<s>
In	O
statistics	O
,	O
the	O
power	O
of	O
a	O
binary	O
hypothesis	O
test	O
is	O
the	O
probability	O
that	O
the	O
test	O
correctly	O
rejects	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
(	O
)	O
when	O
a	O
specific	O
alternative	B-General_Concept
hypothesis	I-General_Concept
(	O
)	O
is	O
true	O
.	O
</s>
<s>
Statistical	B-General_Concept
power	I-General_Concept
ranges	O
from	O
0	O
to	O
1	O
,	O
and	O
as	O
the	O
power	B-General_Concept
of	I-General_Concept
a	I-General_Concept
test	I-General_Concept
increases	O
,	O
the	O
probability	O
of	O
making	O
a	O
type	O
II	O
error	O
by	O
wrongly	O
failing	O
to	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
decreases	O
.	O
</s>
<s>
1	O
−	O
β	O
=	O
probability	O
of	O
a	O
"	O
true	O
positive	O
"	O
,	O
i.e.	O
,	O
correctly	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
For	O
a	O
typeII	O
error	O
probability	O
of	O
,	O
the	O
corresponding	O
statistical	B-General_Concept
power	I-General_Concept
is	O
1−	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
experiment	O
E	O
has	O
a	O
statistical	B-General_Concept
power	I-General_Concept
of	O
0.7	O
,	O
and	O
experiment	O
F	O
has	O
a	O
statistical	B-General_Concept
power	I-General_Concept
of	O
0.95	O
,	O
then	O
there	O
is	O
a	O
stronger	O
probability	O
that	O
experiment	O
E	O
had	O
a	O
typeII	O
error	O
than	O
experiment	O
F	O
.	O
This	O
reduces	O
experiment	O
E	O
's	O
sensitivity	O
to	O
detect	O
significant	O
effects	O
.	O
</s>
<s>
It	O
can	O
be	O
equivalently	O
thought	O
of	O
as	O
the	O
probability	O
of	O
accepting	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
(	O
)	O
when	O
it	O
is	O
true	O
–	O
that	O
is	O
,	O
the	O
ability	O
of	O
a	O
test	O
to	O
detect	O
a	O
specific	O
effect	O
,	O
if	O
that	O
specific	O
effect	O
actually	O
exists	O
.	O
</s>
<s>
If	O
is	O
not	O
an	O
equality	O
but	O
rather	O
simply	O
the	O
negation	O
of	O
(	O
so	O
for	O
example	O
with	O
for	O
some	O
unobserved	O
population	O
parameter	O
we	O
have	O
simply	O
)	O
then	O
power	O
cannot	O
be	O
calculated	O
unless	O
probabilities	O
are	O
known	O
for	O
all	O
possible	O
values	O
of	O
the	O
parameter	O
that	O
violate	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Thus	O
one	O
generally	O
refers	O
to	O
a	O
test	O
's	O
power	O
against	O
a	O
specific	O
alternative	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
A	O
similar	O
concept	O
is	O
the	O
type	O
I	O
error	O
probability	O
,	O
also	O
referred	O
to	O
as	O
the	O
false	O
positive	O
rate	O
or	O
the	O
level	O
of	O
a	O
test	O
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
In	O
the	O
context	O
of	O
binary	B-General_Concept
classification	I-General_Concept
,	O
the	O
power	B-General_Concept
of	I-General_Concept
a	I-General_Concept
test	I-General_Concept
is	O
called	O
its	O
statistical	O
sensitivity	O
,	O
its	O
true	O
positive	O
rate	O
,	O
or	O
its	O
probability	B-General_Concept
of	I-General_Concept
detection	I-General_Concept
.	O
</s>
<s>
Power	O
analysis	O
can	O
be	O
used	O
to	O
calculate	O
the	O
minimum	O
sample	O
size	B-Application
required	O
so	O
that	O
one	O
can	O
be	O
reasonably	O
likely	O
to	O
detect	O
an	O
effect	O
of	O
a	O
given	O
size	B-Application
.	O
</s>
<s>
Power	O
analysis	O
