A Modified Bonferroni Procedure for Multiple Tests

• Activity Number: 343
• Type: Contributed
• Date/Time: Tuesday, July 31, 2007 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Daniel Mundfrom*+ and Michelle Roozeboom and Jamis Perrett
• Companies: University of Northern Colorado and University of Northern Colorado and University of Northern Colorado
• Keywords: regression ; multiple tests ; type I error ; power

Abstract

The Bonferroni adjustment ensures that the overall probability of Type I error is below the nominal level when multiple tests are performed. However, the method results in a Type I error rate that is often well below the nominal level. The purpose of this research was to establish an improved single step method for multiple tests based on the Bonferroni method. This method was compared to the Bonferroni and Holm methods to evaluate statistical power while maintaining a Type I error rate that is no greater than the nominal level. Sample data (n = 25, 50, 200) were simulated to have normal distributions for testing of 20 or fewer coefficients. Correlations between x and y and among the xs were varied. Based on the results, a new smaller divisor resulted in increased statistical power while maintaining a level of significance that is closer to, but still less than, the nominal level.