### Frequentist statistics as a theory of inductive inference

Deborah G. Mayo, D. R. Cox

#### 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.

First Page:
Primary Subjects: 62B15, 62F03
Keywords: statistical inference; significance test; confidence interval; test of hypothesis; Neyman--Pearson theory; selection effect; multiple testing
Full-text: Open access