Statistical Science

Testing Precise Hypotheses

James O. Berger and Mohan Delampady

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


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See also

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