Size (statistics)
From HandWiki
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,
- [math]\displaystyle{ \alpha = P(\text{test rejects } H_0 \mid H_0). }[/math]
In the case of a composite null hypothesis, the size is the supremum over all data generating processes that satisfy the null hypotheses.[1]
- [math]\displaystyle{ \alpha = \sup_{h\in H_0} P(\text{test rejects } H_0 \mid h). }[/math]
A test is said to have significance level [math]\displaystyle{ \alpha }[/math] if its size is less than or equal to [math]\displaystyle{ \alpha }[/math].[2][3] In many cases the size and level of a test are equal.
References
- ↑ Davidson, Russell; MakKinnon, James G. (2004). Econometric theory and methods. New York, NY [u.a.]: Oxford Univ. Press. ISBN 978-0-19-512372-2.
- ↑ Taboga, Marco. "Lectures on Probability Theory and Mathematical Statistics". https://www.statlect.com/fundamentals-of-statistics/hypothesis-testing.
- ↑ "Size of a test and level of significance". https://stats.stackexchange.com/q/51217.
Original source: https://en.wikipedia.org/wiki/Size (statistics).
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