Date of this Version
The Annals of Statistics
Consider a sample from a normal population with mean, μ, and variance unknown. Suppose it is desired to test H0:μ ≤ μ0 versus H1:μ ≥ μ1, with the region HI1:μ0 < μ < μ1 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.
t-test, indifference zone, confidence intervals, admissibility
Brown, L. D., & Sackrowitz, H. (1984). An Alternative to Student's t-Test for Problems With Indifference Zones. The Annals of Statistics, 12 (2), 451-469. http://dx.doi.org/10.1214/aos/1176346499
Date Posted: 27 November 2017
This document has been peer reviewed.