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((refimprove|date=January 2017))
In  [[statistics]], the '''size''' of a [[statistical test|test]] is the probability of [[Type I error#Type I error|falsely rejecting]] the [[null hypothesis]]. That is, it is the probability of making a [[type I error]]. It is denoted by the Greek letter α (alpha). 

For a [[simple hypothesis]],

:<math>\alpha = P(\text{test rejects } H_0 \mid H_0). </math>

In the case of a [[composite hypothesis|composite null hypothesis]], the size is the supremum over all data generating processes that satisfy the null hypotheses.<ref name="DM">((cite book|last1=Davidson|first1=Russell|last2=MakKinnon|first2=James G.|title=Econometric theory and methods|date=2004|publisher=Oxford Univ. Press|location=New York, NY [u.a.]|isbn=978-0-19-512372-2|ref=DM))</ref>

:<math>\alpha = \sup_{h\in H_0} P(\text{test rejects } H_0 \mid h). </math>

A test is said to have [[significance level]] <math> \alpha </math> if its size is less than or equal to <math> \alpha </math>.<ref>((cite web|last1=Taboga|first1=Marco|title=Lectures on Probability Theory and Mathematical Statistics|url=https://www.statlect.com/fundamentals-of-statistics/hypothesis-testing|website=statlect.com|access-date=6 June 2022))</ref><ref>((cite web|title=Size of a test and level of significance|url=https://stats.stackexchange.com/q/51217 |website=[[Stack Exchange]] |access-date=6 June 2022))</ref>
In many cases the size and level of a test are equal.

==References==
((reflist))

[[Category:Statistical hypothesis testing]]


((statistics-stub))

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