政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/33900
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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/33900


    Title: 獨立與非獨立性資料之多重比較
    Authors: 李昀叡
    Contributors: 余清祥
    李昀叡
    Keywords: 多重比較
    電腦模擬
    變異數分析
    型I誤差
    檢定力
    Bonferroni
    Multiple comparison
    computer simulation
    ANOVA
    Type-I error
    power
    Date: 2003
    Issue Date: 2009-09-17 18:45:50 (UTC+8)
    Abstract: 同時比較多個樣本間的差異，可用ANOVA來檢定，但ANOVA只能得到樣本間有差異的訊息，無法明確指出是哪些樣本間有差異，需要使用多重比較找出樣本間的差異。本文主要探討相關的離散型資料的多重比較，以型I誤差與檢定力兩指標找出最適的多重比較法。本文依序探討獨立的連續型資料、相關的連續型資料、獨立的離散型資料、相關的離散型資料，並針對相關型的資料提出修正法。綜合型I誤差與檢定力兩指標來看，在樣本間的平均差異小時，Shaffer’s first procedure Test (1986)、Procedure 4 by Bergmann and Hommel (1988)為兩兩比較下較佳的修正法，Hochberg Test (1988)為多對ㄧ比較下較佳的修正法；樣本間平均差異大時，Bonferroni 為兩兩比較下較佳的修正法，Hochberg (1988)、Simes (1986)為多對ㄧ比較下較佳的修正法。
    Analysis of variance (ANOVA) is usually applied to check whether there are differences among more than two treatments. However, even there are differences, multiple comparison procedures are still needed to determine which pair(s) of treatments are different. In this study, we use simulation to compare the frequently used multiple comparison procedures, including many-to-one and pair-wise, and type-I error and power are used to measure the performance of procedures. Two types of data were considered, independently and correlated distributed data. If the differences among treatments are small, Shaffer’s first procedure test (1986) and Procedure 4 by Bergmann and Hommel (1988) are the best in pair-wise case, and Hochberg test (1988) is the best in many-to-one case. If the differences among treatments are large, the Bonferroni procedure is the best in pair-wise case, and the procedures by Hochberg (1988) and Simes (1986) are the best in many-to-one case.
    Reference: 1. Dunnett, C.W. (1955). A multiple comparison procedure for comparing several treatments with a control. J. Amer. Statist. Assoc., 50, 1096-1121.
    2. Dunnett, C.W. (1964). New Table for multiple comparisons with a control. Biometrics, 20(3) , 482-491.
    3. Hommel, G.. Bernhard, G. (1999). Bonferroni procedures for logically related hypotheses. Journal of Statistical Planning and Inference, 82, 119-128.
    4. Hochberg, Y. and Tamhane, A. C. (1988). Multiple Comparison Procedures. New York：Wiley.
    5. Holm, S. A. (1979). A simple sequentially rejective multiple test procedure. Scand. H. Statist., 6, 65-70.
    6. Hommel, G., (1988). A stagewise rejective multiple test procedure based on a modified Bonferroni test. Biometrika, 75, 383-386.
    7. Montgomery, D.C.(2001), Design and Analysis of Experiments, fifth edition, Wiley.
    8. Shaffer, J. P. (1986). Modified sequentially rejective multiple test procedure. J. American Statistical Association, 81, 826-831.
    9. Simes, R. J. (1986). An improved Bonferroni procedure for multiple tests of significance. Biometrika, 73, 751-754.
    10. Wright, S. P. (1992). Adjusted P-values for Simultaneous Inference. Biometrics, 48, 1005-1013.
    Description: 碩士
    國立政治大學
    統計研究所
    91354008
    92
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0091354008
    Data Type: thesis
    Appears in Collections:[Department of Statistics] Theses

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