<s>
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
is	O
a	O
statistical	O
hypothesis	O
test	O
for	O
analysing	O
2x2	O
contingency	O
tables	O
.	O
</s>
<s>
It	O
examines	O
the	O
association	O
of	O
two	O
Bernoulli	O
distributed	O
random	O
variables	O
and	O
is	O
a	O
uniformly	O
more	O
powerful	O
alternative	O
to	O
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
It	O
was	O
proposed	O
in	O
1970	O
by	O
R	B-Language
.	O
D	O
.	O
Boschloo	O
.	O
</s>
<s>
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
test	I-General_Concept
is	O
designed	O
for	O
the	O
first	O
case	O
and	O
therefore	O
an	O
exact	B-General_Concept
conditional	O
test	O
(	O
because	O
it	O
conditions	O
on	O
the	O
column	O
sums	O
)	O
.	O
</s>
<s>
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
is	O
designed	O
for	O
the	O
second	O
case	O
and	O
therefore	O
an	O
exact	B-General_Concept
unconditional	O
test	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
Boschloo	O
's	O
one-tailed	B-General_Concept
test	I-General_Concept
(	O
high	O
values	O
of	O
favor	O
the	O
alternative	O
hypothesis	O
)	O
is	O
:	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
the	O
one-tailed	B-General_Concept
test	I-General_Concept
can	O
also	O
be	O
formulated	O
in	O
the	O
other	O
direction	O
(	O
small	O
values	O
of	O
favor	O
the	O
alternative	O
hypothesis	O
)	O
:	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
the	O
two-tailed	B-General_Concept
test	I-General_Concept
is	O
:	O
</s>
<s>
There	O
is	O
no	O
universal	O
definition	O
of	O
the	O
two-tailed	O
version	O
of	O
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
Since	O
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
is	O
based	O
on	O
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
test	I-General_Concept
,	O
a	O
universal	O
two-tailed	O
version	O
of	O
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
also	O
does	O
n't	O
exist	O
.	O
</s>
<s>
In	O
the	O
following	O
we	O
deal	O
with	O
the	O
one-tailed	B-General_Concept
test	I-General_Concept
and	O
.	O
</s>
<s>
We	O
denote	O
the	O
desired	O
significance	B-General_Concept
level	I-General_Concept
by	O
.	O
</s>
<s>
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
test	I-General_Concept
is	O
a	O
conditional	O
test	O
and	O
appropriate	O
for	O
the	O
first	O
of	O
the	O
above	O
mentioned	O
cases	O
.	O
</s>
<s>
But	O
if	O
we	O
treat	O
the	O
observed	O
column	O
sum	O
as	O
fixed	O
in	O
advance	O
,	O
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
test	I-General_Concept
can	O
also	O
be	O
applied	O
to	O
the	O
second	O
case	O
.	O
</s>
<s>
The	O
true	O
size	B-General_Concept
of	O
the	O
test	O
then	O
depends	O
on	O
the	O
nuisance	O
parameters	O
and	O
.	O
</s>
<s>
It	O
can	O
be	O
shown	O
that	O
the	O
size	B-General_Concept
maximum	O
is	O
taken	O
for	O
equal	O
proportions	O
and	O
is	O
still	O
controlled	O
by	O
.	O
</s>
<s>
However	O
,	O
Boschloo	O
stated	O
that	O
for	O
small	O
sample	O
sizes	O
,	O
the	O
maximal	O
size	B-General_Concept
is	O
often	O
considerably	O
smaller	O
than	O
.	O
</s>
<s>
This	O
leads	O
to	O
an	O
undesirable	O
loss	O
of	O
power	B-General_Concept
.	O
</s>
<s>
Boschloo	O
proposed	O
to	O
use	O
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
test	I-General_Concept
with	O
a	O
greater	O
nominal	O
level	O
.	O
</s>
<s>
Here	O
,	O
should	O
be	O
chosen	O
as	O
large	O
