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.


 * $$\alpha = \sup_{h\in H_0} P(\text{test rejects } H_0 \mid h). $$

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.