### A Measures of Association for Two-way Contingency Tables by Maximum Association

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Kim, Sang-Giun;Lee, Woo-Rhee

• 발행 : 2005.12.01
• 17 3

#### 초록

Pearson $X^2$ statistics can be used as the measure of association for two-way contingency tables. However, it's magnitude depends on the sample size N, the normalized index ${\phi}^2 = X^2\;/\;N$ has. been widely used in many researches instead of that. In this study, we firstly point out that the actual upper bound of ${\phi}^2$ can be affected by the given marginals of the tables, so that ${\phi}^2$ should be adjusted the actual maximum to get the proper range [ 0, 1]. Also we point out that the maximum could be found easily by using several algorithms like Hu and Mukerjee(2002). With the actual maximum, we propose the relative measure of association which is normalized by it.

#### 키워드

Measure of association;Contingency tables

#### 참고문헌

1. Agresti, A (1990). Categorical Data Analysis, Wiley, New York
2. Goodman, L.A and Kruskal, W.H.(1979). Measures of Association for Cross Classifications, Springer-Velag, New York
3. Hu, X. and Mukerjee, H.(2002). Constructing All Extremes of Contingency Tables with Given Marginals, Journal of Computational and Graphical Statistics, Vol. 11, 910-919 https://doi.org/10.1198/106186002709
4. Kalantari, B., Lari I., Rizzi, A, and Simeon, B.(1993). Sharp Bounds for the Maximum of the Chi-Square index in a Class of Contingency Tables with given Marginals, Computational Statistics & Data Analysis, Vol. 16, 19-34 https://doi.org/10.1016/0167-9473(93)90242-L
5. Lee, A.J.(1997). Some Simple Methods for Generating Correlated Categorical Variates, Computational Statistics & Data Analysis, Vol. 26, 133-148 https://doi.org/10.1016/S0167-9473(97)00030-3
6. Mirkin, B.(2001). Eleven Ways to Look at the Chi-Squared Coefficient for Contingency Tables, American Statistician, Vol. 55, 111-120 https://doi.org/10.1198/000313001750358428
7. Reynolds, H.T.(1977). The Analysis of Cross-Classifications, The Free Press, New York
8. DiFranceisco, W. and Gitelman, Z.(1984). Soviet Political Culture and Covert Participation in Policy Implementation, American Political Science Review, Vol. 78, 603-621 https://doi.org/10.2307/1961832