### Abstract

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 language | English |
---|---|

Pages (from-to) | 209-224 |

Number of pages | 16 |

Journal | Journal of Computational and Graphical Statistics |

Volume | 5 |

Issue number | 3 |

State | Published - Dec 1 1996 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Journal of Computational and Graphical Statistics*,

*5*(3), 209-224.

**Exact tests for interaction in several 2 × 2 tables.** / Hirji, Karim F.; Vollset, Stein E.; Reis, Isildinha; Afifi, Abdelmonem A.

Research output: Contribution to journal › Article

*Journal of Computational and Graphical Statistics*, vol. 5, no. 3, pp. 209-224.

}

TY - JOUR

T1 - Exact tests for interaction in several 2 × 2 tables

AU - Hirji, Karim F.

AU - Vollset, Stein E.

AU - Reis, Isildinha

AU - Afifi, Abdelmonem A.

PY - 1996/12/1

Y1 - 1996/12/1

N2 - 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.

AB - 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.

KW - Exact inference

KW - Fast fourier transform

KW - Network algorithm

KW - Polynomial multiplication algorithm

KW - Test of homogeneity

UR - http://www.scopus.com/inward/record.url?scp=0030305455&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030305455&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030305455

VL - 5

SP - 209

EP - 224

JO - Journal of Computational and Graphical Statistics

JF - Journal of Computational and Graphical Statistics

SN - 1061-8600

IS - 3

ER -