Effect size estimates are primary outcomes of empirical studies, used to describe the extent to which a phenomenon of interest is present in a sample or in the population. They are vital for communicating results of empirical studies, for conducting a-priori power analyses, and for summarizing findings in meta-analyses. Standardized effect sizes scale raw effect sizes to a common, unit-free scale. Cohen's d is the standardized effect size most widely used to report differences in means between two groups. It standardizes the raw mean difference by an estimate of sample variability, providing a scale-free metric for comparisons across different measures and studies. However, because measures of variability reflect both between-person differences and measurement error, Cohen's d conflates effect size with reliability of the measurement instrument, potentially leading to confusion and misinterpretation. Here, I propose to interpret the letter d in Cohen's d to mean detectability, emphasizing that it measures the degree to which an effect is noticeable by an observer, naturally influenced by the precision of the measurement instrument and the study design. Additionally, I demonstrate how to adjust Cohen's d for unreliability, which has practical implications for sample size planning and meta-analyses of mean differences.
Andreas M. Brandmaier (Tue,) studied this question.