Generalized Weighted Analysis of Variance

• Main Authors: Chia-ling Hsu, 徐佳玲
• Other Authors: none
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/79300669501335589207

碩士 === 靜宜大學 === 應用數學研究所 === 95 === To test the mean difference for the heterogeneitic group data, Cheng Shang-Bo developed the weighted ANOVA with an approximate F-test. According the concept of generalized P-value, a modified method is developed by this study, named the generalized weighted ANOVA. The resulted test is compared with one-way ANOVA, Kruskal-Wallis test, generalized F-test, and weighted ANOVA with simulation technique to assess its suitability. It is found that these five methods are all suitable for testing the group mean difference for the homogeneitic data, and their powers of test are closed. However, for the heterogeneitic data, one-way ANOVA and Kruskal-Wallis test are not applicable. The other three methods achieve higher values of powers, and the type I error probabilities for those two methods developed by generalized P-value are smaller . In addition, the effect of the sample size is studied for weighted ANOVA and generalized weighted ANOVA. It is found that the weighted ANOVA is not suitable for small sample, while the type I error probability is within the acceptable range for a middle or a large sample. Generalized weighted ANOVA won’t be affected by the sample size.