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,
α = P ( test rejects H 0 ∣ H 0 ) . {\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.
α = sup h ∈ H 0 P ( test rejects H 0 ∣ h ) . {\displaystyle \alpha =\sup _{h\in H_{0}}P({\text{test rejects }}H_{0}\mid h).}
A test is said to have significance level α {\displaystyle \alpha } if its size is less than or equal to α {\displaystyle \alpha } . In many cases the size and level of a test are equal.
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