On Approximate Optimality of the Sample Size for the Partition Problem

We consider the problem of partitioning a set of normal populations with respect to a control population into two disjoint subsets according to their unknown means. For the purely sequential procedure of Solanky and Wu (2004) which can take c (epsilon 1) observations from the control population at each sampling step, an approximate optimal sampling strategy is derived in order to minimize the total sampling cost. The obtained methodology is easy to implement and it depends only on the sampling costs and the number of populations to be partitioned. More importantly, it does not depend on the design parameters and the unknown parameters. The performance of the obtained optimal strategy is studied via Monte Carlo simulations to investigate the role of unknown parameters and the design parameters on the derived optimality. An example is provided to illustrate the derived optimal allocation strategy.