Equivalence testing for multiple groups

Testing for equivalence, rather than testing for a difference, is an important component of some scientific studies. While the focus of the existing literature is on comparing two groups for equivalence, real-world applications arise regularly that require testing across more than two groups. This paper reviews the existing approaches for testing across multiple groups and proposes a novel framework for multigroup equivalence testing under a Bayesian paradigm. This approach allows for a more scientifically meaningful definition of the equivalence margin and a more powerful test than the few existing alternatives. This approach also allows a new definition of equivalence based on future differences.