On testing the equivalence of treatments using the measure of range

A studentized range test is proposed to test the hypothesis of average equivalence of treat- ments in terms of the distance between means against the alternative hypothesis of in- equivalence. A least favorable configuration (LFC) of means to guarantee the maximum level at a null hypothesis and a LFC of means to guarantee the minimum power at an al- ternative hypothesis are obtained. The level and power of the test are fully independent of the unknown means and variances. For a given level and a given power, the critical value and the required sample size for an experiment can be simultaneously determined, and the tables of critical values and sample sizes are provided for practitioners. A real numeri- cal example to demonstrate the use of the test procedure is provided. In situations where the common population variance is unknown and the equivalence is the actual distance be- tween means without standardization, a two-stage sampling procedure can be employed to find these solutions. It proves to be a quite feasible solution for practitioners.