Equivalence tests for comparing correlation and regression coefficients

Equivalence tests are an alternative to traditional difference-based tests for demonstrating a lack of association between two variables. While there are several recent studies investigating equivalence tests for comparing means, little research has been conducted on equivalence methods for evaluating the equivalence or similarity of two correlation coefficients or two regression coefficients. The current project proposes novel tests for evaluating the equivalence of two regression or correlation coefficients derived from the two one-sided tests (TOST) method (Schuirmann, 1987, J. Pharmacokinet. Biopharm, 15, 657) and an equivalence test by Anderson and Hauck (1983, Stat. Commun., 12, 2663). A simulation study was used to evaluate the performance of these tests and compare them with the common, yet inappropriate, method of assessing equivalence using nonrejection of the null hypothesis in difference-based tests. Results demonstrate that equivalence tests have more accurate probabilities of declaring equivalence than difference-based tests. However, equivalence tests require large sample sizes to ensure adequate power. We recommend the Anderson–Hauck equivalence test over the TOST method for comparing correlation or regression coefficients.