## Statistical Science

- Statist. Sci.
- Volume 2, Number 3 (1987), 317-335.

### Testing Precise Hypotheses

James O. Berger and Mohan Delampady

#### Abstract

Testing of precise (point or small interval) hypotheses is reviewed, with special emphasis placed on exploring the dramatic conflict between conditional measures (Bayes factors and posterior probabilities) and the classical P-value (or observed significance level). This conflict is highlighted by finding lower bounds on the conditional measures over wide classes of priors, in normal and binomial situations, lower bounds, which are much larger than the P-value; this leads to the recommendation of several alternatives to P-values. Results are also given concerning the validity of approximating an interval null by a point null. The overall discussion features critical examination of issues such as the probability of objective testing and the possibility of testing from confidence sets.

#### Article information

**Source**

Statist. Sci., Volume 2, Number 3 (1987), 317-335.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.ss/1177013238

**Digital Object Identifier**

doi:10.1214/ss/1177013238

**Mathematical Reviews number (MathSciNet)**

MR920141

**Zentralblatt MATH identifier**

0955.62545

**JSTOR**

links.jstor.org

**Keywords**

Point null hypothesis P-value Bayes factor posterior probability objectivity robust Bayesian analysis Jeffreys's paradox binomial tests $\chi^2$ tests scientific communication

#### Citation

Berger, James O.; Delampady, Mohan. Testing Precise Hypotheses. Statist. Sci. 2 (1987), no. 3, 317--335. doi:10.1214/ss/1177013238. https://projecteuclid.org/euclid.ss/1177013238

#### See also

- See Comment: D. R. Cox. [Testing Precise Hypotheses]: Comment. Statist. Sci., Volume 2, Number 3 (1987), 335--336.Project Euclid: euclid.ss/1177013239
- See Comment: Morris L. Eaton. [Testing Precise Hypotheses]: Comment. Statist. Sci., Volume 2, Number 3 (1987), 337--338.Project Euclid: euclid.ss/1177013240
- See Comment: Arnold Zellner. [Testing Precise Hypotheses]: Comment. Statist. Sci., Volume 2, Number 3 (1987), 339--341.Project Euclid: euclid.ss/1177013241
- See Comment: M. J. Bayarri. [Testing Precise Hypotheses]: Comment. Statist. Sci., Volume 2, Number 3 (1987), 342--344.Project Euclid: euclid.ss/1177013242
- See Comment: George Casella, Roger L. Berger. [Testing Precise Hypotheses]: Comment. Statist. Sci., Volume 2, Number 3 (1987), 344--347.Project Euclid: euclid.ss/1177013243
- See Comment: Joseph B. Kadane. [Testing Precise Hypotheses]: Comment. Statist. Sci., Volume 2, Number 3 (1987), 347--348.Project Euclid: euclid.ss/1177013244
- See Comment: James O. Berger, Mohan Delampady. [Testing Precise Hypotheses]: Rejoinder. Statist. Sci., Volume 2, Number 3 (1987), 348--352.Project Euclid: euclid.ss/1177013245