A critical value is a threshold for a test statistic used to decide whether to reject a null hypothesis
in a statistical test. For an upper-tailed
test with test statistic 
and a continuous null distribution,
a critical value 
at significance level 
is commonly selected to satisfy
 |
where 
is the null hypothesis. For a discrete
distribution, this equality need not be attainable. A nonrandomized test instead
chooses a rejection region whose probability under 
is at most 
. Lower-tailed and two-tailed
tests use the corresponding lower or paired thresholds.
