Multiple Comparison Procedures for Binomial Distributions

• Activity Number: 32
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Jie Peng*+ and Kalimuthu Krishnamoorthy
• Companies: St. Ambrose University and University of Louisiana at Lafayette
• Keywords: Multiple Comparison ; binomial proportions ; Powers ; Simultaneous confidence intervals ; Size

Abstract

Multiple tests for comparing several binomial proportion are compared with respect to type I error rates and powers. For testing equality of several proportions, we apply Simes (1986, Biometrika) approach and compare it with the usual chi-square test. Our comparison study indicates that the Simes method performs slightly better than the chi-square test in controlling type I error rates. For multiple comparison procedures, we compare the Bonferroni method, Marascuilla approach, Tukey type approach and Holm method. Our numerical studies indicate that the Holm method and the Bonferroni method perform similarly with respect to type I error rates, and the former is slightly more powerful than the latter in some cases. Between Marascuilla method and the Tukey type approach, the former is overly conservative while the latter is too liberal for some cases. Overall, Holm's approach and the Bonferroni approach are preferable for multiple comparison purpose. The methods are illustrated using an example.