Abstract
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 6.
Similar content being viewed by others
References
Alam, K., 1970. A two-sample procedure for selecting the population with the largest mean from k normal populations. Ann. Inst. Statist. Math., 22, 127–136.
Bechhofer, R.E., 1954. A single-sample multiple decision procedure for ranking means of normal populations with known variances. Ann. Inst. Statist. Math., 25, 16–39.
Bechhofer, R.E., Dunnett, C.W., Sobel, M., 1953. A two-sample multiple-decision procedure for ranking means of normal populations with a common unknown variance. Biometrika, 41, 170–176.
Bechhofer, R.E., Sobel, M., 1954. A single-sample multiple-decision procedure for ranking variances of normal populations. Ann. Math. Statist., 25, 273–289.
Cohen, D.S., 1959. A two-sample decision procedure for ranking means of normal populations with a common known variance. M.S. Thesis, Dept. of Operations Research, Cornell Univ., Ithaca, New York.
Dudewicz, E.J., Dalal, S.R., 1975. Allocation of observations in ranking and selection with unequal variances. Sankhy Ser. B, 37, 28–78.
Gupta, S.S., Panchapakesan, S., 1979. Multiple Decision Procedures: Theory and Methodology of Selection and Ranking Populations. John Wiley, New York.
Gupta, S.S., Kim, Woo-Chul, 1984. A two-stage elimination type procedure for selecting the largest of several normal means with a common unknown variance. Statistics: Textbooks and monographs, 56, 77–94.
Tamhane, A.C., Bechhofer, R.E., 1977. A two-stage minimax procedure with screening for selecting the largest normal mean. Commun. Statist. — Theor. Meth., A., 6, 1003–1033.
Tamhane, A.C., Bechhofer, R.E., 1979. A two-stage minimax procedure with screening for selecting the largest normal mean (II): An improved PCS lower bound and associated tables. Commun. Statist. — Theor. Meth., A., 8, 337–358.
Taylor, R.J., David, H.A., 1962. A multistage procedure for the selection of the best of several populations. J. Amer. Statist. Assoc., 57, 785–795.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, C., Govindarajulu, Z. A Balanced Two-Stage Procedure for Selecting the Best of Normal Populations With Unequal Means. J Stat Theory Pract 4, 477–494 (2010). https://doi.org/10.1080/15598608.2010.10411998
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1080/15598608.2010.10411998