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VOL. 49 | 2006 Frequentist statistics as a theory of inductive inference

## Abstract

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.

## Information

Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1268.62006
MathSciNet: MR2337831

Digital Object Identifier: 10.1214/074921706000000400

Subjects:
Primary: 62B15 , 62F03

Keywords: Confidence interval , multiple testing , Neyman--Pearson theory , selection effect , significance test , statistical inference , test of hypothesis