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,

\alpha =P({\text{test rejects }}H_{0}|H_{0}).

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

\alpha =\sup _{h\in H_{0}}P({\text{test rejects }}H_{0}|h).

A test is said to have significance level $\alpha$ if its size is less than or equal to $\alpha$ . 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.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.

[DM-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.