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系統識別號 U0002-2505201122180100
中文論文名稱 平均數等價性之概度比檢定
英文論文名稱 Likelihood Ratio Tests for the Equivalence of Means
校院名稱 淡江大學
系所名稱(中) 數學學系博士班
系所名稱(英) Department of Mathematics
學年度 99
學期 2
出版年 100
研究生中文姓名 徐晉鋒
研究生英文姓名 Ching-feng Hsu
學號 891150020
學位類別 博士
語文別 中文
口試日期 2011-05-13
論文頁數 81頁
口試委員 指導教授-陳順益
委員-黃文瀚
委員-林宗儀
委員-許英麟
委員-沈宗荏
委員-黃逸輝
委員-陳順益
中文關鍵字 區間假設  複合假設  生體等效性假設  覆蓋機率  全距統計量 
英文關鍵字 Interval hypotheses  composite hypothesis  bioequivalence hypothesis  coverage probability  range statistic 
學科別分類
中文摘要 探討兩組或多組母體平均數是否有差異性,傳統方法是用點假設檢定。然而在點假設檢定中,只要樣本數夠大,就會拒絕虛無假設,因此許多研究轉而利用區間假設檢定來取代。本文利用概度比 (LR) 檢定的方法,推導出針對一群母體平均數分佈在非不同區域的常態分佈母體,其等價性的檢定程序。並以蒙地卡羅模擬方法對LR檢定和Bau, Chen和Xiong (1993) 所推導出的student化全距檢定法做比較。由電腦模擬的結果顯示,student化全距檢定法只有在LFC的均數結構下,才有檢定的名目水準。LR檢定程序雖然略顯不太保守,但當樣本數夠大時,在虛無假設成立的條件下皆能得到檢定的名目水準,並比student化全距檢定程序更具檢定力。而且LR檢定程序易於施行,直接使用現有機率分配表格,不需要另外造表,亦無繁雜的計算。另外,亦可應用在母體數k≥2的情形。
英文摘要 The classical hypothesis for testing the difference between two or several normal means is to test the null hypothesis that the population means are equal. However, the null hypothesis will always be rejected for a large enough sample size. We derive likelihood ratio (LR) tests for the null hypothesis of equivalence that the normal means fall into a practical indifference zone. Also, we carry out an extensive simulation study to compare the performance of the LR test and the studentized range test of Bau, Chen and Xiong(1993). Simulation results indicate that the nominal level of the studentized range test occurs only under the least favorable configuration of means. The LR test might be slightly anticonservative statistically, but when the sample sizes are large, it always produces the nominal level for mean configurations under the null hypothesis, more powerful than the studentized range test. The LR test can easily be constructed and is a straightforward application that requires only current existing statistical tables, with no complicated computations. Moreover, the LR test can applied to k≥2 treatments.
論文目次 1 簡介 1
2 變異數已知且相等的母體平均數不等價性之概度比檢定 3
2.1 定理2.1 ..................................... 4
2.1.1 定理2.1證明 ........................... 4
2.2 系理2.1 ..................................... 24
2.2.1 系理2.1證明............................ 24
2.3 系理2.2 ..................................... 25
2.3.1 系理2.2證明 ........................... 26
3 變異數未知但相等的母體平均數不等價性之概度比檢定 39
3.1 定理3.1 ..................................... 39
3.1.1 定理3.1證明 ........................... 40
3.2 系理2.2 ..................................... 57
3.2.1 系理3.1證明............................ 58
3.3 系理3.2 ..................................... 59
3.3.1 系理3.2證明 ........................... 59
4 概度比檢定法和student化全距檢定法之比較 73
5 結論與建議 78
參考資料 80
參考文獻 1.Anderson, S. and Hauck, W. W.,(1983). "A New Procedure for Testing Equivalence in Comparative Bioavailability and Other Clinical Trials". Communications in Statistics- Theory and Methods, 12, 2663-2692.
2.Bau, J.J., Chen, H.J., and Xiong, M., (1993). "Percentage Points of the Studentized Range Test for Dispersion of Normal Means". Journal of the Statistics and Computer Simulation, 44 , 149-163.
3.Berger, R. L.; Jason C. Hsu,(1996). "Bioequivalence Trials, Intersection-union Tests and Equivalence Confidence Sets". Statistical Science, 11(4), 283-302.
4.Chen, S. Y.; Chen, H. J.,(1999). "A Range Test for the Equivalency of Means under Unequal Variances". Technometrics, 41, 250-260.
5.Chow, S. C.; Liu, J. P., "Design and Anakysis of Bioavailability and Bioequivalence Studies". 2nd Edition, Marcel Dekker: New York, 2000.
6.Dunnett C. W.; Gene, M.,(1977). "Significance Testing to Establish Equivalence between Treatments, with Special Reference to Data in the Form of 2×2 Tables". Biometrics, 33. 593-602.
7.Gordon, R D.,(1941) "Values of Mills' Ratio of Area to Bounding Ordinate and of the Normal Probability Integral for Large Values of the Argument". The Annals of Mathematical Statistics, 12, 364-366.
8.Giani, G.; Finner, H.,(1991). "Some General Results on Least Favorable Parameter Configurations with Special Reference to Equivalence Testing and the Range Statistic". Journal of Statistical Planning and Inference, 28, 33-47.
9.Geretschlager, R; Janous, W.,(2001) "Generalized Rearrangement Inequalities". The Americam Mathematical Monthly, 108(2), 158-165.
10.Hauck, W. W., Bois, F., Hyslop, T., Gee, L., Anderson, S.(1997). "A Parametric Approach to Population Bioequivalence". Statistics in Medicine, 16, 441-454.
11.Lakshminarayanan, M. Y.; Patel, H. I.; Stager, W. J.,(1994). "Multistage Test Procedure for Testing Blackwelder's Hypothesis of Equivalence". Journal of Biopharmaceutical Statistics, 4, 165-171.
12.Nam, J. M.,(1995). "Sample Size Determination in Stratified Trials to Establish the Equivalence of Two Treatments". Statistics in Medicine, 14, 2037-2049.
13.Rohatgi, V. K. "An Introduction to Probability Theorem and Mathematical Statistics". John Wiley & Sons, 1976.
14.SAS Institute Inc. (1999), "SAS Language: Reference, Version 8." SAS Institute Inc., Cary, NC.
15.Schuirmann, D. J. "A Comparison of Two One-sided Tests Procedure and the Power Approach for Assessing the Equivalence of Average Bioavailability". Jouranl of Pharmacokinetics and Biopharmaceutics, 15 657-680.
16.Soms, A. P. (1976) "An Asymptotic Expansion for the Tail Area of the t Distribution". Journal of the American Statistical Association, 71, 728-730.
17.Wellek, S.,(1996). "A New Approach to Equivalence Assessment in Standard Comparative Bioavailability Trials by means of Mann-Whitney Statistic". Biometrical Journal, 38, 695-710.
18.Wellek, S., "Testing Statistical Hypotheses of Equivalence". Chapman and Hall/CRC: Boca Raton, FL, 2003.
19.Weslake, W. J.,(1972). "Use of Confidence Intervals in Analysis of Comparative Bioavailability Trials". Journal of Pharmaceutical Science, 61, 1340-1341.
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