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系統識別號 U0026-0812200913374117
論文名稱(中文) 處方等價檢定之研究
論文名稱(英文) Testing the Equivalence of Treatments From the Average
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 95
學期 2
出版年 96
研究生(中文) 謝姍澧
研究生(英文) Shan-Li Shie
電子信箱 slshie@stat.ncku.edu.tw
學號 R2694103
學位類別 碩士
語文別 英文
論文頁數 64頁
口試委員 口試委員-吳宗正
口試委員-陳占平
指導教授-溫敏杰
中文關鍵字 檢定水準  最保守均數組合  等價檢定 
英文關鍵字 Equivalence test  Least favorable mean configuration  Level of a test 
學科別分類
中文摘要 當母體變異數未知且相等時,我們令各母體平均數與所有母體的總平均數之間的最大距離為一測度,它用來檢定母體是否為處方等價,其中等價在實驗設計裡代表處理效應是不存在的。在虛無假設成立下,達到最大水準之均數組合,稱為最大水準均數組合。然而,在均數組合下,水準是與未知平均數、變異數完全獨立的。因此一旦知道虛無假設,我們就可以透過數值方法求得檢定的p值。之後,我用一個實驗設計例子來進行檢定並加以分析。
英文摘要 A distance statistic from the grand mean is proposed to test a null hypothesis of equivalence of treatments, where the "equivalence" stands for an event of treatment means falling into a negligible region around the grand mean. Least favorable mean configuration (LFMC) to guarantee
the maximum level at a null hypothesis is searched. It has been found that the level of the test is fully independent of the unknown means and variances. For a given null hypothesis, the p-value of the test can be evaluated by numerical method. An example to demonstrate the use of the test is given.
論文目次 1 Introduction to Equivalence Test 1
2 Level of a Test by Bonferroni Inequality 2
3 Level of a Test by Simultaneous Probability 8
4 Example 14
4.1 ‰æb}&(ANOVA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 Tj g(Equivalence) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5 Conclusion and Discussion 19
Reference 20
Appendix A 21
Appendix B 43
參考文獻 Berger, J. 0. (1985). Statistical Decision Theory, 2nd edition, Springer-Verlag, N.Y.
Casella, G. and Berger, R. L. (2002). Statistic Inference, 2nd edition, Thomson Learning.
Chen, S.Y. and Chen, H. J. (1999). A Range Test for the Equivalency of Means under Unequal Variances.Technometrics, Vol. 41, No. 3, 250-260.
Chen, H. J. and Lam, K. (1991). Percentage Points of a Studentized Range Statistic Arising from Non-identical Normal Random Variables. Communications in Statistics : Simulation and Computation, 20(4), 995-1047.
Chen, H. J., Xiong, M., and Lam, K. (1993). Range Tests for the Dispersion of Several Location Parameters. Journal of Statistical Planning and Inference, 36, 15-25.
Chow, S. C. and Liu, J. P. (1992). Design and Analysis of Bioavailability and Bioequivalence Studies, New York: Marcel Dekker.
Giani, G. and Finner, H. (1991). Some General Results on Least Favorable Parameter Config-urations with Special Reference to Equivalence Testing and the Range Statistic. Journal of Statistical Planning and Inference, 28, 33-47.
Lehmann, E. L. (1997). Testing Statistical Hypothesis, 2nd edition, Springer, N. Y.
Ott, L. and Longnecker, M. (2001). An introduction to Statistical Methods and Data Analysis, 5th edition, Duxbury.
Schuirmann, D. J. (1987). A Comparison of the Two One-Sided Tests Procedure and the Power Approach for Assessing the Equivalence of Average Bioavailability. Journal of Pharmacokinetics
and Biopharmaceutics, Vol. 15, No. 6, 657-680.
Wen, M. J. and Chen, H. J. (2006). A Studentized Range Test for the Equivalency of Normal Means under Heteroscedasticity. Computational Statistics and Data Analysis. 51, 1022-1038.
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