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Hypothesis Testing for Equivalence Defined on Symmetric Open Intervals

There are many industrial applications for which it is desirable to know whether one product can act as a substitute for another. Examples include product modifications when ingredients change, substitution of generic drugs for brand-name drugs, and modifications of products in response to government regulations. In addition, some companies develop products that are direct substitutes for those of their competitors and make advertising claims concerning their equivalency. Using an open interval within which to define equivalence, exact and approximate methods for testing a null hypothesis of non equivalence are given. In each case, examples are provided. Comparisons are made between these novel methods and existing methods, including the “two one-sided tests” (TOST) method.