Open Access
September, 1956 The WAGR Sequential $t$-Test Reaches a Decision with Probability One
Herbert T. David, William H. Kruskal
Ann. Math. Statist. 27(3): 797-805 (September, 1956). DOI: 10.1214/aoms/1177728186


The WAGR test is a sequential procedure for testing the null hypothesis that the proportion of a normal population greater than a given constant is $p_0$ (given) against the alternative that it is $p_1$ (given). These are equivalent (after a translation) to hypotheses specifying the value of $\mu/\sigma,$ where $\mu$ and $\sigma^2$ are the mean and the variance of the normal population under test. We prove that, with probability one, a decision is reached when the WAGR test is applied. This fact is of importance in its own right; it also has indirect interest because, unless it were true, the standard Wald inequalities on probabilities of error at the two hypothesis points could not be applied.


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Herbert T. David. William H. Kruskal. "The WAGR Sequential $t$-Test Reaches a Decision with Probability One." Ann. Math. Statist. 27 (3) 797 - 805, September, 1956.


Published: September, 1956
First available in Project Euclid: 28 April 2007

zbMATH: 0073.35704
MathSciNet: MR81045
Digital Object Identifier: 10.1214/aoms/1177728186

Rights: Copyright © 1956 Institute of Mathematical Statistics

Vol.27 • No. 3 • September, 1956
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