Determination of the detectable maximum difference among parameters in hypothesis testing / Yap Bee Wah and Pooi Ah Hin

Consider a one-way classification model with r treatments and n, experimental units for the ith treatment. Let μ1, μ2,...,μr be the r treatment means and d the maximum difference between any two treatment means. This study focuses on determining the detectable maximum difference between any two means. We examine the scenario when the null hypothesis that the r treatment means are all equal (H0 : μ1 = μ2 = ...= μr) is accepted. When H0 is accepted, the reliability of the result of the test is given by the power function which is a function of μ = (μ1, μ2,...,μr)T and the error variance σ2. It is not easy to use this power function to assess the reliability of the result of the test because it is a function of many variables. In this study, the information contained in the power function is summarized by an interval [0,d+] which represents the likely values of the detectable maximum difference between any two treatment means. Small value of d+ will indicate that the acceptance result given by the test is reliable.