<s>
In	O
statistics	O
,	O
a	O
power	B-General_Concept
transform	I-General_Concept
is	O
a	O
family	O
of	O
functions	O
applied	O
to	O
create	O
a	O
monotonic	O
transformation	O
of	O
data	O
using	O
power	O
functions	O
.	O
</s>
<s>
It	O
is	O
a	O
data	B-General_Concept
transformation	I-General_Concept
technique	O
used	O
to	O
stabilize	B-General_Concept
variance	I-General_Concept
,	O
make	O
the	O
data	O
more	O
normal	O
distribution-like	O
,	O
improve	O
the	O
validity	O
of	O
measures	O
of	O
association	O
(	O
such	O
as	O
the	O
Pearson	O
correlation	O
between	O
variables	O
)	O
,	O
and	O
for	O
other	O
data	O
stabilization	O
procedures	O
.	O
</s>
<s>
Power	B-General_Concept
transforms	I-General_Concept
are	O
used	O
in	O
multiple	O
fields	O
,	O
including	O
multi-resolution	O
and	O
wavelet	O
analysis	O
,	O
statistical	O
data	O
analysis	O
,	O
medical	O
research	O
,	O
modeling	O
of	O
physical	O
processes	O
,	O
geochemical	O
data	O
analysis	O
,	O
epidemiology	O
and	O
many	O
other	O
clinical	O
,	O
environmental	O
and	O
social	O
research	O
areas	O
.	O
</s>
<s>
The	O
power	B-General_Concept
transformation	I-General_Concept
is	O
defined	O
as	O
a	O
continuously	O
varying	O
function	O
,	O
with	O
respect	O
to	O
the	O
power	O
parameter	O
λ	O
,	O
in	O
a	O
piece-wise	O
function	O
form	O
that	O
makes	O
it	O
continuous	O
at	O
the	O
point	O
of	O
singularity	O
(λ=	O
0	O
)	O
.	O
</s>
<s>
The	O
value	O
at	O
Y	O
=	O
1	O
for	O
any	O
λ	O
is	O
0	O
,	O
and	O
the	O
derivative	B-Algorithm
with	O
respect	O
to	O
Y	O
there	O
is	O
1	O
for	O
any	O
λ	O
.	O
</s>
<s>
The	O
transformation	O
is	O
a	O
power	B-General_Concept
transformation	I-General_Concept
,	O
but	O
done	O
in	O
such	O
a	O
way	O
as	O
to	O
make	O
it	O
continuous	O
with	O
the	O
parameter	O
λ	O
at	O
λ	O
=	O
0	O
.	O
</s>
<s>
The	O
SOCR	B-Algorithm
resource	O
pages	O
contain	O
a	O
number	O
of	O
hands-on	O
interactive	O
activities	O
demonstrating	O
the	O
Box	O
–	O
Cox	O
(	O
power	O
)	O
transformation	O
using	O
Java	O
applets	O
and	O
charts	O
.	O
</s>
<s>
These	O
directly	O
illustrate	O
the	O
effects	O
of	O
this	O
transform	O
on	O
Q	B-Application
–	I-Application
Q	I-Application
plots	I-Application
,	O
X	O
–	O
Y	O
scatterplots	B-Application
,	O
time-series	O
plots	O
and	O
histograms	B-Algorithm
.	O
</s>
