Multiple comparison procedures with the average for scale families: normal and exponential populations

Abstract

In this article, multiple comparison procedures with the average of scale parameters for normal and exponential populations are proposed. A subset selection procedure and a confidence interval procedure are investigated. These procedures will have broad applicability in identifying groups of treatments with smaller than the average, larger than the average and not different from the average variability in various fields. Bonferroni inequality is used to bound the probability of a correct selection and the coverage probability of confidence intervals. The Pearson’s approximation to the sampling distribution of the log chi-square ratio utilized in both subset selection and confidence intervals is shown to be satisfactory compared with the simulation results. Statistical tables to implement these procedures for the case of equal sample sizes are provided for use in practice.

Keywords:

• Subset selection
• simultaneous confidence intervals
• Bonfer-roni inequality
• Pearsonian system
• simulation