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June, 1984 An Alternative to Student's $t$-Test for Problems with Indifference Zones
Lawrence D. Brown, Harold Sackrowitz
Ann. Statist. 12(2): 451-469 (June, 1984). DOI: 10.1214/aos/1176346499

Abstract

Consider a sample from a normal population with mean, $\mu$, and variance unknown. Suppose it is desired to test $H_0:\mu \leq \mu_0$ versus $H_1:\mu \geq \mu_1$, with the region $H^I_1:\mu_0 < \mu < \mu_1$ being a (nonempty) indifference zone. It is shown that the usual Student's $t$-test is inadmissible for this problem. An alternative test is proposed. The two sided problem with indifference region is also discussed. By contrast with the above result, the usual Student's $t$-test is admissible here. However the two sided version of the alternative test mentioned above does offer some practical advantages relative to the two sided $t$-test. A 3-decision version of the two sided problem is also discussed. Here the $t$-test is inadmissible, and is dominated by the appropriate version of the alternative test. The results concerning tests are also reformulated as results about confidence procedures.

Citation

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Lawrence D. Brown. Harold Sackrowitz. "An Alternative to Student's $t$-Test for Problems with Indifference Zones." Ann. Statist. 12 (2) 451 - 469, June, 1984. https://doi.org/10.1214/aos/1176346499

Information

Published: June, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0544.62023
MathSciNet: MR740905
Digital Object Identifier: 10.1214/aos/1176346499

Subjects:
Primary: 62F03
Secondary: 62A99

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 2 • June, 1984
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