<s>
In	O
statistics	O
,	O
Levene	B-General_Concept
's	I-General_Concept
test	I-General_Concept
is	O
an	O
inferential	O
statistic	O
used	O
to	O
assess	O
the	O
equality	O
of	O
variances	O
for	O
a	O
variable	O
calculated	O
for	O
two	O
or	O
more	O
groups	O
.	O
</s>
<s>
Levene	B-General_Concept
's	I-General_Concept
test	I-General_Concept
assesses	O
this	O
assumption	O
.	O
</s>
<s>
It	O
tests	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
the	O
population	O
variances	O
are	O
equal	O
(	O
called	O
homogeneity	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
or	O
homoscedasticity	B-General_Concept
)	O
.	O
</s>
<s>
If	O
the	O
resulting	O
p-value	B-General_Concept
of	O
Levene	B-General_Concept
's	I-General_Concept
test	I-General_Concept
is	O
less	O
than	O
some	O
significance	O
level	O
(	O
typically0.05	O
)	O
,	O
the	O
obtained	O
differences	O
in	O
sample	O
variances	O
are	O
unlikely	O
to	O
have	O
occurred	O
based	O
on	O
random	O
sampling	O
from	O
a	O
population	O
with	O
equal	O
variances	O
.	O
</s>
<s>
Thus	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
equal	O
variances	O
is	O
rejected	O
and	O
it	O
is	O
concluded	O
that	O
there	O
is	O
a	O
difference	O
between	O
the	O
variances	O
in	O
the	O
population	O
.	O
</s>
<s>
Some	O
of	O
the	O
procedures	O
typically	O
assuming	O
homoscedasticity	B-General_Concept
,	O
for	O
which	O
one	O
can	O
use	O
Levene	B-General_Concept
's	I-General_Concept
tests	I-General_Concept
,	O
include	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
and	O
t-tests	B-General_Concept
.	O
</s>
<s>
Levene	B-General_Concept
's	I-General_Concept
test	I-General_Concept
is	O
sometimes	O
used	O
before	O
a	O
comparison	O
of	O
means	O
,	O
informing	O
the	O
decision	O
on	O
whether	O
to	O
use	O
a	O
pooled	O
t-test	B-General_Concept
or	O
the	O
Welch	O
's	O
t-test	B-General_Concept
.	O
</s>
<s>
However	O
,	O
it	O
was	O
shown	O
that	O
such	O
a	O
two-step	O
procedure	O
may	O
markedly	O
inflate	O
the	O
type	O
1	O
error	O
obtained	O
with	O
the	O
t-tests	B-General_Concept
and	O
thus	O
should	O
not	O
be	O
done	O
in	O
the	O
first	O
place	O
.	O
</s>
<s>
Levene	B-General_Concept
's	I-General_Concept
test	I-General_Concept
may	O
also	O
be	O
used	O
as	O
a	O
main	O
test	O
for	O
answering	O
a	O
stand-alone	O
question	O
of	O
whether	O
two	O
sub-samples	O
in	O
a	O
given	O
population	O
have	O
equal	O
or	O
different	O
variances	O
.	O
</s>
<s>
Levene	B-General_Concept
's	I-General_Concept
test	I-General_Concept
was	O
developed	O
by	O
and	O
named	O
after	O
American	O
statistician	O
and	O
geneticist	O
Howard	O
Levene	O
.	O
</s>
<s>
Levene	B-General_Concept
's	I-General_Concept
test	I-General_Concept
is	O
equivalent	O
to	O
a	O
1-way	O
between-groups	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
(	O
ANOVA	B-General_Concept
)	O
with	O
the	O
dependent	O
variable	O
being	O
the	O
absolute	O
value	O
of	O
the	O
difference	O
between	O
a	O
score	O
and	O
the	O
mean	O
of	O
the	O
group	O
to	O
which	O
the	O
score	O
belongs	O
(	O
shown	O
below	O
as	O
)	O
.	O
</s>
<s>
The	O
test	O
statistic	O
,	O
,	O
is	O
equivalent	O
to	O
the	O
statistic	O
that	O
would	O
be	O
produced	O
by	O
such	O
an	O
ANOVA	B-General_Concept
,	O
and	O
is	O
defined	O
as	O
follows	O
:	O
</s>
<s>
(	O
Both	O
definitions	O
are	O
in	O
use	O
though	O
the	O
second	O
one	O
is	O
,	O
strictly	O
speaking	O
,	O
the	O
Brown	B-General_Concept
–	I-General_Concept
Forsythe	I-General_Concept
test	I-General_Concept
–	O
see	O
below	O
for	O
comparison	O
.	O
)	O
</s>
<s>
The	O
test	O
statistic	O
is	O
approximately	O
F-distributed	B-General_Concept
with	O
and	O
degrees	O
of	O
freedom	O
,	O
and	O
hence	O
is	O
the	O
significance	O
of	O
the	O
outcome	O
of	O
tested	O
against	O
where	O
is	O
a	O
quantile	O
of	O
the	O
F-distribution	B-General_Concept
,	O
with	O
and	O
degrees	O
of	O
freedom	O
,	O
and	O
is	O
the	O
chosen	O
level	O
of	O
significance	O
(	O
usually	O
0.05	O
or	O
0.01	O
)	O
.	O
</s>
<s>
The	O
Brown	B-General_Concept
–	I-General_Concept
Forsythe	I-General_Concept
test	I-General_Concept
uses	O
the	O
median	O
instead	O
of	O
the	O
mean	O
in	O
computing	O
the	O
spread	O
within	O
each	O
group	O
(	O
vs.	O
,	O
above	O
)	O
.	O
</s>
<s>
Although	O
the	O
optimal	O
choice	O
depends	O
on	O
the	O
underlying	O
distribution	O
,	O
the	O
definition	O
based	O
on	O
the	O
median	O
is	O
recommended	O
as	O
the	O
choice	O
that	O
provides	O
good	O
robustness	O
against	O
many	O
types	O
of	O
non-normal	O
data	O
while	O
retaining	O
good	O
statistical	B-General_Concept
power	I-General_Concept
.	O
</s>
<s>
Brown	O
and	O
Forsythe	O
performed	O
Monte	B-Algorithm
Carlo	I-Algorithm
studies	O
that	O
indicated	O
that	O
using	O
the	O
trimmed	O
mean	O
performed	O
best	O
when	O
the	O
underlying	O
data	O
followed	O
a	O
Cauchy	O
distribution	O
(	O
a	O
heavy-tailed	O
distribution	O
)	O
and	O
the	O
median	O
performed	O
best	O
when	O
the	O
underlying	O
data	O
followed	O
a	O
chi-squared	O
distribution	O
with	O
four	O
degrees	O
of	O
freedom	O
(	O
a	O
heavily	O
skewed	B-General_Concept
distribution	I-General_Concept
)	O
.	O
</s>
