Size (statistics)

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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,

${\displaystyle \alpha =P({\text{test rejects }}H_{0}\mid H_{0}).}$

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

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

A test is said to have significance level ${\displaystyle \alpha }$ if its size is less than or equal to ${\displaystyle \alpha }$.^[2][3] In many cases the size and level of a test are equal.