can	O
also	O
be	O
used	O
to	O
calculate	O
the	O
minimum	O
effect	B-Application
size	I-Application
that	O
is	O
likely	O
to	O
be	O
detected	O
in	O
a	O
study	O
using	O
a	O
given	O
sample	O
size	B-Application
.	O
</s>
<s>
In	O
addition	O
,	O
the	O
concept	O
of	O
power	O
is	O
used	O
to	O
make	O
comparisons	O
between	O
different	O
statistical	O
testing	O
procedures	O
:	O
for	O
example	O
,	O
between	O
a	O
parametric	B-General_Concept
test	I-General_Concept
and	O
a	O
nonparametric	B-General_Concept
test	I-General_Concept
of	O
the	O
same	O
hypothesis	O
.	O
</s>
<s>
Lehr	O
's	O
(	O
rough	O
)	O
rule	O
of	O
thumb	O
says	O
that	O
the	O
sample	O
size	B-Application
(	O
each	O
group	O
)	O
for	O
a	O
two-sided	O
Two-sample	B-General_Concept
t-test	I-General_Concept
with	O
power	O
80%	O
(	O
)	O
and	O
significance	B-General_Concept
level	I-General_Concept
should	O
be	O
:	O
</s>
<s>
For	O
a	O
one	O
sample	O
t-test	B-General_Concept
16	O
is	O
to	O
be	O
replaced	O
with	O
8	O
.	O
</s>
<s>
For	O
example	O
,	O
to	O
test	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
the	O
mean	O
scores	O
of	O
men	O
and	O
women	O
on	O
a	O
test	O
do	O
not	O
differ	O
,	O
samples	O
of	O
men	O
and	O
women	O
are	O
drawn	O
,	O
the	O
test	O
is	O
administered	O
to	O
them	O
,	O
and	O
the	O
mean	O
score	O
of	O
one	O
group	O
is	O
compared	O
to	O
that	O
of	O
the	O
other	O
group	O
using	O
a	O
statistical	O
test	O
such	O
as	O
the	O
two-sample	O
z-test	B-General_Concept
.	O
</s>
<s>
The	O
power	O
of	O
the	O
test	O
is	O
the	O
probability	O
that	O
the	O
test	O
will	O
find	O
a	O
statistically	B-General_Concept
significant	I-General_Concept
difference	O
between	O
men	O
and	O
women	O
,	O
as	O
a	O
function	O
of	O
the	O
size	B-Application
of	O
the	O
true	O
difference	O
between	O
those	O
two	O
populations	O
.	O
</s>
<s>
Statistical	B-General_Concept
power	I-General_Concept
may	O
depend	O
on	O
a	O
number	O
of	O
factors	O
.	O
</s>
<s>
A	O
significance	O
criterion	O
is	O
a	O
statement	O
of	O
how	O
unlikely	O
a	O
positive	O
result	O
must	O
be	O
,	O
if	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
no	O
effect	O
is	O
true	O
,	O
for	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
to	O
be	O
rejected	O
.	O
</s>
<s>
If	O
the	O
criterion	O
is	O
0.05	O
,	O
the	O
probability	O
of	O
the	O
data	O
implying	O
an	O
effect	O
at	O
least	O
as	O
large	O
as	O
the	O
observed	O
effect	O
when	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
must	O
be	O
less	O
than	O
0.05	O
,	O
for	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
no	O
effect	O
to	O
be	O
rejected	O
.	O
</s>
<s>
One	O
easy	O
way	O
to	O
increase	O
the	O
power	B-General_Concept
of	I-General_Concept
a	I-General_Concept
test	I-General_Concept
is	O
to	O
carry	O
out	O
a	O
less	O
conservative	O
test	O
by	O
using	O
a	O
larger	O
significance	O
criterion	O
,	O
for	O
example	O
0.10	O
instead	O
of	O
0.05	O
.	O
</s>
<s>
This	O
increases	O
the	O
chance	O
of	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
(	O
obtaining	O
a	O
statistically	B-General_Concept
significant	I-General_Concept
result	O
)	O
when	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
false	O
;	O
that	O
is	O
,	O
it	O
reduces	O
the	O
risk	O
of	O
a	O
type	O
II	O
