Traditional and bayesian approaches for testing mean equivalence and a lack of association

Abstract

Researchers are often interested in demonstrating that variables are unrelated. However, declar-ing a lack of relationship (e.g., no mean difference or no correlation) through nonrejection of the traditional null hypothesis (e.g., H0: µ1 − µ2 = 0; H0: ρ = 0) is inappropriate. The two one-sided tests (TOST) method for testing mean equivalence is a popular approach to resolving this issue, and has been adapted for testing equivalence with various test statistics. In this study, two Bayesian alternatives to the TOST method for assessing equivalence of means or a lack of correlation were examined and compared to their equivalence testing analogs. The first is the Bayes factor method, which compares the relative evidence that the data were more likely under one hypothesis than another. The second method is Bayesian parameter estimation, using highest density intervals, which estimates a posterior distribution and seeks to demonstrate that the interval falls within bounds for establishing equivalence. The power rates of these procedures were first compared in a simulation study. Next, empirical examples of each of the approaches are shown using an openly available dataset on personality traits. Results identify the benefits and limitations of these competing alternatives under various testing conditions, and highlight the importance of using equivalence interval based methods in the behavioral sciences.