<s>
In	O
statistical	B-General_Concept
significance	I-General_Concept
testing	O
,	O
a	O
one-tailed	B-General_Concept
test	I-General_Concept
and	O
a	O
two-tailed	B-General_Concept
test	I-General_Concept
are	O
alternative	O
ways	O
of	O
computing	O
the	O
statistical	B-General_Concept
significance	I-General_Concept
of	O
a	O
parameter	O
inferred	O
from	O
a	O
data	O
set	O
,	O
in	O
terms	O
of	O
a	O
test	B-General_Concept
statistic	I-General_Concept
.	O
</s>
<s>
A	O
two-tailed	B-General_Concept
test	I-General_Concept
is	O
appropriate	O
if	O
the	O
estimated	O
value	O
is	O
greater	O
or	O
less	O
than	O
a	O
certain	O
range	O
of	O
values	O
,	O
for	O
example	O
,	O
whether	O
a	O
test	O
taker	O
may	O
score	O
above	O
or	O
below	O
a	O
specific	O
range	O
of	O
scores	O
.	O
</s>
<s>
This	O
method	O
is	O
used	O
for	O
null	B-General_Concept
hypothesis	I-General_Concept
testing	O
and	O
if	O
the	O
estimated	O
value	O
exists	O
in	O
the	O
critical	O
areas	O
,	O
the	O
alternative	O
hypothesis	O
is	O
accepted	O
over	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
A	O
one-tailed	B-General_Concept
test	I-General_Concept
is	O
appropriate	O
if	O
the	O
estimated	O
value	O
may	O
depart	O
from	O
the	O
reference	O
value	O
in	O
only	O
one	O
direction	O
,	O
left	O
or	O
right	O
,	O
but	O
not	O
both	O
.	O
</s>
<s>
In	O
this	O
situation	O
,	O
if	O
the	O
estimated	O
value	O
exists	O
in	O
one	O
of	O
the	O
one-sided	O
critical	O
areas	O
,	O
depending	O
on	O
the	O
direction	O
of	O
interest	O
(	O
greater	O
than	O
or	O
less	O
than	O
)	O
,	O
the	O
alternative	O
hypothesis	O
is	O
accepted	O
over	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Alternative	O
names	O
are	O
one-sided	O
and	O
two-sided	B-General_Concept
tests	I-General_Concept
;	O
the	O
terminology	O
"	O
tail	O
"	O
is	O
used	O
because	O
the	O
extreme	O
portions	O
of	O
distributions	O
,	O
where	O
observations	O
lead	O
to	O
rejection	O
of	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
are	O
small	O
and	O
often	O
"	O
tail	O
off	O
"	O
toward	O
zero	O
as	O
in	O
the	O
normal	O
distribution	O
,	O
colored	O
in	O
yellow	O
,	O
or	O
"	O
bell	O
curve	O
"	O
,	O
pictured	O
on	O
the	O
right	O
and	O
colored	O
in	O
green	O
.	O
</s>
<s>
One-tailed	B-General_Concept
tests	I-General_Concept
are	O
used	O
for	O
asymmetric	O
distributions	O
that	O
have	O
a	O
single	O
tail	O
,	O
such	O
as	O
the	O
chi-squared	O
distribution	O
,	O
which	O
are	O
common	O
in	O
measuring	O
goodness-of-fit	O
,	O
or	O
for	O
one	O
side	O
of	O
a	O
distribution	O
that	O
has	O
two	O
tails	O
,	O
such	O
as	O
the	O
normal	O
distribution	O
,	O
which	O
is	O
common	O
in	O
estimating	O
location	O
;	O
this	O
corresponds	O
to	O
specifying	O
a	O
direction	O
.	O
</s>
<s>
Two-tailed	B-General_Concept
tests	I-General_Concept
are	O
only	O
applicable	O
when	O
there	O
are	O
two	O
tails	O
,	O
such	O
as	O
in	O
the	O
normal	O
distribution	O
,	O
and	O
correspond	O
to	O
considering	O
either	O
direction	O
significant	O
.	O
</s>
<s>
In	O
the	O
approach	O
of	O
Ronald	O
Fisher	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
H0	O
will	O
be	O
rejected	O
when	O
the	O
p-value	B-General_Concept
of	O
the	O
test	B-General_Concept
statistic	I-General_Concept
is	O
sufficiently	O
extreme	O
(	O
vis-a-vis	O
the	O
test	B-General_Concept
statistic	I-General_Concept
's	O
