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Testing Precise Hypotheses
Open accessAbstract
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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“The posterior probability of 'no effect' can be viewed as an approximation to the posterior probability of the effect being 'small,' namely, P lparenOSCASB vertSHT β vertSHT < ε rparenOSCASB , provided that ε is at most about onehalf of a standard error (Berger and Delampady, 1987).”
From Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors (1999) · cites this paper as Berger and Delampady, 1987
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“In fact, p -values arguably overstate the evidence for an effect even when there is no model uncertainty (Edwards, Lindman and Savage, 1963; Berger and Delampady, 1987; Berger and Sellke, 1987).”
From Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors (1999) · cites this paper as Berger and Delampady, 1987
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Metadata
- Authors
- Berger, J. O., & Delampady, M.
- Venue
- Statistical Science
- Publisher
- Institute of Mathematical Statistics
- Published
- 1987-08-01
- Volume
- 2
- Issue
- 3
- Pages
- 317-335
- ISSN
- 0883-4237 (ISSN-L)
- 2168-8745
- OpenAlex
- W2128585330
- Cited by
- 664
- References
- 35
- Citations by year
- 2025: 6 · 2024: 11 · 2023: 14 · 2022: 20 · 2021: 29 · 2020: 24 · 2019: 29 · 2018: 26 · 2017: 22 · 2016: 32 · 2015: 23 · 2014: 21 · 2013: 23 · 2012: 22
- FWCI
- 10.67
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Statistical Science (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Keywords
- point null hypothesis, p-values, Bayes factor, posterior probability, normal distribution, binomial distribution, objective testing, confidence regions
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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