Editing Statistical hypothesis test (section)

== Variations and sub-classes ==
Statistical hypothesis testing is a key technique of both [[frequentist inference]] and [[Bayesian inference]], although the two types of inference have notable differences. Statistical hypothesis tests define a procedure that controls (fixes) the probability of incorrectly ''deciding'' that a default position ([[null hypothesis]]) is incorrect. The procedure is based on how likely it would be for a set of observations to occur if the null hypothesis were true. This probability of making an incorrect decision is ''not'' the probability that the null hypothesis is true, nor whether any specific alternative hypothesis is true. This contrasts with other possible techniques of [[decision theory]] in which the null and [[alternative hypothesis]] are treated on a more equal basis.

One naïve [[Bayesian statistics|Bayesian]] approach to hypothesis testing is to base decisions on the [[posterior probability]],<ref>Schervish, M (1996) ''Theory of Statistics'', p. 218. Springer {{isbn|0-387-94546-6}}</ref><ref>{{cite book|title=Reference Manual on Scientific Evidence|publisher=West National Academies Press|chapter=Reference Guide on Statistics|first1=David H.|last1=Kaye|first2=David A.|last2=Freedman|chapter-url=http://www.nap.edu/openbook.php?record_id=13163&page=211|location=Eagan, MN; Washington, D.C.|year=2011|edition=3rd|page=259|isbn=978-0-309-21421-6}}</ref> but this fails when comparing point and continuous hypotheses. Other approaches to decision making, such as [[Bayesian decision theory]], attempt to balance the consequences of incorrect decisions across all possibilities, rather than concentrating on a single null hypothesis. A number of other approaches to reaching a decision based on data are available via [[decision theory]] and [[optimal decision]]s, some of which have desirable properties. Hypothesis testing, though, is a dominant approach to data analysis in many fields of science. Extensions to the theory of hypothesis testing include the study of the [[statistical power|power]] of tests, i.e. the probability of correctly rejecting the null hypothesis given that it is false. Such considerations can be used for the purpose of [[sample size determination]] prior to the collection of data.