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Hochberg, Y., University of Tel Aviv, Ramat-Aviv, Israel
Marcus, R., University of Tel Aviv, Ramat-Aviv, Israel
The problem of selecting the normal population with largest mean when variances are unknown, is considered. A three stage procedure is proposed. Based on pilot samples of size n from (2 > (> ° each population the total sizes N. > N., f>n) of the two following stages are determined. In the second stage one takes N-n additional observations from the ith population and i o, eliminates a random subset of “bad11 populations. If only one population remains after the second stage we make our final selection at that point; if more than one pppulation remains, we proceed to the third stage. In that case additional -N (1) (2) N. observations are drawn from the ith non-eliminated population and a final selection is then made. A simple conservative procedure is derived and compared with corresponding non-elimination procedures on a restricted set of simulated data. The numerical data show that phe new procedure will be very economical in many realistic applications. Another procedure which is shown to be exact over a “slippage zone” is discussed in an Appendix. © 1981, Taylor & Francis Group, LLC. All rights reserved.
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Three stage elimination type procedures for selecting the best normal population when variances are unknown
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Hochberg, Y., University of Tel Aviv, Ramat-Aviv, Israel
Marcus, R., University of Tel Aviv, Ramat-Aviv, Israel
Three stage elimination type procedures for selecting the best normal population when variances are unknown
The problem of selecting the normal population with largest mean when variances are unknown, is considered. A three stage procedure is proposed. Based on pilot samples of size n from (2 > (> ° each population the total sizes N. > N., f>n) of the two following stages are determined. In the second stage one takes N-n additional observations from the ith population and i o, eliminates a random subset of “bad11 populations. If only one population remains after the second stage we make our final selection at that point; if more than one pppulation remains, we proceed to the third stage. In that case additional -N (1) (2) N. observations are drawn from the ith non-eliminated population and a final selection is then made. A simple conservative procedure is derived and compared with corresponding non-elimination procedures on a restricted set of simulated data. The numerical data show that phe new procedure will be very economical in many realistic applications. Another procedure which is shown to be exact over a “slippage zone” is discussed in an Appendix. © 1981, Taylor & Francis Group, LLC. All rights reserved.
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