Bias corrections for standardized effect size estimates used with single-subject experimental designs

A multilevel meta-analysis can combine the results of several single-subject experimental design studies. However, the estimated effects are biased if the effect sizes are standardized and the number of measurement occasions is small. In this study, the authors investigated 4 approaches to correct for this bias. First, the standardized effect sizes are adjusted using Hedges' small sample bias correction. Next, the within-subject standard deviation is estimated by a 2-level model per study or by using a regression model with the subjects identified using dummy predictor variables. The effect sizes are corrected using an iterative raw data parametric bootstrap procedure. The results indicate that the first and last approach succeed in reducing the bias of the fixed effects estimates. Given the difference in complexity, we recommend the first approach.