Exact simultaneous confidence intervals for multiple comparisons with the mean

摘要

Multiple comparisons with the mean (MCM) is a method of simultaneous inference for comparing each of a set of treatment means with the overall mean. We take the approach of simultaneous confidence intervals estimation. In the earlier studies of MCM, the overall mean was commonly defined by the weighted mean of the means using the sample sizes as weights. It is known that under this common definition exact simultaneous confidence intervals are computable. In recent years, the attention of some studies of MCM was directed toward the overall mean defined by the equally weighted mean or the trimmed mean of the means. It is shown in this article that under these latter definitions exact simultaneous confidence intervals are still computable. To make the implementation of MCM more flexible, we consider a more general definition of the overall mean that includes all of the previous ones as its special cases. A general computation expression is then developed under the proposed general definition. Some special types or cases of MCM that have a computation expression simpler than the general one are explored. Methods of numerical integration for the proposed computation expressions are suggested and tested. Three examples are given.