Size (statistics)

In statistics, the size of a test is the probability of 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,

$\alpha =P({\text{test rejects }}H_{0}|H_{0}).\,$

In the case of a composite null hypothesis, the size is the supremum over all data generating processes that satisfiy the null hypotheses.^[1]

$\alpha =\sup _{{h\in H_{0}}}P({\text{test rejects }}H_{0}|h).\,$

A test is said to have significance level $\alpha$ if its size is less than or equal to $\alpha$. In many cases the size and level of a test are equal.

References

1. Davidson, Russell; MakKinnon, James G. (2004). Econometric theory and methods. New York, NY [u.a.]: Oxford Univ. Press. ISBN 978-0-19-512372-2.