error	O
(	O
false	O
negative	O
regarding	O
whether	O
an	O
effect	O
exists	O
)	O
.	O
</s>
<s>
But	O
it	O
also	O
increases	O
the	O
risk	O
of	O
obtaining	O
a	O
statistically	B-General_Concept
significant	I-General_Concept
result	O
(	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
)	O
when	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
not	O
false	O
;	O
that	O
is	O
,	O
it	O
increases	O
the	O
risk	O
of	O
a	O
type	O
I	O
error	O
(	O
false	O
positive	O
)	O
.	O
</s>
<s>
The	O
magnitude	O
of	O
the	O
effect	O
of	O
interest	O
in	O
the	O
population	O
can	O
be	O
quantified	O
in	O
terms	O
of	O
an	O
effect	B-Application
size	I-Application
,	O
where	O
there	O
is	O
greater	O
power	O
to	O
detect	O
larger	O
effects	O
.	O
</s>
<s>
An	O
effect	B-Application
size	I-Application
can	O
be	O
a	O
direct	O
value	O
of	O
the	O
quantity	O
of	O
interest	O
,	O
or	O
it	O
can	O
be	O
a	O
standardized	O
measure	O
that	O
also	O
accounts	O
for	O
the	O
variability	O
in	O
the	O
population	O
.	O
</s>
<s>
For	O
example	O
,	O
in	O
an	O
analysis	O
comparing	O
outcomes	O
in	O
a	O
treated	O
and	O
control	O
population	O
,	O
the	O
difference	O
of	O
outcome	O
means	O
would	O
be	O
a	O
direct	O
estimate	O
of	O
the	O
effect	B-Application
size	I-Application
,	O
whereas	O
would	O
be	O
an	O
estimated	O
standardized	O
effect	B-Application
size	I-Application
,	O
where	O
is	O
the	O
common	O
standard	O
deviation	O
of	O
the	O
outcomes	O
in	O
the	O
treated	O
and	O
control	O
groups	O
.	O
</s>
<s>
If	O
constructed	O
appropriately	O
,	O
a	O
standardized	O
effect	B-Application
size	I-Application
,	O
along	O
with	O
the	O
sample	O
size	B-Application
,	O
will	O
completely	O
determine	O
the	O
power	O
.	O
</s>
<s>
An	O
unstandardized	O
(	O
direct	O
)	O
effect	B-Application
size	I-Application
is	O
rarely	O
sufficient	O
to	O
determine	O
the	O
power	O
,	O
as	O
it	O
does	O
not	O
contain	O
information	O
about	O
the	O
variability	O
in	O
the	O
measurements	O
.	O
</s>
<s>
The	O
sample	O
size	B-Application
determines	O
the	O
amount	O
of	O
sampling	O
error	O
inherent	O
in	O
a	O
test	O
result	O
.	O
</s>
<s>
Increasing	O
sample	O
size	B-Application
is	O
often	O
the	O
easiest	O
way	O
to	O
boost	O
the	O
statistical	B-General_Concept
power	I-General_Concept
of	O
a	O
test	O
.	O
</s>
<s>
How	O
increased	O
sample	O
size	B-Application
translates	O
to	O
higher	O
power	O
is	O
a	O
measure	O
of	O
the	O
efficiency	O
of	O
the	O
test	O
–	O
for	O
example	O
,	O
the	O
sample	O
size	B-Application
required	O
for	O
a	O
given	O
power	O
.	O
</s>
<s>
The	O
precision	O
with	O
which	O
the	O
data	O
are	O
measured	O
also	O
influences	O
statistical	B-General_Concept
power	I-General_Concept
.	O
</s>
<s>
For	O
example	O
,	O
in	O
a	O
two-sample	O
testing	O
situation	O
with	O
a	O
given	O
total	O
sample	O
size	B-Application
,	O
it	O
is	O
optimal	O
to	O
have	O
equal	O
numbers	O
of	O
observations	O
from	O
the	O
two	O
populations	O
being	O
compared	O
(	O
as	O
long	O
as	O
the	O
variances	O
in	O
the	O
two	O
populations	O
are	O
the	O
same	O
)	O
.	O
</s>
<s>
In	O
regression	O
analysis	O
and	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
,	O
there	O
are	O
extensive	O
theories	O
and	O
practical	O
strategies	O
for	O
improving	O
