Comparing Performances of Multiple Comparison Methods in Commonly Used 2 × C Contingency Tables

Area of Science:

• Statistics
• Biostatistics
• Medical Research

Background:

• Multiple comparison methods are crucial for analyzing contingency tables in medical research.
• Evaluating the performance of these methods under various scenarios is essential for reliable results.

Purpose of the Study:

• To briefly mention multiple comparison methods for contingency tables.
• To examine the performance of these methods via a simulation study.
• To provide a Minitab macro for practical application in scientific research.

Main Methods:

• The study mentions Bonferroni, Holm-Bonferroni, Hochberg, Hommel, Marascuilo, Tukey, Benjamini-Hochberg, and Gavrilov-Benjamini-Sarkar methods.
• A simulation study was constructed with 36 scenarios for 2x4 contingency tables.
• Performance was evaluated based on Type I error rate and statistical power.

Main Results:

• Gavrilov-Benjamini-Sarkar, Holm-Bonferroni, and Bonferroni methods preserve the nominal alpha level when sample size exceeds 100.
• Hommel method showed a consistent Type I error rate of approximately 2%.
• Gavrilov-Benjamini-Sarkar and Holm-Bonferroni demonstrated the best overall performance in simulations.

Conclusions:

• Gavrilov-Benjamini-Sarkar and Holm-Bonferroni methods are recommended for multiple comparisons in contingency tables.
• Hommel and Marascuilo methods are not advised due to suboptimal performance.
• A Minitab macro was developed to aid researchers in applying these multiple comparison techniques.