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 longrun interpretation. A variety of more complicated situations are discussed in which modification of the simple $p$value may be essential.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2006
 arXiv:
 arXiv:math/0610846
 Bibcode:
 2006math.....10846M
 Keywords:

 Mathematics  Statistics;
 62B15;
 62F03 (Primary)
 EPrint:
 Published at http://dx.doi.org/10.1214/074921706000000400 in the IMS Lecture NotesMonograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)