On the Extended Welch Test for Assessing Equivalence of Standardized Means

This article proposes a useful extension of the ANOVA F-test for examining mean differences for evaluating the comparability of standardized mean effects. The equivalence procedure presumably suffers from the same disadvantage as the traditional ANOVA F-statistic regarding the violations of homogeneous variance assumption. In view of the absence of vital clarification for theory development and supportive technique, this article provides a critical exposition of the extended Welch test for the equivalence of standardized means. To enhance the usefulness of equivalence testing, the theoretical properties and practical implications of the Welch-type procedure are demonstrated. Moreover, the corresponding power and sample size algorithms are described for advance planning of equivalence studies. Despite the approximate nature, the accuracy of Type I error rate, statistical power, and sample size calculations of the suggested equivalence test is justified under a wide range of model configurations. The proposed procedures are demonstrated with the data of a clinical trial regarding the comparative study of four antihypertensive treatments. A complete set of computer codes is presented to calculate the corresponding critical values, p-values, power levels, and sample sizes for data analysis and design planning of equivalence studies.