Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A Study on Cell Influences to Chi-square Statistic in Contingency Tables

  • Kim, Hong-Gie (Associate Professor, Department of Statistics, Chungnam National University)
  • Published : 1998.04.01
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Abstract

Once a contingency table is constructed, the first interest will be the hypotheses of either homogeneity or independence depending on the sampling scheme. The most widely used test statistic in practice is the classical Pearson's $\chi^2$ statistic. When the null hypothesis is rejected, another natural interest becomes which cell contributed to the rejection of the null hypothesis more than others. For this purpose, so called cell $\chi^2$ components are investigated. In this paper, the influence function of a cell to the $\chi^2$ statistic is derived, which can be used for the same purpose. This function measures the effect of each cell to the $\chi$$^2$ statistic. A numerical example is given to demonstrate the role of the new function.

Keywords

References

  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 influential 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 Critchley, 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 subdivision of χ² into components Irwin, J.O.
  9. Applied Statistics v.29 An exploratory technique for investigating large quantities of categorical data Kass, G.
  10. Biometrics 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. Journal of the Korean Communications in Statistics v.3 no.2 Influence Functions on χ² statistic in Contingency Tables Kim, H.;Lee, H.S.
  14. Biometrics v.10 Short-cut formulars for the exact partitioning of χ² in contingency tables Kimball, A.W.