sampling	B-General_Concept
distribution	I-General_Concept
)	O
and	O
thus	O
judged	O
unlikely	O
to	O
be	O
the	O
result	O
of	O
chance	O
.	O
</s>
<s>
This	O
is	O
usually	O
done	O
by	O
comparing	O
the	O
resulting	O
p-value	B-General_Concept
with	O
the	O
specified	O
significance	B-General_Concept
level	I-General_Concept
,	O
denoted	O
by	O
,	O
when	O
computing	O
the	O
statistical	B-General_Concept
significance	I-General_Concept
of	O
a	O
parameter	O
.	O
</s>
<s>
In	O
a	O
one-tailed	B-General_Concept
test	I-General_Concept
,	O
"	O
extreme	O
"	O
is	O
decided	O
beforehand	O
as	O
either	O
meaning	O
"	O
sufficiently	O
small	O
"	O
or	O
meaning	O
"	O
sufficiently	O
large	O
"	O
–	O
values	O
in	O
the	O
other	O
direction	O
are	O
considered	O
not	O
significant	O
.	O
</s>
<s>
One	O
may	O
report	O
that	O
the	O
left	O
or	O
right	O
tail	O
probability	O
as	O
the	O
one-tailed	B-General_Concept
p-value	B-General_Concept
,	O
which	O
ultimately	O
corresponds	O
to	O
the	O
direction	O
in	O
which	O
the	O
test	B-General_Concept
statistic	I-General_Concept
deviates	O
from	O
H0	O
.	O
</s>
<s>
In	O
a	O
two-tailed	B-General_Concept
test	I-General_Concept
,	O
"	O
extreme	O
"	O
means	O
"	O
either	O
sufficiently	O
small	O
or	O
sufficiently	O
large	O
"	O
,	O
and	O
values	O
in	O
either	O
direction	O
are	O
considered	O
significant	O
.	O
</s>
<s>
For	O
a	O
given	O
test	B-General_Concept
statistic	I-General_Concept
,	O
there	O
is	O
a	O
single	O
two-tailed	B-General_Concept
test	I-General_Concept
,	O
and	O
two	O
one-tailed	B-General_Concept
tests	I-General_Concept
,	O
one	O
each	O
for	O
either	O
direction	O
.	O
</s>
<s>
When	O
provided	O
a	O
significance	B-General_Concept
level	I-General_Concept
,	O
the	O
critical	O
regions	O
would	O
exist	O
on	O
the	O
two	O
tail	O
ends	O
of	O
the	O
distribution	O
with	O
an	O
area	O
of	O
each	O
for	O
a	O
two-tailed	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
Alternatively	O
,	O
the	O
critical	O
region	O
would	O
solely	O
exist	O
on	O
the	O
single	O
tail	O
end	O
with	O
an	O
area	O
of	O
for	O
a	O
one-tailed	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
For	O
a	O
given	O
significance	B-General_Concept
level	I-General_Concept
in	O
a	O
two-tailed	B-General_Concept
test	I-General_Concept
for	O
a	O
test	B-General_Concept
statistic	I-General_Concept
,	O
the	O
corresponding	O
one-tailed	B-General_Concept
tests	I-General_Concept
for	O
the	O
same	O
test	B-General_Concept
statistic	I-General_Concept
will	O
be	O
considered	O
either	O
twice	O
as	O
significant	O
(	O
half	O
the	O
p-value	B-General_Concept
)	O
if	O
the	O
data	O
is	O
in	O
the	O
direction	O
specified	O
by	O
the	O
test	O
,	O
or	O
not	O
significant	O
at	O
all	O
(	O
p-value	B-General_Concept
above	O
)	O
if	O
the	O
data	O
is	O
in	O
the	O
direction	O
opposite	O
of	O
the	O
critical	O
region	O
specified	O
by	O
the	O
test	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
flipping	O
a	O
coin	O
,	O
testing	O
whether	O
it	O
is	O
biased	O
towards	O
heads	O
is	O
a	O
one-tailed	B-General_Concept
test	I-General_Concept
,	O
and	O
getting	O
data	O
of	O
"	O
all	O
heads	O
"	O
would	O
be	O
seen	O
as	O
highly	O
significant	O
,	O
while	O
getting	O
data	O
of	O
"	O
all	O
tails	O
"	O
would	O
be	O
not	O
significant	O
at	O
all	O
(	O
p	O
=	O
1	O
)	O
.	O
</s>
<s>
By	O
contrast	O
,	O
