Suppose that k normal populations with means μ1,…, μ k and variances are considered. When variances are unknown and equal, Lam (1986) proposed a procedure to select all good populations, where a population is good if μ i ≥ μ[k] − ϵ and μ[k] is the largest normal mean among k normal means. When variances are unknown and possibly unequal, a two-stage procedure selecting all good populations such that the probability of correct selection being at least a pre-specified value of P* is proposed. Without decreasing the probability of correct selection, the confidence interval of pairwise differences of all means to the largest normal mean is presented with the selection procedure. When the additional samples at the second stage could be costly, a data-analysis one-stage procedure selecting all good population is proposed. At last, one real-life example is given to illustrate all procedures.
Communications in Statistics - Simulation and Computation 38(1), pp.46-57