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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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

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

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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

$t$-test indifference zone confidence intervals admissibility


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.

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