In this dissertation, the problem of partitioning a set of treatments with respect to a control treatment is considered. Starting in 1950's a number of researchers have worked on this problem and have proposed alternative solutions. In Tong (1979), the authors proposed a formulation to solve this problem and hundreds of researchers and practitioners have used that formulation for the partition problem. However, Tong's formulation is somewhat rigid and misleading for the practitioners, if the distance between the ``good'' and the ``bad'' populations is large. In this case, the indifference zone gets quite large and the undesirable feature of the Tong's formulation to partition the populations in the indifference zone, without any penalty, can potentially lead Tong's formulation to produce misleading partitions. In this dissertation, a generalization of the Tong's formulation is proposed, under which, the treatments in the indifference zone are not partitioned as ``good'' or ``bad'', but are partitioned as a identifiable set. For this generalized partition, a fully sequential and a two-stage procedure is proposed and its theoretical properties are derived. The proposed procedures are also studied via Monte Carlo Simulation studies. The thesis concludes with some non-parametric partition procedures and the study of robustness of the various available procedures in the statistical literature.

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