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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

Hacking, I. (1965), Logic of Statistical Inference. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kendall, M. G. (1961), The Advanced Theory of Statistics, vol. II. London: Charles Griffin.CrossRefGoogle Scholar
Lehmann, E. L. (1959), Testing Statistical Hypotheses. New York: Wiley.Google Scholar
Mood, A. M., Graybill, F. A., and Boes, D. C. (1950), Introduction to the Theory of Statistics. New York: McGraw-Hill.Google 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, No. 767, 236: 333–380.Google Scholar
Savage, L. J. (1962), The Foundations of Statistical Inference. London: Methuen.Google Scholar
Seidenfeld, T. (1979), Philosophical Problems of Statistical Inference. Dordrecht: Reidel.Google Scholar
Spielman, S. (1973), “A Refutation of the Neyman-Pearson Theory of Testing”, British Journal for the Philosophy of Science 24: 201–222.CrossRefGoogle Scholar