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In Defense of the Neyman-Pearson Theory of Confidence Intervals

Published online by Cambridge University Press:  01 April 2022

Deborah G. Mayo
Deborah G. Mayo*
Affiliation:
Department of Philosophy and Religion Virginia Polytechnic Institute & State University
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Abstract

In Philosophical Problems of Statistical Inference, Seidenfeld argues that the Neyman-Pearson (NP) theory of confidence intervals is inadequate for a theory of inductive inference because, for a given situation, the ‘best’ NP confidence interval, [CIλ], sometimes yields intervals which are trivial (i.e., tautologous). I argue that (1) Seidenfeld's criticism of trivial intervals is based upon illegitimately interpreting confidence levels as measures of final precision; (2) for the situation which Seidenfeld considers, the ‘best’ NP confidence interval is not [CIλ] as Seidenfeld suggests, but rather a one-sided interval [CI0]; and since [CI0] never yields trivial intervals, NP theory escapes Seidenfeld's criticism entirely; (3) Seidenfeld's criterion of non-triviality is inadequate, for it leads him to judge an alternative confidence interval, [CIalt.], superior to [CIλ] although [CIalt.] results in counterintuitive inferences. I conclude that Seidenfeld has not shown that the NP theory of confidence intervals is inadequate for a theory of inductive inference.

Type
Research Article
Information
Philosophy of Science , Volume 48 , Issue 2 , June 1981 , pp. 269 - 280
Copyright
Copyright © 1981 by the Philosophy of Science Association

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Footnotes

†

I would like to thank Ronald Giere and Teddy Seidenfeld for very useful comments on an earlier draft of this paper. I am very grateful to I. J. Good, Klaus Hinkelmann, and George Shapiro for helpful discussions concerning this paper. I am particularly grateful to Klaus Hinkelmann for our discussions of one-sided confidence intervals.

References

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