Exact Tests for Interaction in Several 2 × 2 Tables

Karim F. Hirji, Stein E. Vollset, Isildinha M. Reis, Abdelmonem A. Afifi

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


The investigation of interaction in a series of 2 × 2 tables is warranted in a variety of research endeavors. Though many large-sample approaches for such investigations are available, the exact analysis of the problem has been formulated for the probability statistic only. We present several alternative statistics applicable in this context. We also give an efficient polynomial multiplication algorithm to compute exact distributions and tail areas for the family of stratum-additive statistics. Besides the probability statistic, these include the score, likelihood ratio, and other statistics. In addition to comparing, in empirical terms, the diverse computational strategies for exact interaction analysis, we also explore the theoretical linkages between them. Data from published papers are used for illustration.

Original languageEnglish (US)
Pages (from-to)209-224
Number of pages16
JournalJournal of Computational and Graphical Statistics
Issue number3
StatePublished - Sep 1996
Externally publishedYes


  • Exact inference
  • Fast fourier transform
  • Network algorithm
  • Polynomial multiplication algorithm
  • Test of homogeneity

ASJC Scopus subject areas

  • Mathematics(all)
  • Computational Mathematics
  • Statistics and Probability


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