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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
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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

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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

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