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,

α=P(test rejects H0∣H0).

In the case of a composite null hypothesis, the size is the supremum over all data generating processes that satisfy the null hypotheses.[1]

α=suph∈H0P(test rejects H0∣h).

A test is said to have significance level α if its size is less than or equal to α.[2][3] In many cases the size and level of a test are equal.

## References

1. ↑ Davidson, Russell; MakKinnon, James G. (2004). Econometric theory and methods. New York, NY [u.a.]: Oxford Univ. Press. ISBN 978-0-19-512372-2.
2. ↑ Taboga, Marco. "Lectures on Probability Theory and Mathematical Statistics". https://www.statlect.com/fundamentals-of-statistics/hypothesis-testing.
3. ↑ "Size of a test and level of significance". https://stats.stackexchange.com/q/51217.

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