Evaluation of a class of sequential sampling procedures
Piper, Larry Dean
Barr, Donald R.
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A class of sequential procedures for estimating the mean of a normal distribution having known variance from quantal response data is discussed. This class includes as special; members the up-and-down method and other procedures commonly used in biological assay. A method of evaluating alternative procedures belonging to a given subset of the class id presented. This method is essentially an application of Wald's decision theory. A loss plus cost objective function is used and the efficiency of a particular procedure is determined by its ability to satisfy one of the four criteria considered. Criteria are discussed for use with both the expected value and variance of the total loss, which may be determined from matrix equations that are derived. Two applications are given. The first is an application to procedures commonly used in biological assay. In the second, an application to the elevation procedure of the precision registration technique used by U.S. Army and Marin Corps field artillery units, it is seen that under certain conditions, Dixon's modified up-and-down method strictly dominates the elevation procedure currently in use.
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