Open Access
August, 1987 Testing Precise Hypotheses
James O. Berger, Mohan Delampady
Statist. Sci. 2(3): 317-335 (August, 1987). DOI: 10.1214/ss/1177013238


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.


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James O. Berger. Mohan Delampady. "Testing Precise Hypotheses." Statist. Sci. 2 (3) 317 - 335, August, 1987.


Published: August, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0955.62545
MathSciNet: MR920141
Digital Object Identifier: 10.1214/ss/1177013238

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

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.2 • No. 3 • August, 1987
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