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題名 離散資料之多重比較
On multiple comparisons for discrete data
作者 蘇聖珠
貢獻者 宋文昌
蘇聖珠
日期 1991
1990
上傳時間 2-May-2016 17:02:43 (UTC+8)
摘要 在生物學，醫學，社會科學等領域中，吾人常須分析離散資料。例如:生物學家培育新品種動植物之存活率資料; 醫生臨床實驗所得數據;社會工作專家藉抽樣調查所得之問卷資料多為離散資料。若欲同時比較離散資料各類別均值間之差異最適當的統計方法之一是統計多重比較。
     針對離散性資料，傳統的多重比較方法幾全是Scheffe的卡方投影或自其衍生之方法。一般而言，Scheffe的方法失之過份保守，即聯合信賴域的周界太長。本文之主旨即在研究改善傳統的方法並提出較精確的多重比較計算法則。值得強調的是:我們所提的比較方法皆奠基於大樣本之常態近似法則。此乃因應小樣本時，待比較參數的估計式，其分配函數常極其複雜的情況下，所必須採取的權宜措施。
     在研究結構方面，本文係採確立聯合信賴區間的方式，並依所欲比較參數之三種常見型態，分別探討離散資料之三種抽樣模式:多項、二項、波松分配模式。在參數估計方面，我們皆盡可能將資料試以適當之log-linear 模式，再以該模式為基礎進行所欲比較參數的估計。經典著名離散資料實例(散見於著名離散資料分析著作中)驗證，本論文所提之多重比較方法確實能改善傳統的方法。
參考文獻 1. Bihapkar,V.P.and Somes,G.W. (1976).Multiple comparisons of matched proportions. Communications in Statistics, Ser.A,5,17-25.
     2. Bishop.Y.M.M,Fienberg,S.E. & Holland.P.W. (1975). Discrete Multivariate Analysis: Theory and Practice. MIT Press, Cambridge. Mass.
     3. Bofinger,E. (1985). Multiple comparisions and type III errors. Journal of the American Statistical Association 80,433-437.
     4. Cochran,W. (1950). The comparision of percentages in matched samples. Biometrika 37.256-266.
     5. Dorn,H.F. (1954).The relationship of cancer of the lung and the use of tobacco. American Statistician 8.7-13.
     6. Dowdall,J.A. (1974). Women`s attitudes toward employment and family roles. Sociological Analysis 35,251-262.
     7. Dunnett,C.W. (1980). Pairwise multiple comparisions In the homogeneous variance. unequal sample size case. Journal of the American Statistical Association 75.789-795.
     8. Dunnett,C.W. (1980).Pairwise multiple comparisions in the unequal variance case. Journal of the American Statistical Association 75.796-800.
     9. Fleiss,J. (1981). Statistial Methods for Rates and Proportions,2nd edition. Wiley , New York.
     10.Gold,R.Z. (1963). Tests auxiliary to x2 tests in a markov chain. Annuals of Mathematical Statistics 34.56-74.
     11.Goodman,L.A. (1964) .Simultaneous confidence limits for cross-product ratios in contingency tables. Journal of the Royal Statistical Society.Ser.B,26,86-102.
     12.Goodman,L.A. (1965) .On simultaneous confidence intervals for multinomial proportions. Technometrics 7.247-254.
     13.Haberman,S.J. (1978). Anaiysis of Qualitative Data, Vol.1. Academic Press. New York.
     14.Haldane.J.B.S. (1955). The estimation and significance of the logarithm of a ratio of frequencies. Ann.Hum.Genet.20,309-311.
     15.Hayter,A.J. (1984). A proof of the conjecture that the Tukey-Kramer multiple comparisons procedure is conservative. The Annals of Statistics 12,61-75.
     16.Hayter,A.J. (1985). A study of the Tukey multiple comparisons procedure including a proof of the Tukey conjecture for unequal sample sizes. unpublished doctoral dissertation, cornell University.
     17.Hochberg,Y.and Tamhane, A.C. (1987). Multiple comparison Procedures. Wiley,New York.
     18.Hsu.J.C. (1981).Simultaneous confidence intervals for all distances from the best. The Annals of Statistics 9,1026-1034.
     19.Hsu,J.C. (1989) .Simultaneous confidence intervals in the General Linear Models.Computer Sciense and Statistic:Proceedings of the 20th Symposium on the Interface,E.J.Wegman.D.T.Gantz.J.J.Miller editors. American Statistical Association. Alexandria, Virginia.
     20.Hsu,J.C.Soong,W.C. (1990) Using the Fast Fourier Transform to compute multiple comparisons with the best and subset selection critical values.Communications in Statistics 19(4) ,1377-1391.
