A two-sample procedure for selecting the population with the largest mean from several normal populations with unknown variances

SUMMARY This paper gives a two-sample procedure for selecting the population with the largest mean from k normal populations with unknown variances. The method is based on a twosample procedure proposed by Stein (1945). Tables necessary for the application of the procedure are given for selected values of k. Comparisons of the minimum values of the expected sample sizes using the proposed procedure are made with the corresponding single-sample sizes for known variances (Bechhofer, 1954). Comparisons are also made of the expected total sample sizes for the single-sample procedure, the two-sample procedure given in this paper and the two-sample procedure proposed by Bechhofer, Dunnett & Sobel (1954) which assumes that the populations have known variance ratios. It is shown that the expected total sample sizes are not much increased by ignorance of the variance ratios.