Tests on Group Means for Heterogeneitic Data

• Main Authors: Shang-Bo Chen, 陳尚伯
• Other Authors: Tai-Fang Chen
• Format: Others
• Language: zh-TW
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/55502565999612093225

碩士 === 靜宜大學 === 應用數學研究所 === 93 === In this study, a weighted ANOVA, which uses the reciprocal of standard deviations as the weights, was proposed to test the mean difference for the heterogeneitic data. The proposed method was compared with other existing methods including one-way ANOVA, Kruskal-Wallis test and the generalized F-test for one-way ANOVA by Weerahandi (1995). By using simulation techniques, the probability of type I error and the power of test were estimated to evaluate the suitability and efficiency of these methods. According to the results of this study, for the homogeneitic data, any of these four methods is suitable and no obvious differences on the power were detectable. For the heterogeneitic data, the weighted ANOVA is suitable and also has higher power than any other methods. The Weerahandi’s method is also suitable, but its power is lower than the weighted ANOVA for the heterogeneitic data. As regards to the other two methods, both the suitability and efficiency are relatively low.