     21.Jonnson.R.A.and Wichern.D.W. (1982). Appliced Multivariate Statistical Analysis. Prentice-Hall,Enflwood Cliffs, New Jersey.
     22.McCullagh.P.and Nelder.J.A. (1983) Generalized Linear Models Chapman and Hall.Hew York.
     23.Miller,R.G. (1981) .Simultanlous Statistical Inference,2nd edition. Springer-Verlag. New York.,Jukey,J.W. (1953) .The Promblem for multiple comparisons. Unpublished manuscript.
     24.Plackett,P.L. (1954).A reduction formula for normal multivariate integrals. Biometrika 41,351-360.
     25.Plackett,P.L. (1962).A note fo interactions in contingency tables. Journal of the Royal Statistical Society, Ser.B,24,162-166.
     26.Quesenberry, C.P.and Hurst,D.C. (1964) . Large sample simultaneous confidence intervals for multinomial proportions. Technometrics 6,191-195.
     27.Scheffe,H. (1959). The Analysis of Variance. Wiley,New York.
     28.Soong,vl.C. (1989) .Multiple comparisons for complex experimental designs. THESIS.
     29.Spurrier.J.D.and Isham,S.P. (1985).Exact simultaneous confidence intervals for pairwise comparisions of three normal means. Journal of the American Statistical Association 80.438-442.
     30.Tukey,J.W. (1953). The problem of multiple comparisons. Unpublished manuscript.
     31.Uusipaikka,E. (1985).Exact simultaneous confidence intervals for multiple comparisons among three or four values. Journal of the American Statistical Association 80.196-201.
     32.Welsch,R.E. (1977) . Stepwise multiple comparison procedure.Journal of the American Statistical Association 72,566-574.
描述 碩士
國立政治大學
統計學系
資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002005027
資料類型 thesis
dc.contributor.advisor 宋文昌zh_TW
dc.contributor.author (Authors) 蘇聖珠zh_TW
dc.creator (作者) 蘇聖珠zh_TW
dc.date (日期) 1991en_US
dc.date (日期) 1990en_US
dc.date.accessioned 2-May-2016 17:02:43 (UTC+8)-
dc.date.available 2-May-2016 17:02:43 (UTC+8)-
dc.date.issued (上傳時間) 2-May-2016 17:02:43 (UTC+8)-
dc.identifier (Other Identifiers) B2002005027en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/89640-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description.abstract (摘要) 在生物學，醫學，社會科學等領域中，吾人常須分析離散資料。例如:生物學家培育新品種動植物之存活率資料; 醫生臨床實驗所得數據;社會工作專家藉抽樣調查所得之問卷資料多為離散資料。若欲同時比較離散資料各類別均值間之差異最適當的統計方法之一是統計多重比較。
     針對離散性資料，傳統的多重比較方法幾全是Scheffe的卡方投影或自其衍生之方法。一般而言，Scheffe的方法失之過份保守，即聯合信賴域的周界太長。本文之主旨即在研究改善傳統的方法並提出較精確的多重比較計算法則。值得強調的是:我們所提的比較方法皆奠基於大樣本之常態近似法則。此乃因應小樣本時，待比較參數的估計式，其分配函數常極其複雜的情況下，所必須採取的權宜措施。
     在研究結構方面，本文係採確立聯合信賴區間的方式，並依所欲比較參數之三種常見型態，分別探討離散資料之三種抽樣模式:多項、二項、波松分配模式。在參數估計方面，我們皆盡可能將資料試以適當之log-linear 模式，再以該模式為基礎進行所欲比較參數的估計。經典著名離散資料實例(散見於著名離散資料分析著作中)驗證，本論文所提之多重比較方法確實能改善傳統的方法。		zh_TW
dc.description.tableofcontents 第一章 緒論
     第一節研究動機與目地........................1
     第二節 研究方法與架構........................2
     第三節 文獻回顧 ........................10
     第二章 離散資料多重比較分析
     第一節 簡介........................11
     第二節 多項分配的抽樣模式........................12
     第三節 列聯表形式之多項分配的抽樣模式........................18
     第四節 二項分配的抽樣模式........................24
     第五節 波松分配的抽樣模式........................29
     第三章 結論. ........................35
     參考文獻........................38		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002005027en_US
dc.title (題名) 離散資料之多重比較zh_TW
dc.title (題名) On multiple comparisons for discrete dataen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) 1. Bihapkar,V.P.and Somes,G.W. (1976).Multiple comparisons of matched proportions. Communications in Statistics, Ser.A,5,17-25.
