In this article we propose a two-stage procedure for multiple comparisons with the average for normal distributions under heteroscedasity. One-sided and two-sided confidence intervals are proposed. These intervals can be used to identify a subset which includes all no-worse-than-the-average treatments in an experimental design and to identify better-than-the-average, worse-than-the-average and not-much-different-from-the-average products in agriculture, stock market, medical research, and auto models. An upper limit of critical values are obatined using Bonferroni inequality. But the approximate values are shown to be too conservative compared with the simulation critical values in Table 7. Therefore, simulation critical values should be used in our multiple comparison procedures. Statistical tables and software programs are provided for use in practice.
Computational Statistics and Data Analysis 33(2), pp.201-213