The difference between one and the critical function. Suppose that a certain hypothesis $H_0$ concerning the distribution of a random variable $X$ is being tested, using a test based on a statistic $T(X)$ the distribution function of which — provided $H_0$ is true — is $G(t)$. If the critical region for the test is defined by an equality $T(X)>t$, then the critical level is given by $1-G\{T(X)\}$.

References

[1] E.L. Lehmann, "Testing statistical hypotheses" , Wiley (1959)
[2] J. Hájek, Z. Sidák, "Theory of rank tests" , Acad. Press (1967)
How to Cite This Entry:
Critical level. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Critical_level&oldid=32505
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article