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.

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

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.