Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-10T12:28:27.181Z Has data issue: false hasContentIssue false
  • English
  • Français

On After-Trial Properties of Best Neyman-Pearson Confidence Intervals

Published online by Cambridge University Press:  01 April 2022

Teddy Seidenfeld
Teddy Seidenfeld*
Affiliation:
Department of Philosophy Washington University, St. Louis
Get access Rights & Permissions [Opens in a new window]

Extract

On pp. 55–58 of Philosophical Problems of Statistical Inference (Seidenfeld 1979), I argue that in light of unsatisfactory after-trial properties of “best” Neyman-Pearson confidence intervals, we can strengthen a traditional criticism of the orthodox N-P theory. The criticism is that, once particular data become available, we see that the pre-trial concern for tests of maximum power (and for their derivative confidence intervals of shortest expected length) may then misrepresent the conclusion of such a test (or interval estimate). Specifically, I offer a statistical example where there exists a Uniformly Most Powerful test (a UMP-test), a test of highest N-P credentials, which generates a system of “best” confidence intervals (the [CIλ] interval system) with exact confidence coefficients. But the [CIλ] intervals have the unsatisfactory feature that, for a recognizable set of outcomes, the interval estimates cover all parameter values consistent with the data, at strictly less than 100% confidence.

Type
Research Article
Information
Philosophy of Science , Volume 48 , Issue 2 , June 1981 , pp. 281 - 291
Copyright
Copyright © 1981 by the Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

I thank Isaac Levi and Carl Posy for helpful comments on an earlier draft of this paper. Also, I appreciate the opportunity to read and discuss Professor Mayo's paper (Mayo 1981) with her and Ronald Giere in advance of its publication.

References

Ghosh, J. K. (1961), “On the Relation Among Shortest Confidence Intervals of Different Types”, Calcutta Statistical Association Bulletin 10: 147–152.CrossRefGoogle Scholar
Mayo, D. G. (1981), “In Defense of the Neyman-Pearson Theory of Confidence Intervals”, Philosophy of Science 48: pp. 269–80.CrossRefGoogle Scholar
Neyman, J. (1937), “Outline of a theory of statistical estimation based on the classical theory of probability”, Philosophical Transactions of the Royal Society of London Ser A, 236: 333–380. Reprinted as paper 20 in A Selection of Early Statistical Papers of J. Neyman (1967), Berkeley and Los Angeles: University of California Press, pp. 250–290. Page references are to this reprinting.CrossRefGoogle Scholar
Pratt, R. (1961), “Length of Confidence Intervals”, Journal of the American Statistical Association 56, #295: 549–567.CrossRefGoogle Scholar
Seidenfeld, T. (1979), Philosophical Problems of Statistical Inference. Dordrecht: Reidel.Google Scholar
von Mises, R. (1941), “On the Foundations of Probability and Statistics”, Annals of Mathematical Statistics 12: 191–205.CrossRefGoogle Scholar