the	O
power	O
based	O
on	O
optimally	O
setting	O
the	O
values	O
of	O
the	O
independent	O
variables	O
in	O
the	O
model	O
.	O
</s>
<s>
Power	O
analysis	O
is	O
appropriate	O
when	O
the	O
concern	O
is	O
with	O
the	O
correct	O
rejection	O
of	O
a	O
false	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
In	O
many	O
contexts	O
,	O
the	O
issue	O
is	O
less	O
about	O
determining	O
if	O
there	O
is	O
or	O
is	O
not	O
a	O
difference	O
but	O
rather	O
with	O
getting	O
a	O
more	O
refined	O
estimate	O
of	O
the	O
population	O
effect	B-Application
size	I-Application
.	O
</s>
<s>
For	O
example	O
,	O
if	O
we	O
were	O
expecting	O
a	O
population	O
correlation	O
between	O
intelligence	O
and	O
job	O
performance	O
of	O
around	O
0.50	O
,	O
a	O
sample	O
size	B-Application
of	O
20	O
will	O
give	O
us	O
approximately	O
80%	O
power	O
(=	O
0.05	O
,	O
two-tail	O
)	O
to	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
zero	O
correlation	O
.	O
</s>
<s>
In	O
this	O
context	O
we	O
would	O
need	O
a	O
much	O
larger	O
sample	O
size	B-Application
in	O
order	O
to	O
reduce	O
the	O
confidence	O
interval	O
of	O
our	O
estimate	O
to	O
a	O
range	O
that	O
is	O
acceptable	O
for	O
our	O
purposes	O
.	O
</s>
<s>
Techniques	O
similar	O
to	O
those	O
employed	O
in	O
a	O
traditional	O
power	O
analysis	O
can	O
be	O
used	O
to	O
determine	O
the	O
sample	O
size	B-Application
required	O
for	O
the	O
width	O
of	O
a	O
confidence	O
interval	O
to	O
be	O
less	O
than	O
a	O
given	O
value	O
.	O
</s>
<s>
For	O
instance	O
,	O
in	O
multiple	O
regression	O
analysis	O
,	O
the	O
power	O
for	O
detecting	O
an	O
effect	O
of	O
a	O
given	O
size	B-Application
is	O
related	O
to	O
the	O
variance	O
of	O
the	O
covariate	O
.	O
</s>
<s>
Any	O
statistical	O
analysis	O
involving	O
multiple	B-General_Concept
hypotheses	I-General_Concept
is	O
subject	O
to	O
inflation	O
of	O
the	O
typeI	O
error	O
rate	O
if	O
appropriate	O
measures	O
are	O
not	O
taken	O
.	O
</s>
<s>
Such	O
measures	O
typically	O
involve	O
applying	O
a	O
higher	O
threshold	O
of	O
stringency	O
to	O
reject	O
a	O
hypothesis	O
in	O
order	O
to	O
compensate	O
for	O
the	O
multiple	B-General_Concept
comparisons	I-General_Concept
being	O
made	O
(	O
e.g.	O
</s>
<s>
as	O
in	O
the	O
Bonferroni	B-General_Concept
method	I-General_Concept
)	O
.	O
</s>
<s>
In	O
this	O
situation	O
,	O
the	O
power	O
analysis	O
should	O
reflect	O
the	O
multiple	B-General_Concept
testing	I-General_Concept
approach	O
to	O
be	O
used	O
.	O
</s>
<s>
Thus	O
,	O
for	O
example	O
,	O
a	O
given	O
study	O
may	O
be	O
well	O
powered	O
to	O
detect	O
a	O
certain	O
effect	B-Application
size	I-Application
when	O
only	O
one	O
test	O
is	O
to	O
be	O
made	O
,	O
but	O
the	O
same	O
effect	B-Application
size	I-Application
may	O
have	O
much	O
lower	O
power	O
if	O
several	O
tests	O
are	O
to	O
be	O
performed	O
.	O
</s>
<s>
It	O
is	O
also	O
important	O
to	O
consider	O
the	O
statistical	B-General_Concept
power	I-General_Concept
of	O
a	O
hypothesis	O
test	O
when	O
interpreting	O
its	O
results	O
.	O
</s>
<s>
A	O
test	O
's	O
power	O
is	O
the	O
probability	O
of	O
correctly	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
when	O
it	O
is	O
false	O
;	O
a	O
test	O
's	O
power	O
is	O
influenced	O
by	O
the	O
choice	O
