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Keywords:

  • Categorical variables;
  • Association test;
  • Contingency table;
  • Exact distribution;
  • Variable selection;
  • Selection bias

Abstract

We address the problem of maximally selected chi-square statistics in the case of a binary Y variable and a nominal X variable with several categories. The distribution of the maximally selected chi-square statistic has already been derived when the best cutpoint is chosen from a continuous or an ordinal X, but not when the best split is chosen from a nominal X. In this paper, we derive the exact distribution of the maximally selected chi-square statistic in this case using a combinatorial approach. Applications of the derived distribution to variable selection and hypothesis testing are discussed based on simulations. As an illustration, our method is applied to a birth data set. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)