Frequentist statistics as a theory of inductive inference

Details Frequentist statistics as a theory of inductive inference Frequentist statistics as a theory of inductive inference

2006-10-27

arxiv.org/abs/math/0610846v1

IMS Lecture Notes--Monograph Series 2006, Vol. 49, 77-97

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/074921706000000400 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

10.1214/074921706000000400

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.

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