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 treatments in terms of the distance between means against the alternative hypothesis of inequivalence. 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 alternative 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 numerical 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 between 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.
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