testing	O
whether	O
it	O
is	O
biased	O
in	O
either	O
direction	O
is	O
a	O
two-tailed	B-General_Concept
test	I-General_Concept
,	O
and	O
either	O
"	O
all	O
heads	O
"	O
or	O
"	O
all	O
tails	O
"	O
would	O
both	O
be	O
seen	O
as	O
highly	O
significant	O
data	O
.	O
</s>
<s>
In	O
medical	O
testing	O
,	O
while	O
one	O
is	O
generally	O
interested	O
in	O
whether	O
a	O
treatment	O
results	O
in	O
outcomes	O
that	O
are	O
better	O
than	O
chance	O
,	O
thus	O
suggesting	O
a	O
one-tailed	B-General_Concept
test	I-General_Concept
;	O
a	O
worse	O
outcome	O
is	O
also	O
interesting	O
for	O
the	O
scientific	O
field	O
,	O
therefore	O
one	O
should	O
use	O
a	O
two-tailed	B-General_Concept
test	I-General_Concept
that	O
corresponds	O
instead	O
to	O
testing	O
whether	O
the	O
treatment	O
results	O
in	O
outcomes	O
that	O
are	O
different	O
from	O
chance	O
,	O
either	O
better	O
or	O
worse	O
.	O
</s>
<s>
In	O
the	O
archetypal	O
lady	O
tasting	O
tea	O
experiment	O
,	O
Fisher	O
tested	O
whether	O
the	O
lady	O
in	O
question	O
was	O
better	O
than	O
chance	O
at	O
distinguishing	O
two	O
types	O
of	O
tea	O
preparation	O
,	O
not	O
whether	O
her	O
ability	O
was	O
different	O
from	O
chance	O
,	O
and	O
thus	O
he	O
used	O
a	O
one-tailed	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
In	O
coin	O
flipping	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
a	O
sequence	O
of	O
Bernoulli	O
trials	O
with	O
probability	O
0.5	O
,	O
yielding	O
a	O
random	O
variable	O
X	O
which	O
is	O
1	O
for	O
heads	O
and	O
0	O
for	O
tails	O
,	O
and	O
a	O
common	O
test	B-General_Concept
statistic	I-General_Concept
is	O
the	O
sample	O
mean	O
(	O
of	O
the	O
number	O
of	O
heads	O
)	O
If	O
testing	O
for	O
whether	O
the	O
coin	O
is	O
biased	O
towards	O
heads	O
,	O
a	O
one-tailed	B-General_Concept
test	I-General_Concept
would	O
be	O
used	O
–	O
only	O
large	O
numbers	O
of	O
heads	O
would	O
be	O
significant	O
.	O
</s>
<s>
This	O
would	O
have	O
and	O
would	O
be	O
significant	O
(	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
)	O
if	O
the	O
test	O
was	O
analyzed	O
at	O
a	O
significance	B-General_Concept
level	I-General_Concept
of	O
(	O
the	O
significance	B-General_Concept
level	I-General_Concept
corresponding	O
to	O
the	O
cutoff	O
bound	O
)	O
.	O
</s>
<s>
However	O
,	O
if	O
testing	O
for	O
whether	O
the	O
coin	O
is	O
biased	O
towards	O
heads	O
or	O
tails	O
,	O
a	O
two-tailed	B-General_Concept
test	I-General_Concept
would	O
be	O
used	O
,	O
and	O
a	O
data	O
set	O
of	O
five	O
heads	O
(	O
sample	O
mean	O
1	O
)	O
is	O
as	O
extreme	O
as	O
a	O
data	O
set	O
of	O
five	O
tails	O
(	O
sample	O
mean	O
0	O
)	O
.	O
</s>
<s>
As	O
a	O
result	O
,	O
the	O
p-value	B-General_Concept
would	O
be	O
and	O
this	O
would	O
not	O
be	O
significant	O
(	O
not	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
)	O
if	O
the	O
test	O
was	O
analyzed	O
at	O
a	O
significance	B-General_Concept
level	I-General_Concept
of	O
.	O
</s>
<s>
The	O
p-value	B-General_Concept
was	O
introduced	O
by	O
Karl	O
Pearson	O
in	O
the	O
Pearson	B-General_Concept
's	I-General_Concept
chi-squared	I-General_Concept
test	I-General_Concept
,	O
where	O
he	O
defined	O
P	O
(	O
original	O
notation	O
)	O
as	O
the	O
probability	O
that	O
the	O
statistic	O
would	O
be	O
at	O
or	O
above	O
a	O
given	O
level	O
.	O
</s>
<s>
This	O
is	O
a	O
one-tailed	B-General_Concept
