Translator Disclaimer
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


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.


Download Citation

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.


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

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

Primary: 62F03
Secondary: 62A99

Rights: Copyright © 1984 Institute of Mathematical Statistics


Vol.12 • No. 2 • June, 1984
Back to Top