     2. Bishop.Y.M.M,Fienberg,S.E. & Holland.P.W. (1975). Discrete Multivariate Analysis: Theory and Practice. MIT Press, Cambridge. Mass.
     3. Bofinger,E. (1985). Multiple comparisions and type III errors. Journal of the American Statistical Association 80,433-437.
     4. Cochran,W. (1950). The comparision of percentages in matched samples. Biometrika 37.256-266.
     5. Dorn,H.F. (1954).The relationship of cancer of the lung and the use of tobacco. American Statistician 8.7-13.
     6. Dowdall,J.A. (1974). Women`s attitudes toward employment and family roles. Sociological Analysis 35,251-262.
     7. Dunnett,C.W. (1980). Pairwise multiple comparisions In the homogeneous variance. unequal sample size case. Journal of the American Statistical Association 75.789-795.
     8. Dunnett,C.W. (1980).Pairwise multiple comparisions in the unequal variance case. Journal of the American Statistical Association 75.796-800.
     9. Fleiss,J. (1981). Statistial Methods for Rates and Proportions,2nd edition. Wiley , New York.
     10.Gold,R.Z. (1963). Tests auxiliary to x2 tests in a markov chain. Annuals of Mathematical Statistics 34.56-74.
     11.Goodman,L.A. (1964) .Simultaneous confidence limits for cross-product ratios in contingency tables. Journal of the Royal Statistical Society.Ser.B,26,86-102.
     12.Goodman,L.A. (1965) .On simultaneous confidence intervals for multinomial proportions. Technometrics 7.247-254.
     13.Haberman,S.J. (1978). Anaiysis of Qualitative Data, Vol.1. Academic Press. New York.
     14.Haldane.J.B.S. (1955). The estimation and significance of the logarithm of a ratio of frequencies. Ann.Hum.Genet.20,309-311.
     15.Hayter,A.J. (1984). A proof of the conjecture that the Tukey-Kramer multiple comparisons procedure is conservative. The Annals of Statistics 12,61-75.
     16.Hayter,A.J. (1985). A study of the Tukey multiple comparisons procedure including a proof of the Tukey conjecture for unequal sample sizes. unpublished doctoral dissertation, cornell University.
     17.Hochberg,Y.and Tamhane, A.C. (1987). Multiple comparison Procedures. Wiley,New York.
     18.Hsu.J.C. (1981).Simultaneous confidence intervals for all distances from the best. The Annals of Statistics 9,1026-1034.
     19.Hsu,J.C. (1989) .Simultaneous confidence intervals in the General Linear Models.Computer Sciense and Statistic:Proceedings of the 20th Symposium on the Interface,E.J.Wegman.D.T.Gantz.J.J.Miller editors. American Statistical Association. Alexandria, Virginia.
     20.Hsu,J.C.Soong,W.C. (1990) Using the Fast Fourier Transform to compute multiple comparisons with the best and subset selection critical values.Communications in Statistics 19(4) ,1377-1391.
     21.Jonnson.R.A.and Wichern.D.W. (1982). Appliced Multivariate Statistical Analysis. Prentice-Hall,Enflwood Cliffs, New Jersey.
     22.McCullagh.P.and Nelder.J.A. (1983) Generalized Linear Models Chapman and Hall.Hew York.
     23.Miller,R.G. (1981) .Simultanlous Statistical Inference,2nd edition. Springer-Verlag. New York.,Jukey,J.W. (1953) .The Promblem for multiple comparisons. Unpublished manuscript.
     24.Plackett,P.L. (1954).A reduction formula for normal multivariate integrals. Biometrika 41,351-360.
     25.Plackett,P.L. (1962).A note fo interactions in contingency tables. Journal of the Royal Statistical Society, Ser.B,24,162-166.
     26.Quesenberry, C.P.and Hurst,D.C. (1964) . Large sample simultaneous confidence intervals for multinomial proportions. Technometrics 6,191-195.
     27.Scheffe,H. (1959). The Analysis of Variance. Wiley,New York.
     28.Soong,vl.C. (1989) .Multiple comparisons for complex experimental designs. THESIS.
     29.Spurrier.J.D.and Isham,S.P. (1985).Exact simultaneous confidence intervals for pairwise comparisions of three normal means. Journal of the American Statistical Association 80.438-442.
     30.Tukey,J.W. (1953). The problem of multiple comparisons. Unpublished manuscript.
     31.Uusipaikka,E. (1985).Exact simultaneous confidence intervals for multiple comparisons among three or four values. Journal of the American Statistical Association 80.196-201.
     32.Welsch,R.E. (1977) . Stepwise multiple comparison procedure.Journal of the American Statistical Association 72,566-574.		zh_TW