A Balanced Two-Stage Procedure for Selecting the Best of Normal Populations With Unequal Means

摘要

This paper introduces a balanced two-stage procedure (BTSP) for selecting the best of k normal populations with known or unknown common variance. The BTSP equally splits the upper bound of probability of incorrect selection (PICS) between the two stages. The modified upper bound of PICS gives a better approximation to the true PICS. In the 20 examples considered with k = 3;20;000 groups of simulations show that the modified upper bounds are much closer than the old upper bounds. The range of absolute improvement, which is defined as PICS(Original) – PICS(Modified), is (0.013,0.028). The range of percentage improvement, which is defined as (PICS(Original) - PICS(Modified)) /PICS(Modified) is (33.33%, 47.32%). For k normal populations with unknown common variance, the above results approximately hold as well. Simulation study regarding total expected number of observations is carried out in Section 5. Comparison with the results of Gupta and Kim (1984) is made in Section