<s>
In	O
statistics	O
,	O
pooled	B-General_Concept
variance	I-General_Concept
(	O
also	O
known	O
as	O
combined	B-General_Concept
variance	I-General_Concept
,	O
composite	B-General_Concept
variance	I-General_Concept
,	O
or	O
overall	B-General_Concept
variance	I-General_Concept
,	O
and	O
written	O
)	O
is	O
a	O
method	O
for	O
estimating	O
variance	O
of	O
several	O
different	O
populations	O
when	O
the	O
mean	O
of	O
each	O
population	O
may	O
be	O
different	O
,	O
but	O
one	O
may	O
assume	O
that	O
the	O
variance	O
of	O
each	O
population	O
is	O
the	O
same	O
.	O
</s>
<s>
The	O
numerical	O
estimate	O
resulting	O
from	O
the	O
use	O
of	O
this	O
method	O
is	O
also	O
called	O
the	O
pooled	B-General_Concept
variance	I-General_Concept
.	O
</s>
<s>
Under	O
the	O
assumption	O
of	O
equal	O
population	O
variances	O
,	O
the	O
pooled	O
sample	O
variance	O
provides	O
a	O
higher	O
precision	B-General_Concept
estimate	O
of	O
variance	O
than	O
the	O
individual	O
sample	O
variances	O
.	O
</s>
<s>
This	O
higher	O
precision	B-General_Concept
can	O
lead	O
to	O
increased	O
statistical	B-General_Concept
power	I-General_Concept
when	O
used	O
in	O
statistical	O
tests	O
that	O
compare	O
the	O
populations	O
,	O
such	O
as	O
the	O
t-test	B-General_Concept
.	O
</s>
<s>
The	O
square	O
root	O
of	O
a	O
pooled	B-General_Concept
variance	I-General_Concept
estimator	O
is	O
known	O
as	O
a	O
pooled	B-General_Concept
standard	I-General_Concept
deviation	I-General_Concept
(	O
also	O
known	O
as	O
combined	B-General_Concept
standard	I-General_Concept
deviation	I-General_Concept
,	O
composite	B-General_Concept
standard	I-General_Concept
deviation	I-General_Concept
,	O
or	O
overall	B-General_Concept
standard	I-General_Concept
deviation	I-General_Concept
)	O
.	O
</s>
<s>
Reasonable	O
estimates	O
of	O
variance	O
can	O
be	O
determined	O
by	O
using	O
the	O
principle	O
of	O
pooled	B-General_Concept
variance	I-General_Concept
after	O
repeating	O
each	O
test	O
at	O
a	O
particular	O
x	O
only	O
a	O
few	O
times	O
.	O
</s>
<s>
The	O
pooled	B-General_Concept
variance	I-General_Concept
is	O
an	O
estimate	O
of	O
the	O
fixed	O
common	O
variance	O
underlying	O
various	O
populations	O
that	O
have	O
different	O
means	O
.	O
</s>
<s>
Assuming	O
uniform	O
sample	O
sizes	O
,	O
,	O
then	O
the	O
pooled	B-General_Concept
variance	I-General_Concept
can	O
be	O
computed	O
by	O
the	O
arithmetic	O
mean	O
:	O
</s>
<s>
If	O
the	O
sample	O
sizes	O
are	O
non-uniform	O
,	O
then	O
the	O
pooled	B-General_Concept
variance	I-General_Concept
can	O
be	O
computed	O
by	O
the	O
weighted	O
average	O
,	O
using	O
as	O
weights	O
the	O
respective	O
degrees	O
of	O
freedom	O
(	O
see	O
also	O
:	O
Bessel	B-General_Concept
's	I-General_Concept
correction	I-General_Concept
)	O
:	O
</s>
<s>
The	O
number	O
of	O
trials	O
,	O
mean	O
,	O
variance	O
and	O
standard	B-General_Concept
deviation	I-General_Concept
are	O
presented	O
in	O
the	O
next	O
table	O
.	O
</s>
<s>
These	O
statistics	O
represent	O
the	O
variance	O
and	O
standard	B-General_Concept
deviation	I-General_Concept
for	O
each	O
subset	O
of	O
data	O
at	O
the	O
various	O
levels	O
of	O
x	O
.	O
</s>
<s>
If	O
