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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/94412
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/94412


    Title: 相似性指數與卡方檢定之探討
    Authors: 歐陽致平
    Contributors: 余清祥
    歐陽致平
    Keywords: 卡方檢定
    適合度檢定
    相似性指數
    電腦模擬
    Date: 2007
    Issue Date: 2016-05-06 16:35:56 (UTC+8)
    Abstract: 適合度檢定(Goodness-of-fit Test)用於檢測觀察值是否符合某種特質,是統計學應用非常廣泛的檢定,其中卡方檢定(Chi-Squared Test)更是適合度檢定最常用的方法。卡方檢定廣受歡迎的原因之一在於其彈性,通常只要求分組後每一組觀察值的期望個數不少於5,若樣本較少需考慮併組,但如何併組至今仍無定論。本文即針對樣本數不足時,運用計算模擬的方法探討卡方適合度檢定,希冀研究結果可提供卡方適合度檢定併組的參考;另外,相似性指數(Similarity Indices)一般用於比較兩個母體的異同,使用上並不受限於觀察值期望個數的限制,我們也同時探討相似指數是否也可用於適合度檢定。
    過去研究顯示當母體接近均勻分配時,適合度檢定或有較為不同特性,因此我們將研究分成當母體服從(或接近)均勻分配、或是幾何分配兩種情形。當母體接近均勻分配時,我們發現卡方適合度檢定並不受限於期望個數不大於5的限制,不考慮併組的卡方檢定的型一誤差符合顯著水準的要求,而且比併組的卡方檢定有更大的檢力(Power);然而,在母體服從幾何分配時,卡方檢定必須依賴併組以改善型一誤差。另外,我們也發現相似性指數確實在各種假設條件之下,檢定力皆不如併組修正的卡方檢定優越。
    Reference: [1] Cochran, W.G. (1952), “The χ2 Test of Goodness of fit.”, Ann. Math. Statist., 23, 315-342.
    [2] Good, P.I. (1999), Resampling Methods – A Practical Guide to Data Analysis., Birkhauser, Boston.
    [3] Cramér, H. (1946), Mathematical Methods of Statistics. Princeton University Press, Princeton, NJ.
    [4] Greenwood, P.E. and Nikulin, M.S. (1996), A Guide to Chi-Squared Testing., Wiley, New York.
    [5] Haber, M. (1980), “A Comparison of Some Continuity Corrections for the Chi-Square test on Tables.”, J. Amer. Statist. Assoc., 75(373), 510-515.
    [6] Haberman, S.J. (1988), “A Warning on the Use of Chi-Squared Statistics With Frequency Tables With Small Expected Cell Counts.”, J. Amer. Statist. Assoc. 83, 555-560.
    [7] Haldane, J.B.S. (1937), “The Exact Value of the Moments of the Distribution of χ2, Used As a Test of Goodness of Fit.”, Biometrika, 29, 133-143.
    [8] Kolmogorov, A.N. (1933), “Sulla determinazione empirica di una legge di distribuzione.”, Giorn. Inst. Ital. Attuari, 4, 83-91.
    [9] Kullback S. (1959), Information Theory and Statistics., Wiley, New York.
    [10] Pearson, K. (1922), “On the χ2 Test of Goodness of fit.”, Biometrica, 14, 186-191.
    [11] Pearson, K. (1932), “Experimental Discussion of the χ2 test for Goodness-of-fit.”, Biometrika, 24, 351-381.
    [12] Roscoe, J.T. and Byars, J.A. (1971), “An Investigation of the Restraints with respect to Sample Size Commonly Imposed on the Use of the Chi-Squared Statistics.”, J. Amer. Statist. Assoc., 66, 755-759
    [13] Rubinstein, R.Y. (1981), Simulation and Monte Carlo Method., Wiley, New York.
    [14] Smirnov, N.V. (1944), “An Approximation to the Distribution Laws of Random Quantiles Determined by Empirical Data.” Uspehi Mat. Nauk, 10, 179-206.
    [15] Smith, W., Solow, A.R. and Preston, P.E. (1996), “An Estimator of Species Overlap Using a Modified Beta-binomial Model.”, Biometrics, 52, 1472-1477.
    [16] Yarnold, J.K. (1970), “The Minimum Expectation in χ2 Goodness of fit Tests and the Accuracy of Approximations for the Null Distribution.”, J. Amer. Statist. Assoc., 65, 864-886.
    [17] Yue, C.J. and Clayton, M.K. (2001), “A Nonparametric Estimator of Species Overlap”, Biometrics, 57(3), 743-749.
    [18] Yue, C.J. and Clayton, M.K. (2005). “Similarity Measures Based on Species Proportions”, Communications in Statistics: Theory and Methods.
    Description: 碩士
    國立政治大學
    統計學系
    94354008
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0094354008
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

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