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Size (statistics)

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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,

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

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

References

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  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". statlect.com. Retrieved 6 June 2022.
  3. ^ "Size of a test and level of significance". Stack Exchange. Retrieved 6 June 2022.