Design considerations for neyman-pearson and wald hypothesis testing |
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Authors: | Noel Cressie Peter B. Morgan |
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Affiliation: | (1) Department of Statistics, Iowa State University, 50011 Ames, IA, USA;(2) Department of Economics, University of Western Ontario, N6A 5C2 London, Ontario, Canada |
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Abstract: | Summary The Neyman-Pearson Lemma describes a test for two simple hypotheses that, for a given sample size, is most powerful for its level. It is usually implemented by choosing the smallest sample size that achieves a prespecified power for a fixed level. The Lemma does not describe how to select either the level or the power of the test. In the usual Wald decision-theoretic structure there exists a sampling cost function, an initial prior over the hypothesis space and various payoffs to right/wrong hypothesis selections. The optimal Wald test is a Bayes decision rule that maximizes the expected payoff net of sampling costs. This paper shows that the Wald-optimal test and the Neyman-Pearson test can be the same and how the Neyman-Pearson test, with fixed level and power, can be viewed as a Wald test subject to restrictions on the payoff vector, cost function and prior distribution. |
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Keywords: | cost function decision theory level maximizing expected net gain power prior sequential test |
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