The majority of studies published in the emergency medicine literature attempt to show a difference between two interventions, but often fail to do so. Failing to detect a difference, however, is not the same as demonstrating that one intervention is at least as effective as or better than the other intervention, or that the two interventions are equivalent--a fine point that is often overlooked. The purpose of this paper is to review classical hypothesis testing and then introduce the methodology to determine whether one intervention is at least as effective as another intervention, or whether two interventions are equivalent. Appreciating the conceptual differences between failing to find a difference, demonstrating that one intervention is at least as effective as another, and demonstrating equivalence may lead to a better understanding of the true significance or potential significance of study results.