<s>
In	O
probability	O
theory	O
and	O
statistics	O
,	O
the	O
F-distribution	B-General_Concept
or	O
F-ratio	B-General_Concept
,	O
also	O
known	O
as	O
Snedecor	B-General_Concept
's	I-General_Concept
F	I-General_Concept
distribution	I-General_Concept
or	O
the	O
Fisher	O
–	O
Snedecor	O
distribution	O
(	O
after	O
Ronald	O
Fisher	O
and	O
George	O
W	O
.	O
Snedecor	O
)	O
is	O
a	O
continuous	O
probability	O
distribution	O
that	O
arises	O
frequently	O
as	O
the	O
null	B-General_Concept
distribution	I-General_Concept
of	O
a	O
test	B-General_Concept
statistic	I-General_Concept
,	O
most	O
notably	O
in	O
the	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
(	O
ANOVA	B-General_Concept
)	O
and	O
other	O
F-tests	B-General_Concept
.	O
</s>
<s>
The	O
F-distribution	B-General_Concept
is	O
a	O
particular	O
parametrization	O
of	O
the	O
beta	O
prime	O
distribution	O
,	O
which	O
is	O
also	O
called	O
the	O
beta	O
distribution	O
of	O
the	O
second	O
kind	O
.	O
</s>
<s>
A	O
random	O
variate	O
of	O
the	O
F-distribution	B-General_Concept
with	O
parameters	O
and	O
arises	O
as	O
the	O
ratio	O
of	O
two	O
appropriately	O
scaled	O
chi-squared	O
variates	O
:	O
</s>
<s>
In	O
instances	O
where	O
the	O
F-distribution	B-General_Concept
is	O
used	O
,	O
for	O
example	O
in	O
the	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
,	O
independence	O
of	O
and	O
might	O
be	O
demonstrated	O
by	O
applying	O
Cochran	O
's	O
theorem	O
.	O
</s>
<s>
In	O
a	O
frequentist	B-General_Concept
context	O
,	O
a	O
scaled	O
F-distribution	B-General_Concept
therefore	O
gives	O
the	O
probability	O
,	O
with	O
the	O
F-distribution	B-General_Concept
itself	O
,	O
without	O
any	O
scaling	O
,	O
applying	O
where	O
is	O
being	O
taken	O
equal	O
to	O
.	O
</s>
<s>
This	O
is	O
the	O
context	O
in	O
which	O
the	O
F-distribution	B-General_Concept
most	O
generally	O
appears	O
in	O
F-tests	B-General_Concept
:	O
where	O
the	O
null	O
hypothesis	O
is	O
that	O
two	O
independent	O
normal	O
variances	O
are	O
equal	O
,	O
and	O
the	O
observed	O
sums	O
of	O
some	O
appropriately	O
selected	O
squares	O
are	O
then	O
examined	O
to	O
see	O
whether	O
their	O
ratio	O
is	O
significantly	O
incompatible	O
with	O
this	O
null	O
hypothesis	O
.	O
</s>
<s>
In	O
this	O
context	O
,	O
a	O
scaled	O
F-distribution	B-General_Concept
thus	O
gives	O
the	O
posterior	O
probability	O
,	O
where	O
the	O
observed	O
sums	O
and	O
are	O
now	O
taken	O
as	O
known	O
.	O
</s>
<s>
The	O
noncentral	O
F-distribution	B-General_Concept
simplifies	O
to	O
the	O
F-distribution	B-General_Concept
if	O
.	O
</s>
