The Extended Anderson and Hauck Tests and Sample Size Procedures for Equivalence Assessment in Simple Linear Regressions

This study describes extended Anderson and Hauck procedures for equivalence testing of slope coefficients and mean responses in one and two regression lines. The general formulation of asymmetric equivalence ranges permits a wide variety of equivalence questions to be tested for a target magnitude or a negligible value. Specifically, the equivalence tests are useful for assessing negligible trend and similar response in a single regression line, and for evaluating unimportant interaction-moderation effect and comparable simple effect between two linear regression lines. The associated power functions and sample size procedures are also derived and compared under the random and fixed model settings. According to the analytic justification and empirical assessment, the exact approaches have a clear advantage over the approximate formulas for accommodating the full stochastic nature of both the response and predictor variables. Computer algorithms are also provided for conducting the proposed equivalence tests, power calculations, and sample size determinations in simple linear regressions.