Calculating Effect Sizes for Single-Case Research: An Introduction to the SingleCaseES and scdhlm Web Applications and R Packages


James E. Pustejovsky


April 26, 2023


Small is Beautiful {Once More}



This workshop will provide an introduction to effect size calculations for single-case research designs, focused on two interactive web applications (or “apps”) and accompanying R packages. I will begin by describing how to organize raw data from a single-case or n-of-1 study for purposes of using the apps, as well as for archiving and sharing with the research community. I will then introduce the SingleCaseES app, which provides tools for calculating case-specific effect size indices such as the non-overlap of all pairs, within-case standardized mean difference, and log-response ratio. All of these effect sizes describe intervention effects at the level of the individual participant. I will demonstrate use of the SingleCaseES app for calculating an effect size from a single data series as well as for calculating one or multiple effect sizes across multiple data series (with the latter being especially useful when conducting meta-analyses across multiple cases and studies). In the final section of the workshop, I will introduce the scdhlm app, which provides an interface for calculating between-case standardized mean difference (BC-SMD, also known as “design-comparable”) effect sizes. BC-SMDs are study-level summary effect sizes that are theoretically comparable to effect size indices commonly used in between-group experimental designs. BC-SMDs are defined based on a hierarchical model for the data from a single-case design that includes multiple participants. I will discuss the data requirements, model-building process, and choice of summary effect size for calculating a BC-SMD, while demonstrating how to use the scdhlm app. In each section of the workshop, I will also show how the interactive apps can facilitate learning to carry out effect size calculations using reproducible R code.

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