| Summary: | 博士 === 淡江大學 === 數學學系博士班 === 99 === The classical hypothesis for testing the difference between two or several normal means is to test the null hypothesis that the population means are equal. However, the null hypothesis will always be rejected for a large enough sample size. We derive likelihood ratio (LR) tests for the null hypothesis of equivalence that the normal means fall into a practical indifference zone. Also, we carry out an extensive simulation study to compare the performance of the LR test and the studentized range test of Bau, Chen and Xiong(1993). Simulation results indicate that the nominal level of the studentized range test occurs only under the least favorable configuration of means. The LR test might be slightly anticonservative statistically, but when the sample sizes are large, it always produces the nominal level for mean configurations under the null hypothesis, more powerful than the studentized range test. The LR test can easily be constructed and is a straightforward application that requires only current existing statistical tables, with no complicated computations. Moreover, the LR test can applied to k≥2 treatments.
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