that three-level modeling is a valid statistical method to make inferences from unstandardized data from a set of single-subject experimental studies, especially when a homogeneous set of at least 30 studies are included ( Moeyaert, Ugille, Ferron, Beretvas, & Van den Noortgate, 2013a ). When single-subject data from multiple studies are combined, however, it often occurs that the dependent variable is measured on a different scale, requiring standardization of the data before combining them over studies. One approach is to divide the dependent variable by the residual standard deviation. In this study we use Monte Carlo methods to evaluate this approach. We examine how well the fixed effects (e.g., immediate treatment effect and treatment effect on the time trend) and the variance components (the between- and within-subject variance) are estimated under a number of realistic conditions. The three-level synthesis of standardized single-subject data is found appropriate for the estimation of the treatment effects, especially when many studies (30 or more) and many measurement occasions within subjects (20 or more) are included and when the studies are rather homogeneous (with small between-study variance). The estimates of the variance components are less accurate.

One way to combine data from single-subject experimental design studies is by performing a multilevel meta-analysis, with unstandardized or standardized regression coefficients as the effect size metrics. This study evaluates the performance of this approach. The results indicate that a multilevel meta-analysis of unstandardized effect sizes results in good estimates of the effect. The multilevel meta-analysis of standardized effect sizes, on the other hand, is suitable only when the number of measurement occasions for each subject is 20 or more. The effect of the treatment on the intercept is estimated with enough power when the studies are homogeneous or when the number of studies is large; the power of the effect on the slope is estimated with enough power only when the number of studies and the number of measurement occasions are large.

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The quantitative methods for analyzing single-subject experimental data have expanded during the last decade, including the use of regression models to statistically analyze the data, but still a lot of questions remain. One question is how to specify predictors in a regression model to account for the specifics of the design and estimate the effect size of interest. These quantitative effect sizes are used in retrospective analyses and allow synthesis of single-subject experimental study results which is informative for evidence-based decision making, research and theory building, and policy discussions. We discuss different design matrices that can be used for the most common single-subject experimental designs (SSEDs), namely, the multiple-baseline designs, reversal designs, and alternating treatment designs, and provide empirical illustrations. The purpose of this article is to guide single-subject experimental data analysts interested in analyzing and meta-analyzing SSED data.