Communications for Statistical Applications and Methods

  • 제3권2호
  • /
  • Pages.69-76
  • /
  • 1996
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

Influence Functions on $ {\chi}^2$ Statistic in Contingency Tables

  • Honggie Kim (Assistant Professor, Department of Statistics, Chungnam National University, Daejon, 305-746, Korea) ;
  • Hee-Sook Lee (Lecturer, Department of Computer & Information Engineering, Kongju National Junior College, Chungnam, 314-060, Korea)
  • 발행 : 1996.08.01
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초록

In a two-way contingency table, the analyst is most interested in the hypotheses of either homogeneity or independence. For testing this as a null hypothesis, Pearson's ${\chi}^2$ statistic is most commonly used in practice. Once the null Hypothesis is rejected, he will further search forcells which caused the rejection of the null hypothesis. For this purpose, so called cell${\chi}^2$ components are used. In this paper, we derive the influence function of an obsevation to the ${\chi}^2$ statistic, with which cells with high influence can be identified.

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참고문헌

  1. Applied Statistics v.27 The influence function as an aid in outlier detection in discriminant analysis Campbell, N.A.
  2. Technometris v.22 Characterizations of an empirical influence function for detecting cases in regression Cook, R.D.;Weisberg, S.
  3. Residuals and Influence in Regression Cook, R.D.;Weisberg, S.
  4. Biometrika v.72 Influence in principal components analysis Critchlyey, F.
  5. Theory and Applications of Correspondence Analysis Greenacre, M.J.
  6. Psychometrika v.36 Measurement as structural theory Guttman, L.
  7. Journal of American Statistical Association v.69 The influence curve and its role in robust estimation Hampel, F.
  8. Biometrika v.36 A note on the sudbivision of x² into components Irwin, J.O.
  9. Applied Statistics v.29 An exploratory technique for investigating large quantities of categorical data Kass, G.
  10. Biometrika v.16 A note on the additive partitioning of chi-square in contingency tables Kastenbaum, M.A.
  11. Journal of Statistical Computation and Simulation v.40 Measures of influence in correspondence analysis Kim, H.
  12. The Korean Journal of Applied Statistics v.7 Influence functions in multiple correspondence analysis Kim, H.
  13. Biometrics v.10 Short-cut formulars for the exact partitioning of x² in contingency tables Kimball, A.W.