An 
-test is a statistical
test whose test statistic has an F-distribution
under the null hypothesis. Such tests arise naturally
when comparing independent estimates of variance. They
include the classical test for equality of the variances
of two populations and the overall test in ANOVA
(Casella and Berger 2002).
For the two-population variance test, let statistically independent random samples have sample
sizes 
and 
and be drawn from normal
distributions with variances 
and 
. Let 
and 
be the corresponding unbiased sample variances.
Under the null hypothesis 
, the statistic
 |
(1)
|
Here, 
denotes the F-distribution
with numerator and denominator degrees of freedom 
and 
.
If 
is the 
th quantile of that distribution,
a two-tailed test of significance
level 
rejects 
when
 |
(2)
|
or
 |
(3)
|
A one-tailed test uses the corresponding single tail. The exact 
null distribution requires
each population to have a normal
distribution and the two samples to be statistically independent.
