<s>
In	O
statistics	O
,	O
Barnard	O
’s	O
test	O
is	O
an	O
exact	B-General_Concept
test	I-General_Concept
used	O
in	O
the	O
analysis	O
of	O
contingency	B-Application
tables	I-Application
with	O
one	O
margin	O
fixed	O
.	O
</s>
<s>
Barnard	O
’s	O
tests	O
are	O
really	O
a	O
class	O
of	O
hypothesis	O
tests	O
,	O
also	O
known	O
as	O
unconditional	O
exact	B-General_Concept
tests	I-General_Concept
for	O
two	O
independent	O
binomials	O
.	O
</s>
<s>
These	O
tests	O
examine	O
the	O
association	O
of	O
two	O
categorical	O
variables	O
and	O
are	O
often	O
a	O
more	O
powerful	B-General_Concept
alternative	O
than	O
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
test	I-General_Concept
for	O
contingency	B-Application
tables	I-Application
.	O
</s>
<s>
Barnard	O
’s	O
test	O
is	O
used	O
to	O
test	O
the	O
independence	O
of	O
rows	O
and	O
columns	O
in	O
a	O
contingency	B-Application
table	I-Application
.	O
</s>
<s>
Under	O
independence	O
,	O
there	O
are	O
three	O
types	O
of	O
study	O
designs	O
that	O
yield	O
a	O
table	O
,	O
and	O
Barnard	B-General_Concept
's	I-General_Concept
test	I-General_Concept
applies	O
to	O
the	O
second	O
type	O
.	O
</s>
<s>
This	O
type	O
of	O
design	O
is	O
rare	O
,	O
but	O
has	O
the	O
same	O
structure	O
as	O
the	O
lady	O
tasting	O
tea	O
study	O
that	O
led	O
R.A.	O
Fisher	O
to	O
create	O
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
The	O
operational	O
difference	O
between	O
Barnard	O
’s	O
exact	B-General_Concept
test	I-General_Concept
and	O
Fisher	O
’s	O
‘	O
exact’	O
test	O
is	O
how	O
they	O
handle	O
the	O
nuisance	O
parameter(s )	O
of	O
the	O
common	O
success	O
probability	O
,	O
when	O
calculating	O
the	O
value	O
.	O
</s>
<s>
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
test	I-General_Concept
avoids	O
estimating	O
the	O
nuisance	O
parameter(s )	O
by	O
conditioning	O
on	O
both	O
margins	O
,	O
an	O
approximately	O
ancillary	O
statistic	O
that	O
constrains	O
the	O
possible	O
outcomes	O
.	O
</s>
<s>
However	O
,	O
even	O
when	O
the	O
data	O
come	O
from	O
double-binomial	O
distribution	O
,	O
the	O
conditioning	O
(	O
that	O
leads	O
to	O
using	O
the	O
hypergeometric	O
distribution	O
for	O
calculating	O
the	O
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
p-value	O
)	O
produces	O
a	O
valid	O
test	O
.	O
</s>
<s>
However	O
,	O
Barnard	O
’s	O
test	O
can	O
be	O
more	O
powerful	B-General_Concept
than	O
Fisher	O
’s	O
test	O
because	O
it	O
considers	O
more	O
‘	O
as	O
or	O
more	O
extreme’	O
tables	O
,	O
by	O
not	O
conditioning	O
on	O
the	O
second	O
margin	O
,	O
which	O
the	O
procedure	O
for	O
Fisher	O
’s	O
test	O
ignores	O
.	O
</s>
<s>
In	O
fact	O
,	O
one	O
variant	O
of	O
Barnard	O
’s	O
test	O
,	O
called	O
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
,	O
is	O
uniformly	B-General_Concept
more	I-General_Concept
powerful	I-General_Concept
than	O
Fisher	O
’s	O
test	O
.	O
</s>
<s>
Under	O
specious	O
pressure	O
from	O
Fisher	O
,	O
Barnard	O
retracted	O
his	O
test	O
in	O
a	O
published	O
paper	O
,	O
however	O
many	O
researchers	O
prefer	O
Barnard	O
’s	O
exact	B-General_Concept
test	I-General_Concept
over	O
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
test	I-General_Concept
for	O
analyzing	O
contingency	B-Application
tables	I-Application
,	O
since	O
its	O
statistics	O
are	O
more	O
powerful	B-General_Concept
for	O
the	O
vast	O
majority	O
of	O
experimental	O
designs	O
,	O
whereas	O
Fisher	O
’s	O
exact	B-General_Concept
test	I-General_Concept
statistics	O
are	O
conservative	O
,	O
meaning	O
the	O
significance	O
shown	O
by	O
its	O
values	O
are	O
too	O
high	O
,	O
leading	O
the	O
experimenter	O
to	O
dismiss	O
as	O
insignificant	O
results	O
that	O
would	O
be	O
statistically	O
significant	O
using	O
the	O
less	O
conservative	O
double-binomial	O
statistics	O
of	O
Barnard	B-General_Concept
's	I-General_Concept
tests	I-General_Concept
rather	O
than	O
the	O
hypergeometric	O
statistics	O
of	O
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
Barnard	B-General_Concept
's	I-General_Concept
tests	I-General_Concept
are	O
not	O
appropriate	O
in	O
the	O
rare	O
case	O
of	O
an	O
experimental	O
design	O
that	O
constrains	O
both	O
marginal	O
results	O
(	O
e.g.	O
</s>
<s>
Barnard	B-General_Concept
's	I-General_Concept
test	I-General_Concept
can	O
be	O
applied	O
to	O
larger	O
tables	O
,	O
but	O
the	O
computation	O
time	O
increases	O
and	O
the	O
power	O
advantage	O
quickly	O
decreases	O
.	O
</s>
<s>
It	O
remains	O
unclear	O
which	O
test	O
statistic	O
is	O
preferred	O
when	O
implementing	O
Barnard	B-General_Concept
's	I-General_Concept
test	I-General_Concept
;	O
however	O
,	O
most	O
test	O
statistics	O
yield	O
uniformly	B-General_Concept
more	I-General_Concept
powerful	I-General_Concept
tests	I-General_Concept
than	O
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
test	I-General_Concept
.	O
</s>