definition	O
,	O
and	O
the	O
chi-squared	O
distribution	O
is	O
asymmetric	O
,	O
only	O
assuming	O
positive	O
or	O
zero	O
values	O
,	O
and	O
has	O
only	O
one	O
tail	O
,	O
the	O
upper	O
one	O
.	O
</s>
<s>
It	O
measures	O
goodness	O
of	O
fit	O
of	O
data	O
with	O
a	O
theoretical	O
distribution	O
,	O
with	O
zero	O
corresponding	O
to	O
exact	O
agreement	O
with	O
the	O
theoretical	O
distribution	O
;	O
the	O
p-value	B-General_Concept
thus	O
measures	O
how	O
likely	O
the	O
fit	O
would	O
be	O
this	O
bad	O
or	O
worse	O
.	O
</s>
<s>
The	O
distinction	O
between	O
one-tailed	B-General_Concept
and	O
two-tailed	B-General_Concept
tests	I-General_Concept
was	O
popularized	O
by	O
Ronald	O
Fisher	O
in	O
the	O
influential	O
book	O
Statistical	O
Methods	O
for	O
Research	O
Workers	O
,	O
where	O
he	O
applied	O
it	O
especially	O
to	O
the	O
normal	O
distribution	O
,	O
which	O
is	O
a	O
symmetric	O
distribution	O
with	O
two	O
equal	O
tails	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
a	O
symmetric	O
distribution	O
such	O
as	O
the	O
normal	O
distribution	O
,	O
the	O
one-tailed	B-General_Concept
p-value	B-General_Concept
is	O
exactly	O
half	O
the	O
two-tailed	O
p-value	B-General_Concept
:	O
</s>
<s>
Fisher	O
emphasized	O
the	O
importance	O
of	O
measuring	O
the	O
tail	O
–	O
the	O
observed	O
value	O
of	O
the	O
test	B-General_Concept
statistic	I-General_Concept
and	O
all	O
more	O
extreme	O
–	O
rather	O
than	O
simply	O
the	O
probability	O
of	O
specific	O
outcome	O
itself	O
,	O
in	O
his	O
The	O
Design	O
of	O
Experiments	O
(	O
1935	O
)	O
.	O
</s>
<s>
He	O
explains	O
this	O
as	O
because	O
a	O
specific	O
set	O
of	O
data	O
may	O
be	O
unlikely	O
(	O
in	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
)	O
,	O
but	O
more	O
extreme	O
outcomes	O
likely	O
,	O
so	O
seen	O
in	O
this	O
light	O
,	O
the	O
specific	O
but	O
not	O
extreme	O
unlikely	O
data	O
should	O
not	O
be	O
considered	O
significant	O
.	O
</s>
<s>
If	O
the	O
test	B-General_Concept
statistic	I-General_Concept
follows	O
a	O
Student	O
's	O
t-distribution	O
in	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
–	O
which	O
is	O
common	O
where	O
the	O
underlying	O
variable	O
follows	O
a	O
normal	O
distribution	O
with	O
unknown	O
scaling	O
factor	O
,	O
then	O
the	O
test	O
is	O
referred	O
to	O
as	O
a	O
one-tailed	B-General_Concept
or	O
two-tailed	O
t-test	B-General_Concept
.	O
</s>
<s>
If	O
the	O
test	O
is	O
performed	O
using	O
the	O
actual	O
population	O
mean	O
and	O
variance	O
,	O
rather	O
than	O
an	O
estimate	O
from	O
a	O
sample	O
,	O
it	O
would	O
be	O
called	O
a	O
one-tailed	B-General_Concept
or	O
two-tailed	O
Z-test	B-General_Concept
.	O
</s>
<s>
The	O
statistical	O
tables	O
for	O
t	O
and	O
for	O
Z	O
provide	O
critical	O
values	O
for	O
both	O
one	B-General_Concept
-	I-General_Concept
and	I-General_Concept
two-tailed	I-General_Concept
tests	I-General_Concept
.	O
</s>
<s>
That	O
is	O
,	O
they	O
provide	O
the	O
critical	O
values	O
that	O
cut	O
off	O
an	O
entire	O
region	O
at	O
one	O
or	O
the	O
other	O
end	O
of	O
the	O
sampling	B-General_Concept
distribution	I-General_Concept
as	O
well	O
as	O
the	O
critical	O
values	O
that	O
cut	O
off	O
the	O
regions	O
(	O
of	O
half	O
the	O
size	O
)	O
at	O
both	O
ends	O
of	O
the	O
sampling	B-General_Concept
distribution	I-General_Concept
.	O
</s>
