The Equivalence Tests of Standardized and Unstandardized Mean Differences: Similar But Distinct

Abstract The usage and implications of equivalence testing of treatment means have received increased attention in applied sciences. Although the two one-sided tests (TOST) procedure of mean equivalence is widely used, the concept and implementation of equivalence procedures for standardized mean difference are not yet well elucidated. This paper presents a critical comparison of a uniformly most powerful test for standardized mean differences and the TOST method for unstandardized mean difference. Their distinctive features and technical relevance are examined and compared with respect to the rejection rules, confidence intervals, power functions, and equivalence bounds. This study adds to the fundamental understanding and general recognition of the two equivalence procedures. The statistical properties and computer algorithms in the equivalence assessment of standardized mean difference are also applicable to the evaluation of standardized mean effect in one- and paired-sample designs. Moreover, the findings can be readily extended to the appraisal of standardized contrast of treatment effects in factorial study.