of	O
significance	B-General_Concept
level	I-General_Concept
for	O
the	O
test	O
,	O
the	O
size	B-Application
of	O
the	O
effect	O
being	O
measured	O
,	O
and	O
the	O
amount	O
of	O
data	O
available	O
.	O
</s>
<s>
A	O
hypothesis	O
test	O
may	O
fail	O
to	O
reject	O
the	O
null	O
,	O
for	O
example	O
,	O
if	O
a	O
true	O
difference	O
exists	O
between	O
two	O
populations	O
being	O
compared	O
by	O
a	O
t-test	B-General_Concept
but	O
the	O
effect	O
is	O
small	O
and	O
the	O
sample	O
size	B-Application
is	O
too	O
small	O
to	O
distinguish	O
the	O
effect	O
from	O
random	O
chance	O
.	O
</s>
<s>
Many	O
clinical	O
trials	O
,	O
for	O
instance	O
,	O
have	O
low	O
statistical	B-General_Concept
power	I-General_Concept
to	O
detect	O
differences	O
in	O
adverse	O
effects	O
of	O
treatments	O
,	O
since	O
such	O
effects	O
may	O
be	O
rare	O
and	O
the	O
number	O
of	O
affected	O
patients	O
small	O
.	O
</s>
<s>
Post-hoc	O
analysis	O
of	O
"	O
observed	O
power	O
"	O
is	O
conducted	O
after	O
a	O
study	O
has	O
been	O
completed	O
,	O
and	O
uses	O
the	O
obtained	O
sample	O
size	B-Application
and	O
effect	B-Application
size	I-Application
to	O
determine	O
what	O
the	O
power	O
was	O
in	O
the	O
study	O
,	O
assuming	O
the	O
effect	B-Application
size	I-Application
in	O
the	O
sample	O
is	O
equal	O
to	O
the	O
effect	B-Application
size	I-Application
in	O
the	O
population	O
.	O
</s>
<s>
In	O
particular	O
,	O
it	O
has	O
been	O
shown	O
that	O
post-hoc	O
"	O
observed	O
power	O
"	O
is	O
a	O
one-to-one	O
function	O
of	O
the	O
p-value	B-General_Concept
attained	O
.	O
</s>
<s>
This	O
has	O
been	O
extended	O
to	O
show	O
that	O
all	O
post-hoc	O
power	O
analyses	O
suffer	O
from	O
what	O
is	O
called	O
the	O
"	O
power	O
approach	O
paradox	O
"	O
(	O
PAP	O
)	O
,	O
in	O
which	O
a	O
study	O
with	O
a	O
null	O
result	O
is	O
thought	O
to	O
show	O
more	O
evidence	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
actually	O
true	O
when	O
the	O
p-value	B-General_Concept
is	O
smaller	O
,	O
since	O
the	O
apparent	O
power	O
to	O
detect	O
an	O
actual	O
effect	O
would	O
be	O
higher	O
.	O
</s>
<s>
In	O
fact	O
,	O
a	O
smaller	O
p-value	B-General_Concept
is	O
properly	O
understood	O
to	O
make	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
relatively	O
less	O
likely	O
to	O
be	O
true	O
.	O
</s>
<s>
In	O
frequentist	B-General_Concept
statistics	I-General_Concept
,	O
an	O
underpowered	O
study	O
is	O
unlikely	O
to	O
allow	O
one	O
to	O
choose	O
between	O
hypotheses	O
at	O
the	O
desired	O
significance	B-General_Concept
level	I-General_Concept
.	O
</s>
<s>
However	O
,	O
power	O
remains	O
a	O
useful	O
measure	O
of	O
how	O
much	O
a	O
given	O
experiment	O
size	B-Application
can	O
be	O
expected	O
to	O
refine	O
one	O
's	O
beliefs	O
.	O
</s>
<s>
The	O
following	O
is	O
an	O
example	O
that	O
shows	O
how	O
to	O
compute	O
power	O
for	O
a	O
randomized	O
experiment	O
:	O
Suppose	O
the	O
goal	O
of	O
an	O
experiment	O
is	O
to	O
study	O
the	O
effect	O
of	O
a	O
treatment	O
on	O
some	O
quantity	O
,	O
and	O
compare	O
research	O
subjects	O
by	O
measuring	O
the	O
quantity	O
before	O
and	O
after	O
the	O
treatment	O
,	O
analyzing	O
the	O
data	O
using	O
a	O
paired	B-General_Concept
t-test	I-General_Concept
.	O
</s>
<s>
