Two stage multiple comparisons with the average for exponential location parameters under heteroscedasticity

In this article, two-stage procedures for multiple comparisons with the average for location parameters of two-parameter exponential distributions under heterocedasity including one- 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 obtained using the recent techniques given in Lam (Proceedings of the Second International Advanced Seminar/Workshop on Inference Procedures Associated with Statistical Ranking and Selection, Sydney, Australia, August 1987; Comm. Statist. Simulation Comput. B17(3) (1988) 55). These approximate critical values are shown to have better results than the approximate critical values using the Bonferroni inequality developed in this paper. An example of comparing four drugs in the treatment of leukemia is given to demonstrate the proposed methodology.