A SEQUENTIAL PROCEDURE WITH ELIMINATION FOR PARTITIONING A SET OF NORMAL POPULATIONS HAVING A COMMON UNKNOWN VARIANCE.

We consider the problem of partitioning a set of normal populations, with respect to a control population, into two subsets according to their unknown means, under the indifference zone formulation. For this problem Tong (1969) constructed a two-stage and purely sequential procedures and recently Datta and Mukhopadhyay (1998) have considered various multistage methodologies emphasizing the second-order asymptotics. However, all these methodologies adopt a vector-at-a-time sampling approach and lack the desirable feature of eliminating treatments from further sampling at an earlier stage. We propose an elimination type sequential procedure using the Paulson's (1964) elimination idea and design a sampling methodology which eliminates “superior” and “inferior” treatments during the sampling, thereby reducing the average sample size considerably. Theoretical results are obtained to show that the proposed elimination-type procedure maintains the probability of correct partition above a pre specified level. The proposed procedure is studied and compared via the Monte Carlo simulation studies with other competitive procedures known in the literature, under both the LFC and a few non-LFC configurations. The elimination-type procedure is found to be vastly more efficient than its competitors in terms of average sample size. [ABSTRACT FROM AUTHOR]