簡易檢索 / 詳目顯示

回結果列表
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：207  下載：9 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 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

    References：
    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.
    6. Elliott, G.C. (1988), “Interpreting higher order interactions in log-linear analysis.” Psychologi-cal Bulletin, V103:121~130.
    7. Fleiss, J.L. (1981), Statistical methods for rates and proportions.(2th), John Wiley & Sons, New York.
    8. Gibbons, J.D. & Chakraborti, S. (1992), Nonparametric statistical inference.(3th), Marcel Dekker, New York.
    9. Glass, G.V. & Hopkins, K.D. (1996), Statistical methods in education and psychology.(3th), Allyn&Bacon, U.S.A.
    10. Goodman, L.A. & Kruskal, W.H. (1979), Measures of association for cross classifications. Springer-Verlag, U.S.A.
    11. Guilford, J.P. (1965), Fundamental statistics in psychology and education.(4th), McGraw-Hill, New York.
    12. Holley, J.W. & Guilford, J.P. (1964), “A note on the G index of agreement.” Educational and Psychological Measurement, V24:749~753.
    13. Howell, D.C. (1992), Statistical methods for psychology.(3th), PWS-KENT, U.S.A.
    14. Janson, S. & Vegelius, J. (1979), “On generalizations of the G index and the phi coefficient to nominal scales.” Multivariate Behavioral Research, V14:255~269.
    15. Janson, S. & Vegelius, J. (1980), “The relationship between the phi coefficient and the G in-dex.” Educational and Psychological Measurement, V40:569~574.
    16. Kendall, M.G. & Gibbons, J.D. (1990), Rank correlation methods.(5th), Edward Arnold, Lon-don.
    17. Lehmann, E.L. (1999), Elements of large-sample theory. Springer-Verlag, New York.
    18. Levy, S.G. (1968), Inferential statistics in the behavioral sciences. Holt, Rinehart & Winston, U.S.A.
    19. Lienert, G.A. & Reynolds, J. & Wall, K.D. (1979), “Comparing associations in two independ-ent fourfold tables.” Biometrika, V21, No5:473~491.
    20. Lord, F.M. & Novick, M.R. (1968), Statistical theories of mental test scores. Addison-Wesley, U.S.A.
    21. Miller, R.G. (1981), Simultaneous statistical inference.(2th), Springer-Verlag, New York.
    22. Nelson, T.O. (1984), “A comparison of current measures of the accuracy of feeling-of-knowing predictions.” Psychological Bulletin, V95, No1:109~133.
    23. Rao, C.R. (1973), Linear statistical inference and its applications.(2th), John Wiley & Sons, New York.
    24. Reynolds, H.T. (1977), The analysis of cross-classifications. Free Press, New York.
    25. Serfling, R.J. (1980), Approximation theorems of mathematical statistics. John Wiley & Sons, New York.
    26. Sewell, W.H. & Orenstein, A.M. (1965), “Community of residence and occupational choice.” The American Journal of Sociology, V70:551~563.
    27. Siegel, S. & Castellan, N.J. (1988), Nonparametric statistics for the behavioral sciences.(2th), McGraw-Hill, U.S.A.
    28. The CSMS Math Team, (1981), Children's understanding of mathematics: 11~16. Oxford London and Northampton, Great Britain.
    29. Wichern, D.W. & Johnson, R.A. (1998), Applied multivariate statistical analysis.(4th), Pren-tice-Hall, U.S.A.
    30. Yule, G.U. (1912), “On the methods of measuring association between two attributes.” Journal of the Royal Statistical Society, V75:579~642.

    QR CODE