Size (statistics) explained

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( testrejects 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]

\alpha = \sup _{h\in H _{0}} P( testrejects H _{0} \mid h). \alpha if its size is less than or equal to \alpha .^{[2] [3]} In many cases the size and level of a test are equal.

Notes and References

1. Book: Davidson. Russell. MakKinnon. James G.. Econometric theory and methods. 2004. Oxford Univ. Press. New York, NY [u.a.]. 978-0-19-512372-2. DM.
2. Web site: Taboga. Marco. Lectures on Probability Theory and Mathematical Statistics. statlect.com. 6 June 2022.
3. Web site: Size of a test and level of significance. . 6 June 2022.