Difference between revisions of "Critical level"
From Encyclopedia of Mathematics
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| − | The difference between one and the [[Critical function|critical function]]. Suppose that a certain hypothesis | + | {{TEX|done}} |
| + | The difference between one and the [[Critical function|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==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> E.L. Lehmann, "Testing statistical hypotheses" , Wiley (1959)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> J. Hájek, Z. Sidák, "Theory of rank tests" , Acad. Press (1967)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> E.L. Lehmann, "Testing statistical hypotheses" , Wiley (1959)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> J. Hájek, Z. Sidák, "Theory of rank tests" , Acad. Press (1967)</TD></TR></table> | ||
Latest revision as of 15:52, 22 July 2014
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=13353
Critical level. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Critical_level&oldid=13353
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article