<s>
In	O
applied	O
statistics	O
,	O
a	O
variance-stabilizing	B-General_Concept
transformation	I-General_Concept
is	O
a	O
data	B-General_Concept
transformation	I-General_Concept
that	O
is	O
specifically	O
chosen	O
either	O
to	O
simplify	O
considerations	O
in	O
graphical	O
exploratory	O
data	O
analysis	O
or	O
to	O
allow	O
the	O
application	O
of	O
simple	O
regression-based	O
or	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
techniques	O
.	O
</s>
<s>
The	O
aim	O
behind	O
the	O
choice	O
of	O
a	O
variance-stabilizing	B-General_Concept
transformation	I-General_Concept
is	O
to	O
find	O
a	O
simple	O
function	O
ƒ	O
to	O
apply	O
to	O
values	O
x	O
in	O
a	O
data	O
set	O
to	O
create	O
new	O
values	O
such	O
that	O
the	O
variability	O
of	O
the	O
values	O
y	O
is	O
not	O
related	O
to	O
their	O
mean	O
value	O
.	O
</s>
<s>
While	O
variance-stabilizing	B-General_Concept
transformations	I-General_Concept
are	O
well	O
known	O
for	O
certain	O
parametric	O
families	O
of	O
distributions	O
,	O
such	O
as	O
the	O
Poisson	O
and	O
the	O
binomial	O
distribution	O
,	O
some	O
types	O
of	O
data	O
analysis	O
proceed	O
more	O
empirically	O
:	O
for	O
example	O
by	O
searching	O
among	O
power	B-General_Concept
transformations	I-General_Concept
to	O
find	O
a	O
suitable	O
fixed	O
transformation	O
.	O
</s>
<s>
Alternatively	O
,	O
if	O
data	O
analysis	O
suggests	O
a	O
functional	O
form	O
for	O
the	O
relation	O
between	O
variance	O
and	O
mean	O
,	O
this	O
can	O
be	O
used	O
to	O
deduce	O
a	O
variance-stabilizing	B-General_Concept
transformation	I-General_Concept
.	O
</s>
<s>
If	O
is	O
a	O
positive	O
random	O
variable	O
and	O
the	O
variance	O
is	O
given	O
as	O
then	O
the	O
standard	O
deviation	O
is	O
proportional	O
to	O
the	O
mean	O
,	O
which	O
is	O
called	O
fixed	O
relative	B-Algorithm
error	I-Algorithm
.	O
</s>
<s>
That	O
is	O
,	O
the	O
variance-stabilizing	B-General_Concept
transformation	I-General_Concept
is	O
the	O
logarithmic	O
transformation	O
.	O
</s>
<s>
That	O
is	O
,	O
the	O
variance-stabilizing	B-General_Concept
transformation	I-General_Concept
is	O
the	O
inverse	O
hyperbolic	O
sine	O
of	O
the	O
scaled	O
value	O
for	O
.	O
</s>
<s>
Here	O
,	O
the	O
delta	O
method	O
is	O
presented	O
in	O
a	O
rough	O
way	O
,	O
but	O
it	O
is	O
enough	O
to	O
see	O
the	O
relation	O
with	O
the	O
variance-stabilizing	B-General_Concept
transformations	I-General_Concept
.	O
</s>
<s>
Notice	O
the	O
relation	O
between	O
the	O
variance	O
and	O
the	O
mean	O
,	O
which	O
implies	O
,	O
for	O
example	O
,	O
heteroscedasticity	B-General_Concept
in	O
a	O
linear	O
model	O
.	O
</s>
