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}\mid H_{0}).

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

\alpha =\sup _{h\in H_{0}}P({\text{test rejects }}H_{0}\mid 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

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

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[DM-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.