A quotient effect size for educational interventions

This paper introduces a simple, quotient effect size, termed 𝑞 (for ‘quotient’), suitable for reporting on the effectiveness of educational interventions. The quotient effect size for a pre-test-post-test design is defined as the gain score (i.e., post-test minus pre-test) for the intervention group, divided by the gain score for the control group. This quotient effect size measure is easy to calculate and interpret, and, like Cohen’s 𝑑, is scale-free. However, it achieves scale independence without acquiring the well-reported difficulties that arise with standardized effect sizes, such as Cohen’s 𝑑, as a result of incorporating the standard deviation. Since the standard deviation is sensitive to many factors that are unrelated to ‘the effect’, Cohen’s 𝑑 is not a pure measure of ‘effect’. By contrast, the quotient effect size, 𝑞, is dimensionless, without needing to involve the standard deviation, and is consequently intuitively easy to comprehend and communicate. For example, a 𝑞 of 1.2 would mean that the intervention group improved by 20% more than the control group did. This paper explores the advantages of using 𝑞 as an effect size for reporting on the effectiveness of educational interventions, as compared with Cohen’s 𝑑, and addresses some possible objections.