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

Two-stage multiple comparisons with the average for location parameters of two-parameter exponential distributions under heteroscedasticity are proposed by Wu and Wu [Wu, S.F., Wu, C.C., 2005. Two stage multiple comparisons with the average for exponential location parameters under heteroscedasticity. Journal of Statistical Planning and Inference 134, 392-408]. When the additional sample for the second stage may not be available, one-stage procedures including one-sided and two-sided confidence intervals are proposed in this paper. 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, the stock market, pharmaceutical industries. Tables of upper limits of critical values are obtained using the technique given in Lam [Lam, K., 1987. Subset selection of normal populations under heteroscedasticity. In: Proceedings of the Second International Advanced Seminar/Workshop on Inference Procedures Associated with Statistical Ranking and Selection. Sydney, Australia. August 1987. Lam, K., 1988. An improved two-stage selection procedure. Communications in Statistics-Simulation and Computation 17 (3), 995-1006]. An example of comparing four drugs in the treatment of leukemia is given to demonstrate the proposed procedures. The relationship between the one-stage and the two-stage procedures is also elaborated in this paper.