Maximally selected χ2 statistics for k x 2 tables

Rebecca A. Betensky, Daniel Rabinowitz

Research output: Contribution to journalArticlepeer-review


It is common in epidemiologic analyses to summarize continuous outcomes as falling above or below a threshold. With such a dichotomized outcome, the usual χ2 statistics for association or trend can be used to test for equality of proportions across strata of the study population. However, if the threshold is chosen to maximize the test statistic, the nominal χ2 reference distributions are incorrect. In this paper, the asymptotic distributions of maximally selected χ2 statistics for association and for trend for the k x 2 table are derived. The methodology is illustrated with data from an AIDS clinical trial. The results of simulation experiments that assess the accuracy of the asymptotic distributions in moderate sample sizes are also reported.

Original languageEnglish (US)
Pages (from-to)317-320
Number of pages4
Issue number1
StatePublished - Mar 1999


  • Association
  • Brownian bridge
  • Categorical data
  • Independence
  • Multivariate diffusion
  • Trend

ASJC Scopus subject areas

  • Statistics and Probability
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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