On the Relationship between Stepwise Decision Procedures and Confidence Sets

This article considers the relationship between two standard methods of inference on a set of A: unknown parameters, namely stepwise decision procedures and the construction of simultaneous confidence intervals. Illustrative examples with k = 2 are discussed for one-sided step-down and step-up decision procedures and for a two-sided step-down decision procedure. For these examples with normal distributional assumptions, a set of confidence intervals associated with the decision procedure is constructed that provides additional information at no increase in the error rate. The implication of this work is that commonly used stepwise decision procedures are per se not providing as complete an inference as is available. The construction of new decision procedures and confidence sets designed specifically to meet an experimenter's particular requirements is also discussed.