The	O
effect	O
of	O
the	O
treatment	O
can	O
be	O
analyzed	O
using	O
a	O
one-sided	O
t-test	B-General_Concept
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
no	O
effect	O
will	O
be	O
that	O
the	O
mean	O
difference	O
will	O
be	O
zero	O
,	O
i.e.	O
</s>
<s>
In	O
this	O
case	O
,	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
states	O
a	O
positive	O
effect	O
,	O
corresponding	O
to	O
The	O
test	B-General_Concept
statistic	I-General_Concept
is	O
:	O
</s>
<s>
is	O
the	O
sample	O
size	B-Application
and	O
is	O
the	O
standard	O
error	O
.	O
</s>
<s>
The	O
test	B-General_Concept
statistic	I-General_Concept
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
follows	O
a	O
Student	O
t-distribution	O
with	O
the	O
additional	O
assumption	O
that	O
the	O
data	O
is	O
identically	O
distributed	O
.	O
</s>
<s>
Furthermore	O
,	O
assume	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
will	O
be	O
rejected	O
at	O
the	O
significance	B-General_Concept
level	I-General_Concept
of	O
Since	O
is	O
large	O
,	O
one	O
can	O
approximate	O
the	O
t-distribution	O
by	O
a	O
normal	O
distribution	O
and	O
calculate	O
the	O
critical	O
value	O
using	O
the	O
quantile	O
function	O
,	O
the	O
inverse	O
of	O
the	O
cumulative	O
distribution	O
function	O
of	O
the	O
normal	O
distribution	O
.	O
</s>
<s>
Now	O
suppose	O
that	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
and	O
.	O
</s>
<s>
According	O
to	O
this	O
formula	O
,	O
the	O
power	O
increases	O
with	O
the	O
values	O
of	O
the	O
parameter	O
For	O
a	O
specific	O
value	O
of	O
a	O
higher	O
power	O
may	O
be	O
obtained	O
by	O
increasing	O
the	O
sample	O
size	B-Application
.	O
</s>
<s>
If	O
it	O
is	O
desirable	O
to	O
have	O
enough	O
power	O
,	O
say	O
at	O
least	O
0.90	O
,	O
to	O
detect	O
values	O
of	O
the	O
required	O
sample	O
size	B-Application
can	O
be	O
calculated	O
approximately	O
:	O
</s>
<s>
In	O
the	O
frequentist	B-General_Concept
setting	O
,	O
parameters	O
are	O
assumed	O
to	O
have	O
a	O
specific	O
value	O
which	O
is	O
unlikely	O
to	O
be	O
true	O
.	O
</s>
<s>
Both	O
frequentist	B-General_Concept
power	O
and	O
Bayesian	O
power	O
use	O
statistical	B-General_Concept
significance	I-General_Concept
as	O
the	O
success	O
criterion	O
.	O
</s>
<s>
However	O
,	O
statistical	B-General_Concept
significance	I-General_Concept
is	O
often	O
not	O
enough	O
to	O
define	O
success	O
.	O
</s>
<s>
The	O
success	O
criterion	O
for	O
PPOS	O
is	O
not	O
restricted	O
to	O
statistical	B-General_Concept
significance	I-General_Concept
and	O
is	O
commonly	O
used	O
in	O
clinical	O
trial	O
designs	O
.	O
</s>
<s>
Numerous	O
free	O
and/or	O
open	O
source	O
programs	O
are	O
available	O
for	O
performing	O
power	O
and	O
sample	O
size	B-Application
calculations	O
.	O
</s>
<s>
provides	O
convenient	O
excel-based	O
functions	O
to	O
determine	O
minimum	O
detectable	O
effect	B-Application
size	I-Application
and	O
minimum	O
required	O
sample	O
size	B-Application
for	O
various	O
experimental	O
and	O
quasi-experimental	O
designs	O
.	O
</s>
<s>
and	O
additionally	O
includes	O
functions	O
to	O
determine	O
sample	O
size	B-Application
for	O
various	O
multilevel	O
randomized	O
experiments	O
with	O
or	O
without	O
budgetary	O
constraints	O
.	O
</s>
