SELECTION OF THE BEST IN 2X2 FACTORIAL-DESIGNS

Selection of the cell in a 2x2 factorial design with the greatest mean is considered. A general class of ranking and selection procedures (RSP) is constructed to include methods based on the largest marginal cell means (SP1) or on the largest cell mean (SP3). Using the preference zone approach the minimum probability of a correct solution is found. In this paper a RSP which maximizes the minimum probability of a correct solution over the preference zone is found. In this way selection of the cell with the greatest observed mean is proven to be admissible.