Testing for individual and population equivalence based on the proportion of similar responses

This paper focuses on the classical problem of comparison of treatment effects. We show that we can base a simple and intuitive approach to comparison of two treatments on the proportion of similar responses. This approach is equivalent to the standard comparison of the treatment means in the normal case with equal known variances, but is quite different in other cases. Our approach applies under two different settings: testing a null hypothesis of no treatment difference against an alternative hypothesis of a difference, and testing the null hypothesis of at least a specific difference against an alternative hypothesis of equivalence. We develop our approach both for parallel groups (independent samples), and cross-over (paired samples) studies. The two situations give rise to the known concepts of population and individual equivalence. We present a graphical procedure to supplement the method.