Abstract
In this paper, two two-stage selection procedures (factorial procedure FP and interaction procedure IP) are studied for the goal of selecting largest normal mean in complete factorial experiments with interactions and with common unknown variance. It is proven that procedure FP performs better than the procedure IP in terms of expected total sample size when there are no interactions in the model (in which case both the procedures satisfy probability requirement); and that procedure FP fails to satisfy the probability requirement whereas procedure IP does satisfy it when there are non-zero interactions in the model. It is noted that a procedure is being developed which acts as does FP when interactions are insignificant and as does IP when interactions are significant.
