Simulation Study of Multiple Comparisons with the Average under Heteroscedasticity
| Autor: | Bang-Xing Liao, 廖邦幸 |
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| Rok vydání: | 2001 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 89 In many experimental situations, the average treatment performance within its own group is used as a benchmark to be compared with each individual treatment. Our study propose is to identify better than the average, worse than the average and not much difference from the average subsets based on the simultaneous two-sided confidence interval of each normal mean away from its average. One can use this procedure to screen a great number of wheat varieties better than the average in an agricultural experiment, or to screen drugs with longer hours of pain-relief than the average in a clinical trial. In this article, a simulation study of traditional, single-stage and two-stage multiple comparison procedures with the average for normal distribution under heteroscedasticity is investigated by the Monte-Carlo techniques. The length of simultaneous confidence interval and confidence coefficient for three procedures are simulated and it’s found that the simulated confidence coefficients can reach its nominal confidence coefficients for single-stage and two-stage multiple comparison procedures with the average while the traditional procedure fails to under heteroscedasticity. A biometrical example is given to illustrate the single-stage and two-stage procedures. These simultaneous confidence intervals are also used as an Analysis of Means(ANOM) to compared with the analysis of Variance proposed by 陳順益(1998) by their level of significance and their power. A generalized arithmetic mean as a benchmark is also considered. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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