The Comparability of the Standardized Mean Difference Effect Size Across Different Measures of the Same Construct

Abstract

One of the most important effect sizes used in meta-analysis is the standardized mean difference (SMD). In this article, the conditions under which SMD effect sizes based on different measures of the same construct are directly comparable are investigated. The results show that SMD effect sizes from different measures of the same construct are directly comparable if and only if (Condition 1) there is a linear relationship between the true scores, and (Condition 2) there is a special linear relationship between the magnitude of the error variances of the involved measures. If only Condition 1 is met, then the reliability-corrected SMD effect sizes from the different measures are directly comparable. However, if Condition 1 is not met, then there will be nonlinear relationships between the true score metrics of two or more of the measures and systematic variability between SMD effect sizes that reflects these nonlinear relationships.

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