Exploratory graphical analysis of SCED effect sizes at different levels: Sensitivity analysis using modified Brinley plots

The data gathered via single-case experimental designs usually lead to obtaining more than one effect size, quantifying the difference between each baseline condition (A) and intervention condition (B). These effect sizes resulting from the A-B comparisons present a nested structure, as there can be several effect sizes for the same participant, or one or several effect sizes per participant if there are several participants in the same study. There is no single optimal way to quantitatively aggregate these effect sizes within a study without making assumptions. Thus, in the current text, we propose to depict several possible means of effect sizes, weighted and unweighted, at different levels. Specifically, we propose to extend modified Brinley plots, so that they can be used for performing a sensitivity analysis, in order to explore the degree to which the conclusions about intervention effectiveness would vary according to how the aggregate value is computed. We focus on exploratory or descriptive quantifications and plots, in order to avoid using inferential tools requiring parametric assumptions or any sophisticated analytical techniques that may not be fully and correctly understood. The proposals are illustrated with previously published behavioral data and implemented in a user-friendly freely available website.