Investigation of Regression-Based Effect Size Methods Developed in Single-Subject Studies.
Your choice of regression-based effect-size formula can swing Cohen’s d from near-zero to very large on the same single-case data, so report the method explicitly.
01Research in Context
What this study did
Sen (2022) ran the same single-case data set through five different regression-based formulas for Cohen’s d.
Each formula is supposed to measure how big the treatment effect is. The paper shows, step-by-step, how much the answers move.
What they found
The five methods gave Cohen’s d values from almost zero to very large on the exact same graph.
One formula said the effect was tiny. Another said it was huge. The spread was 0.003 to 3.47.
How this fits with other research
Campbell (2004) already warned that four older indices can disagree; Sen (2022) proves the same mess happens with newer regression tools.
Carter (2013) argued overlap metrics are fine if you separate control from size—Nihal’s numbers show why that split matters, because size itself is unstable.
Barnard-Brak et al. (2020) offered Bayesian N-of-1 as one stable alternative; Nihal doesn’t reject it, but shows regression d is still shaky.
Manolov et al. (2022) give fresh consistency checks with Brinley plots; pairing their plots with Nihal’s d values may help you spot when a big number is real or just a formula quirk.
Why it matters
When you write a report or grant, always name the exact regression formula you used. Add a line like “Cohen’s d = 1.8 (split-middle regression).” This small note keeps your meta-analysis from mixing apples and oranges and saves the next BCBA from chasing a ghost effect.
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02At a glance
03Original abstract
The purpose of this study is to provide a brief introduction to effect size calculation in single-subject design studies, including a description of nonparametric and regression-based effect sizes. We then focus the rest of the tutorial on common regression-based methods used to calculate effect size in single-subject experimental studies. We start by first describing the difference between five regression-based methods (Gorsuch, White et al., Center et al., Allison and Gorman, Huitema and McKean). This is followed by an example using the five regression-based effect size methods and a demonstration how these methods can be applied using a sample data set. In this way, the question of how the values obtained from different effect size methods differ was answered. The specific regression models used in these five regression-based methods and how these models can be obtained from the SPSS program were shown. R2 values obtained from these five methods were converted to Cohen's d value and compared in this study. The d values obtained from the same data set were estimated as 0.003, 0.357, 2.180, 3.470, and 2.108 for the Allison and Gorman, Gorsuch, White et al., Center et al., as well as for Huitema and McKean methods, respectively. A brief description of selected statistical programs available to conduct regression-based methods was given.
Behavior modification, 2022 · doi:10.1177/01454455211054018