Institute of Mathematical Statistics Lecture Notes - Monograph Series

Frequentist statistics as a theory of inductive inference

Deborah G. Mayo and D. R. Cox

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After some general remarks about the interrelation between philosophical and statistical thinking, the discussion centres largely on significance tests. These are defined as the calculation of $p$-values rather than as formal procedures for ``acceptance'' and ``rejection.'' A number of types of null hypothesis are described and a principle for evidential interpretation set out governing the implications of $p$-values in the specific circumstances of each application, as contrasted with a long-run interpretation. A variety of more complicated situations are discussed in which modification of the simple $p$-value may be essential.

Chapter information

Javier Rojo, ed., Optimality: The Second Erich L. Lehmann Symposium (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 77-97

First available in Project Euclid: 28 November 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62B15: Theory of statistical experiments 62F03: Hypothesis testing

statistical inference significance test confidence interval test of hypothesis Neyman--Pearson theory selection effect multiple testing

Copyright © 2006, Institute of Mathematical Statistics


Mayo, Deborah G.; Cox, D. R. Frequentist statistics as a theory of inductive inference. Optimality, 77--97, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000400.

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