Subset selection of the T best populations

Selection of the “best” t out of k populations has been considered in the indifference zone formulation by Bechhofer (1954) and in the subset selection formulation by Carroll, Gupta and Huang (1975). The latter approach is used here to obtain conservative solutions for the goals of selecting (i) all the “good” or (ii) only “good” populations, where “good” means having a location parameter among the largest t. For the case of normal distributions with common unknown variance, tables are produced for implementing these procedures. Also, for this case, simulation results suggest that the procedures may not be too conservative.