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研究生： 林俊廷
LIN, CHUN-TING
論文名稱： 多維phi係數的齊性檢定研究
On Testing The Homogeneity of Multivariate Phi Coefficients
指導教授： 張少同
學位類別： 碩士
Master
系所名稱： 數學系
Department of Mathematics
論文出版年： 2002
畢業學年度： 90
語文別： 英文
論文頁數： 46
中文關鍵詞： Phi係數 、列聯表 、臨界值 、檢定力
英文關鍵詞： phi coefficient, contingency table, critical value, power of test
論文種類： 學術論文
相關次數： 點閱：189  下載：9 
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    • Phi係數的歷史相當悠久，它主要是用在兩個自然的二分類變項所形成的2×2列聯表，可以測量這兩個變項的關聯性。本論文的目的是把傳統上由兩個二分類變項所得的phi係數推廣到任意k個二分類變項，而推得 k*(k-1)/2 個phi係數滿足近似聯合常態分佈，並進而導出多個phi係數的聯合信賴區間，多維phi係數的雙尾檢定，模擬較小樣本的臨界值，並討論檢定力。

    The phi coefficient has been developed long ago. It is mainly used in the case of 2×2 contingency tables involving two variables that are dichotomous in nature. It can measure the association of the two dichotomous variables. In this thesis, we extend the traditional phi coefficient that formed by two variables to arbitrary k variables, and show that k*(k-1)/2 phi coefficients are asymptotically normal. Moreover, we derive confidence regions and two-sided test of mul-tivariate phi coefficients, simulate critical values with smaller sample size, and discuss the powers of tests.

    CONTENTS Abstract 1、Introduction 1.1 Literature review 1.2 Comparison of phi with other measures 2、Univariate phi coefficients 2.1 Asymptotic distributions of univariate phi coefficients 2.2 Confidence intervals and hypothesis testing 2.3 Properties of phi coefficient 3、Multivariate phi coefficients 3.1 Asymptotic distributions of multivariate phi coefficients 3.2 Confidence regions and hypothesis testing 4、Multiple comparisons 4.1 Scheffé's approach 4.2 Bonferroni's approach 4.3 One-at-a-time approach 5、Simulation 5.1 Critical values of small sample sizes 5.2 Power analysis 6、Applications 6.1 Example 6.2 Future study Appendix A、Referred theorems Appendix B、Some useful coefficients of contingency tables Appendix C、C+ + source code for five types of tests References

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