A quotient effect size for educational interventions

<p>This paper introduces a simple, quotient effect size, termed �� (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 ��, is scale-free. However, it achieves scale independence without acquiring the well-reported difficulties that arise with standardized effect sizes, such as Cohen’s ��, 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 �� is not a pure measure of ‘effect’. By contrast, the quotient effect size, ��, is dimensionless, without needing to involve the standard deviation, and is consequently intuitively easy to comprehend and communicate. For example, a �� 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 �� as an effect size for reporting on the effectiveness of educational interventions, as compared with Cohen’s ��, and addresses some possible objections.</p>