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,

${\displaystyle \alpha =P(\text{test rejects }{H}_0\mid H_0).}$

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

${\displaystyle \alpha =\underset{h\in H_0}{\sup }P(\text{test rejects }{H}_0\mid h).}$

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.

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