we	O
can	O
assume	O
that	O
the	O
same	O
phenomena	O
are	O
generating	O
random	O
error	O
at	O
every	O
level	O
of	O
x	O
,	O
the	O
above	O
data	O
can	O
be	O
“	O
pooled	O
”	O
to	O
express	O
a	O
single	O
estimate	O
of	O
variance	O
and	O
standard	B-General_Concept
deviation	I-General_Concept
.	O
</s>
<s>
In	O
a	O
sense	O
,	O
this	O
suggests	O
finding	O
a	O
mean	O
variance	O
or	O
standard	B-General_Concept
deviation	I-General_Concept
among	O
the	O
five	O
results	O
above	O
.	O
</s>
<s>
The	O
pooled	B-General_Concept
variance	I-General_Concept
of	O
the	O
data	O
shown	O
above	O
is	O
therefore	O
:	O
</s>
<s>
Pooled	B-General_Concept
variance	I-General_Concept
is	O
an	O
estimate	O
when	O
there	O
is	O
a	O
correlation	O
between	O
pooled	O
data	O
sets	O
or	O
the	O
average	O
of	O
the	O
data	O
sets	O
is	O
not	O
identical	O
.	O
</s>
<s>
Rather	O
than	O
estimating	O
pooled	B-General_Concept
standard	I-General_Concept
deviation	I-General_Concept
,	O
the	O
following	O
is	O
the	O
way	O
to	O
exactly	O
aggregate	O
standard	B-General_Concept
deviation	I-General_Concept
when	O
more	O
statistical	O
information	O
is	O
available	O
.	O
</s>
<s>
Standard	B-General_Concept
deviations	I-General_Concept
of	O
non-overlapping	O
(	O
)	O
sub-populations	O
can	O
be	O
aggregated	O
as	O
follows	O
if	O
the	O
size	O
(	O
actual	O
or	O
relative	O
to	O
one	O
another	O
)	O
and	O
means	O
of	O
each	O
are	O
known	O
:	O
</s>
<s>
For	O
example	O
,	O
suppose	O
it	O
is	O
known	O
that	O
the	O
average	O
American	O
man	O
has	O
a	O
mean	O
height	O
of	O
70inches	O
with	O
a	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
three	O
inches	O
and	O
that	O
the	O
average	O
American	O
woman	O
has	O
a	O
mean	O
height	O
of	O
65inches	O
with	O
a	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
two	O
inches	O
.	O
</s>
<s>
If	O
the	O
size	O
(	O
actual	O
or	O
relative	O
to	O
one	O
another	O
)	O
,	O
mean	O
,	O
and	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
two	O
overlapping	O
populations	O
are	O
known	O
for	O
the	O
populations	O
as	O
well	O
as	O
their	O
intersection	O
,	O
then	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
overall	O
population	O
can	O
still	O
be	O
calculated	O
as	O
follows	O
:	O
</s>
<s>
If	O
two	O
or	O
more	O
sets	O
of	O
data	O
are	O
being	O
added	O
together	O
datapoint	O
by	O
datapoint	O
,	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
result	O
can	O
be	O
calculated	O
if	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
each	O
data	O
set	O
and	O
the	O
covariance	O
between	O
each	O
pair	O
of	O
data	O
sets	O
is	O
known	O
:	O
</s>
<s>
Standard	B-General_Concept
deviations	I-General_Concept
of	O
non-overlapping	O
(	O
)	O
sub-samples	O
can	O
be	O
aggregated	O
as	O
follows	O
if	O
the	O
actual	O
size	O
and	O
means	O
of	O
each	O
are	O
known	O
:	O
</s>
<s>
If	O
the	O
size	O
,	O
mean	O
,	O
and	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
two	O
overlapping	O
samples	O
are	O
known	O
for	O
the	O
samples	O
as	O
well	O
as	O
their	O
intersection	O
,	O
then	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
aggregated	O
sample	O
can	O
still	O
be	O
calculated	O
.	O
</s>
