The Annals of Statistics
- Ann. Statist.
- Volume 12, Number 2 (1984), 451-469.
An Alternative to Student's $t$-Test for Problems with Indifference Zones
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.
Ann. Statist., Volume 12, Number 2 (1984), 451-469.
First available in Project Euclid: 12 April 2007
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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