Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-04T02:07:12.029Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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 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