It is not uncommon that we encounter the situations in which our goal is to establish an equivalence rather than to detect a difference between the distributions of the two comparison groups. When the underlying proportions vary substantially between categories, we may wish to consider use of the proportion ratio (PR) in establishing equivalence. This paper develops test procedures for detecting equivalence based on the PR in paired-sample data for both nominal and ordinal scales. This paper further develops procedures to accommodate the case of testing for symmetric equivalence. Finally, this paper includes examples to illustrate the practical use of the procedures developed here.

equivalence test, proportion ratio, paired-sample, intersection-union test.