Hierarchical linear models for the quantitative integration of effect sizes in single-case research

In this article, the calculation of effect size measures in single-case research and the use of hierarchical linear models for combining these measures are discussed. Special attention is given to meta-analyses that take into account a possible linear trend in the data. We show that effect size measures that have been proposed for this situation appear to be systematically affected by the duration of the experiment and fail to distinguish between effects on level and slope. To avoid these flaws, we propose to perform a multivariate meta-analysis on the standardized ordinary least squares regression coefficients from the study-specific regression equations describing the response variable.