Elements of significance testing with equivalence problems

The paper outlines an approach to the general methodological problem of equivalence assessment which is based on the classical theory of testing statistical hypotheses. Within this frame of reference it is natural to search for decision rules satisfying the same criteria of optimality which are customarily applied in deriving solutions to one- and two-sided testing problems. For three standard situations very frequently encountered in medical applications of statistics, a concise account of such an optimal test for equivalence is presented. It is pointed out that tests based on the well-known principle of confidence interval inclusion are valid in the sense of guaranteeing the prespecified level of significance, but tend to have an unnecessarily low efficiency.