<s>
The	O
Brown	B-General_Concept
–	I-General_Concept
Forsythe	I-General_Concept
test	I-General_Concept
is	O
a	O
statistical	O
test	O
for	O
the	O
equality	O
of	O
group	O
variances	O
based	O
on	O
performing	O
an	O
Analysis	B-General_Concept
of	I-General_Concept
Variance	I-General_Concept
(	O
ANOVA	B-General_Concept
)	O
on	O
a	O
transformation	B-General_Concept
of	O
the	O
response	O
variable	O
.	O
</s>
<s>
When	O
a	O
one-way	B-General_Concept
ANOVA	I-General_Concept
is	O
performed	O
,	O
samples	O
are	O
assumed	O
to	O
have	O
been	O
drawn	O
from	O
distributions	O
with	O
equal	O
variance	O
.	O
</s>
<s>
If	O
this	O
assumption	O
is	O
not	O
valid	O
,	O
the	O
resulting	O
F-test	B-General_Concept
is	O
invalid	O
.	O
</s>
<s>
The	O
Brown	B-General_Concept
–	I-General_Concept
Forsythe	I-General_Concept
test	I-General_Concept
statistic	O
is	O
the	O
F	B-General_Concept
statistic	I-General_Concept
resulting	O
from	O
an	O
ordinary	O
one-way	B-General_Concept
analysis	I-General_Concept
of	I-General_Concept
variance	I-General_Concept
on	O
the	O
absolute	O
deviations	O
of	O
the	O
groups	O
or	O
treatments	O
data	O
from	O
their	O
individual	O
medians	O
.	O
</s>
<s>
The	O
Brown	B-General_Concept
–	I-General_Concept
Forsythe	I-General_Concept
test	I-General_Concept
statistic	O
is	O
the	O
model	O
F	B-General_Concept
statistic	I-General_Concept
from	O
a	O
one	B-General_Concept
way	I-General_Concept
ANOVA	I-General_Concept
on	O
zij	O
:	O
</s>
<s>
This	O
F-statistic	O
follows	O
the	O
F-distribution	B-General_Concept
with	O
degrees	O
of	O
freedom	O
and	O
under	O
the	O
null	O
hypothesis	O
.	O
</s>
<s>
If	O
the	O
variances	O
are	O
indeed	O
heterogeneous	O
,	O
techniques	O
that	O
allow	O
for	O
this	O
(	O
such	O
as	O
the	O
Welch	O
one-way	B-General_Concept
ANOVA	I-General_Concept
)	O
may	O
be	O
used	O
instead	O
of	O
the	O
usual	O
ANOVA	B-General_Concept
.	O
</s>
<s>
Levene	B-General_Concept
's	I-General_Concept
test	I-General_Concept
uses	O
the	O
mean	O
instead	O
of	O
the	O
median	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
χ2	O
distribution	O
with	O
four	O
degrees	O
of	O
freedom	O
(	O
a	O
sharply	O
skewed	B-General_Concept
distribution	I-General_Concept
)	O
.	O
</s>
<s>
O'Brien	O
tested	O
several	O
ways	O
of	O
using	O
the	O
traditional	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
to	O
test	O
heterogeneity	O
of	O
spread	O
in	O
factorial	O
designs	O
with	O
equal	O
or	O
unequal	O
sample	O
sizes	O
.	O
</s>
