A Comparison of Maximum Likelihood Ratio Test and Studentized Range Test for Interval Hypotheses

• Main Authors: Wei-Sheng Su, 蘇煒盛
• Other Authors: 陳順益
• Format: Others
• Language: zh-TW
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/38622539524896458264

碩士 === 淡江大學 === 數學學系碩士班 === 93 === In the classical hypothesis testing concerning several normal means the interest is to test the null hypothesis that the population means are equal. However, it is well known that the null hypothesis will always be rejected for a large enough sample size (See Berger (1985)). Recently, the problem of testing the hypothesis of equivalence of normal means (or the interval hypothesis) has been investigated by several authors. In this paper, an extensive simulation study was carried out to compare the performance of the likelihood ratio test of Chen and Hsu (2005), the studentized range test of Bau, Chen and Xiong (1993), and the intersection-union test of Casella and Berger (1990). The simulation results indicate that, for two populations (K=2), the nominal significance levels of all three tests occur at the boundary, and the performance of powers are similar. For the case of three populations (K=3), the nominal level of the studentized range test occurs only under the least favorable configuration of means. The likelihood ratio test can achieve the nominal level for any configuration of means and its power is larger than that of the studentized range test.