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

Two-stage multiple comparisons with the control for location parameters of two-parameter exponential distributions under heteroscedasticity are proposed by Lam and Ng [Lam, K., Ng, C.K., 1990. Two-stage procedures for comparing several exponential populations with a control when the scale parameters are unknown and unequal. Sequential Analysis 9 (2) 151–164]. 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-control treatments in an experimental design and to identify better-than-the-control, worse-than-the-control and not-much-different-from-the-control products in agriculture, stock market, medical research, and automodels. 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 procedure is also discussed in this paper.