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• W2333682216 abstract "A sequential procedure for selecting the best one of several normal populations with a common unknown variance was described in [1]; a later paper [2] reported on the results of Monte Carlo sampling experiments designed to study some of the performance characteristics of that procedure. In these papers it was asserted that the procedure guaranteed a certain probability requirement ([1] pp. 411-12), and also that it possessed the desirable property that it can capitalize on any favorable configuration of the population means ([1] p. 415). The purpose of this note is to comment on these assertions based on the current state of knowledge concerning this problem. As will be pointed out below, the first assertion has not yet been proved (or disproved) analytically; however, the second assertion is now known to be false (and, in fact, the procedure has a highly undesirable feature in this regard). For these reasons the writer recommends that the procedure not be used. In order to economize on space we shall not formulate the problem and describe the procedure here, but shall use the same notation as in [1] and [2], and refer the reader to those papers for details. At the time that [1] was written, it was thought (see [5]) that the procedure under consideration (referred to in [1] as Procedure D), was a generalization of the corresponding procedure for the common known variance case (referred to in [1] as Procedure C), and that the method of proof that Proceedure C guarantees the probability requirement carried over with minor modifications to Procedure D. (The proof that Procedure C guarantees the probability requirement is contained in [4].) It is now known that the proof does not carry over, and that Procedure D has an entirely different structure from Procedure C. To the present time the author has not been able to determine whether or not Procedure D does in fact guarantee the probability requirement (although he conjectures that it does asymptotically as 6* 0 for fixed P*). However, in any event, Procedure D is now known to have an extremely serious deficiency. It was called to the writer's attention by Professor Edward Paulson (in a personal communication) that this procedure does not capitalize on certain favorable configurations of the population means, but rather that Procedure D has the highly undesirable property that the expected number of" @default.
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• W2333682216 title "Correction Note: An Undesirable Feature of a Sequential Multiple-Decision Procedure for Selecting the Best One of Several Normal Populations with a Common Unknown Variance" @default.
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