Statistics Papers

Document Type

Journal Article

Date of this Version

1984

Publication Source

The Annals of Statistics

Volume

12

Issue

2

Start Page

451

Last Page

469

DOI

10.1214/aos/1176346499

Abstract

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.

Keywords

t-test, indifference zone, confidence intervals, admissibility

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Date Posted: 27 November 2017

This document has been peer reviewed.