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,

[math]\displaystyle{ \alpha = P(\text{test rejects } H_0 \mid H_0). }[/math]

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

[math]\displaystyle{ \alpha = \sup_{h\in H_0} P(\text{test rejects } H_0 \mid h). }[/math]

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