The Annals of Statistics

An Alternative to Student's $t$-Test for Problems with Indifference Zones

Lawrence D. Brown and Harold Sackrowitz

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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.

Article information

Source
Ann. Statist., Volume 12, Number 2 (1984), 451-469.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346499

Digital Object Identifier
doi:10.1214/aos/1176346499

Mathematical Reviews number (MathSciNet)
MR740905

Zentralblatt MATH identifier
0544.62023

JSTOR
links.jstor.org

Subjects
Primary: 62F03: Hypothesis testing
Secondary: 62A99: None of the above, but in this section

Keywords
$t$-test indifference zone confidence intervals admissibility

Citation

Brown, Lawrence D.; Sackrowitz, Harold. An Alternative to Student's $t$-Test for Problems with Indifference Zones. Ann. Statist. 12 (1984), no. 2, 451--469. doi:10.1214/aos/1176346499. https://projecteuclid.org/euclid.aos/1176346499


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