<s>
In	O
statistics	O
,	O
an	O
F-test	B-General_Concept
of	I-General_Concept
equality	I-General_Concept
of	I-General_Concept
variances	I-General_Concept
is	O
a	O
test	O
for	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
two	O
normal	O
populations	O
have	O
the	O
same	O
variance	O
.	O
</s>
<s>
Notionally	O
,	O
any	O
F-test	B-General_Concept
can	O
be	O
regarded	O
as	O
a	O
comparison	O
of	O
two	O
variances	O
,	O
but	O
the	O
specific	O
case	O
being	O
discussed	O
in	O
this	O
article	O
is	O
that	O
of	O
two	O
populations	O
,	O
where	O
the	O
test	B-General_Concept
statistic	I-General_Concept
used	O
is	O
the	O
ratio	O
of	O
two	O
sample	O
variances	O
.	O
</s>
<s>
This	O
particular	O
situation	O
is	O
of	O
importance	O
in	O
mathematical	O
statistics	O
since	O
it	O
provides	O
a	O
basic	O
exemplar	O
case	O
in	O
which	O
the	O
F-distribution	B-General_Concept
can	O
be	O
derived	O
.	O
</s>
<s>
has	O
an	O
F-distribution	B-General_Concept
with	O
n1	O
and	O
m1	O
degrees	O
of	O
freedom	O
if	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
equality	O
of	O
variances	O
is	O
true	O
.	O
</s>
<s>
Otherwise	O
it	O
follows	O
an	O
F-distribution	B-General_Concept
scaled	O
by	O
the	O
ratio	O
of	O
true	O
variances	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
rejected	O
if	O
F	O
is	O
either	O
too	O
large	O
or	O
too	O
small	O
based	O
on	O
the	O
desired	O
alpha	O
level	O
(	O
i.e.	O
,	O
statistical	B-General_Concept
significance	I-General_Concept
)	O
.	O
</s>
<s>
This	O
F-test	B-General_Concept
is	O
known	O
to	O
be	O
extremely	O
sensitive	O
to	O
non-normality	O
,	O
so	O
Levene	B-General_Concept
's	I-General_Concept
test	I-General_Concept
,	O
Bartlett	B-General_Concept
's	I-General_Concept
test	I-General_Concept
,	O
or	O
the	O
Brown	B-General_Concept
–	I-General_Concept
Forsythe	I-General_Concept
test	I-General_Concept
are	O
better	O
tests	O
for	O
testing	O
the	O
equality	O
of	O
two	O
variances	O
.	O
</s>
<s>
(	O
However	O
,	O
all	O
of	O
these	O
tests	O
create	O
experiment-wise	O
type	O
I	O
error	O
inflations	O
when	O
conducted	O
as	O
a	O
test	O
of	O
the	O
assumption	O
of	O
homoscedasticity	B-General_Concept
prior	O
to	O
a	O
test	O
of	O
effects	O
.	O
)	O
</s>
<s>
F-tests	B-General_Concept
for	O
the	O
equality	O
of	O
variances	O
can	O
be	O
used	O
in	O
practice	O
,	O
with	O
care	O
,	O
particularly	O
where	O
a	O
quick	O
check	O
is	O
required	O
,	O
and	O
subject	O
to	O
associated	O
diagnostic	O
checking	O
:	O
practical	O
text-books	O
suggest	O
both	O
graphical	O
and	O
formal	O
checks	O
of	O
the	O
assumption	O
.	O
</s>
<s>
F-tests	B-General_Concept
are	O
used	O
for	O
other	O
statistical	O
tests	O
of	O
hypotheses	O
,	O
such	O
as	O
testing	O
for	O
differences	O
in	O
means	O
in	O
three	O
or	O
more	O
groups	O
,	O
or	O
in	O
factorial	O
layouts	O
.	O
</s>
<s>
These	O
F-tests	B-General_Concept
are	O
generally	O
not	O
robust	O
when	O
there	O
are	O
violations	O
of	O
the	O
assumption	O
that	O
each	O
population	O
follows	O
the	O
normal	O
distribution	O
,	O
particularly	O
for	O
small	O
alpha	O
levels	O
and	O
unbalanced	O
layouts	O
.	O
</s>
<s>
However	O
,	O
for	O
large	O
alpha	O
levels	O
(	O
e.g.	O
,	O
at	O
least	O
0.05	O
)	O
and	O
balanced	O
layouts	O
,	O
the	O
F-test	B-General_Concept
is	O
relatively	O
robust	O
,	O
although	O
(	O
if	O
the	O
normality	O
assumption	O
does	O
not	O
hold	O
)	O
it	O
suffers	O
from	O
a	O
loss	O
in	O
comparative	O
statistical	O
power	O
as	O
compared	O
with	O
non-parametric	O
counterparts	O
.	O
</s>
<s>
This	O
is	O
the	O
problem	O
treated	O
by	O
Hartley	B-General_Concept
's	I-General_Concept
test	I-General_Concept
and	O
Bartlett	B-General_Concept
's	I-General_Concept
test	I-General_Concept
.	O
</s>
