多維phi係數的齊性檢定研究

On Testing The Homogeneity of Multivariate Phi Coefficients

林俊廷(CHUN-TING LIN)

指導教授 ： 張少同

國立臺灣師範大學/理學院/數學系/碩士(2001年)

摘要

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。

關鍵字

Phi係數 ； 列聯表 ； 臨界值 ； 檢定力

並列摘要

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.

並列關鍵字

phi coefficient ； contingency table ； critical value ； power of test

參考文獻

1. Agresti, A. (1990), Categorical data analysis. McGraw-Hill, U.S.A.

2. Bishop, Y.M.M. & Fienberg, S.E. & Holland, P.W. (1975), Discrete multivariate analysis: Theory and practice. MA:MIT Press, Cambridge.

3. Carroll, J.B. (1961), “The nature of the data, or how to choose a correlation coefficient.” Psy-chometrika, V26:347~372.

4. Conover, W.J. (1999), Practical nonparametric statistics.(3th), John Wiley & Sons,U.S.A.

5. Cureton, E.E. (1959), “Note on .” Psychometrika, V24:89~91.