A Comparison of the Performances of Procedures for Selecting the Normal Population Having the Largest Mean when the Variances are Known and Equal

We study the performance characteristics of procedures for selecting the normal population which has the largest mean when the variances are known and equal. The procedures studied are the single-stage procedure of Bechhofer, the closed two-stage procedure of Tamhane and Bechhofer, the open sequential procedure of Bechhofer, Kiefer, and Sobel and a truncated version of that procedure by Bechhofer and Goldsman, the closed multi-stage procedure with elimination of Paulson and improved closed versions of that procedure by Fabian and by Hartmann. The performance characteristics studied are the achieved probability of a correct selection, the expected number of stages required to terminate experimentation, and the expected total number of observations required to terminate experimentation. Except for the single-stage procedure, all performance characteristics are estimated by Monte Carlo sampling. Based on these results, recommendations are made concerning which procedure to use in different circumstances.