Equivalence Test and Sample Size Procedures for Standardized Mean Differences in ANCOVA Studies

This article presents exact equivalence tests of standardized mean differences in ANCOVA studies. As an alternative to the traditional hypothesis testing for confirming the existence of substantial differences, the proposed equivalence procedure helps appraise whether the target effect is practically identical to a meaningful magnitude or a trivial value. The general formulation of standardized mean differences permits a wide range of research hypotheses to be examined, including the contrast effect for treatment comparisons and the interaction effect in factorial designs. The associated power and sample size formulas are also described to accommodate the stochastic features of response and covariate variables. The usefulness and applicability of the suggested techniques are illustrated with two examples for the comparison of intervention effects and the assessment of training interactions. Extensive empirical investigations demonstrate the importance of random features and disparity of covariate variables in power and sample size calculations.