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Pairwise Comparisons of k $$ k $$ Binomial Responses.

Dennis D Boos1, James Schmidt1

  • 1Department of Statistics, North Carolina State University, Raleigh, North Carolina, USA.

Statistics in Medicine
|March 20, 2026
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Summary
This summary is machine-generated.

This study introduces a new statistical method for analyzing binomial data, enhancing pairwise comparisons in research. The approach ensures accurate identification of significant differences while maintaining strong error rate control.

Keywords:
closed methodfamily‐wise error ratemultiple comparisons

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Area of Science:

  • Statistics
  • Biostatistics
  • Clinical Trials

Background:

  • Binomially distributed data are common in clinical trials, quality control, and stratified sampling.
  • Multinomial data from 2 x k contingency tables can be analyzed as k conditionally independent binomial variables.
  • Fisher's conditional test is standard for testing equality of binomial success probabilities but doesn't identify pairwise differences.

Purpose of the Study:

  • To develop a statistical method for pairwise comparisons of binomial data.
  • To provide strong control of the Family-Wise Error Rate (FWER).
  • To achieve excellent statistical power in detecting differences.

Main Methods:

  • Combined the closed method of pairwise comparisons with unconditional exact tests for 2x2 tables.
  • Utilized Fisher's conditional test for tables larger than 2x2.
  • Applied these methods to generate p-values for pairwise comparisons.

Main Results:

  • The proposed method achieves strong control of the Family-Wise Error Rate.
  • The method demonstrates excellent power properties for detecting pairwise differences.
  • The approach is applicable to analyzing binomial and multinomial data.

Conclusions:

  • The new method offers an effective way to perform pairwise comparisons for binomial data.
  • This approach enhances the analysis of data from 2xk contingency tables.
  • The findings are relevant for single-site studies in various research fields.