as	O
possible	O
such	O
that	O
the	O
maximal	O
size	B-General_Concept
is	O
still	O
controlled	O
by	O
:	O
.	O
</s>
<s>
This	O
made	O
performing	O
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
computationally	O
easy	O
.	O
</s>
<s>
The	O
decision	O
rule	O
of	O
Boschloo	O
's	O
approach	O
is	O
based	O
on	O
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
An	O
equivalent	O
way	O
of	O
formulating	O
the	O
test	O
is	O
to	O
use	O
the	O
p-value	O
of	O
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
test	I-General_Concept
as	O
test	B-General_Concept
statistic	I-General_Concept
.	O
</s>
<s>
For	O
a	O
specified	O
significance	B-General_Concept
level	I-General_Concept
the	O
critical	O
value	O
of	O
is	O
the	O
maximal	O
value	O
that	O
satisfies	O
.	O
</s>
<s>
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
deals	O
with	O
the	O
unknown	O
nuisance	O
parameter	O
by	O
taking	O
the	O
maximum	O
over	O
the	O
whole	O
parameter	O
space	O
.	O
</s>
<s>
This	O
results	O
in	O
a	O
modified	O
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
which	O
is	O
also	O
exact	B-General_Concept
.	O
</s>
<s>
All	O
exact	B-General_Concept
tests	I-General_Concept
hold	O
the	O
specified	O
significance	B-General_Concept
level	I-General_Concept
but	O
can	O
have	O
varying	O
power	B-General_Concept
in	O
different	O
situations	O
.	O
</s>
<s>
compared	O
the	O
power	B-General_Concept
of	O
some	O
exact	B-General_Concept
tests	I-General_Concept
in	O
different	O
situations	O
.	O
</s>
<s>
The	O
results	O
regarding	O
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
are	O
summarized	O
in	O
the	O
following	O
.	O
</s>
<s>
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
and	O
the	O
modified	O
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
have	O
similar	O
power	B-General_Concept
in	O
all	O
considered	O
scenarios	O
.	O
</s>
<s>
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
has	O
slightly	O
more	O
power	B-General_Concept
in	O
some	O
cases	O
,	O
and	O
vice	O
versa	O
in	O
some	O
other	O
cases	O
.	O
</s>
<s>
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
is	O
by	O
construction	O
uniformly	O
more	O
powerful	O
than	O
Fisher	B-General_Concept
's	I-General_Concept
exact	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
10	O
per	O
group	O
)	O
the	O
power	B-General_Concept
difference	O
is	O
large	O
,	O
ranging	O
from	O
16	O
to	O
20	O
percentage	O
points	O
in	O
the	O
regarded	O
cases	O
.	O
</s>
<s>
The	O
power	B-General_Concept
difference	O
is	O
smaller	O
for	O
greater	O
sample	O
sizes	O
.	O
</s>
<s>
The	O
power	B-General_Concept
of	O
this	O
test	O
is	O
similar	O
to	O
that	O
of	O
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
in	O
most	O
scenarios	O
.	O
</s>
<s>
In	O
some	O
cases	O
,	O
the	O
-Pooled	O
test	O
has	O
greater	O
power	B-General_Concept
,	O
with	O
differences	O
mostly	O
ranging	O
from	O
1	O
to	O
5	O
percentage	O
points	O
.	O
</s>
<s>
However	O
,	O
the	O
resulting	O
test	O
has	O
very	O
similar	O
power	B-General_Concept
to	O
the	O
unmodified	O
test	O
in	O
all	O
scenarios	O
.	O
</s>
<s>
The	O
power	B-General_Concept
of	O
this	O
test	O
is	O
similar	O
to	O
that	O
of	O
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
in	O
many	O
scenarios	O
.	O
</s>
<s>
In	O
some	O
cases	O
,	O
the	O
-Unpooled	O
test	O
has	O
greater	O
power	B-General_Concept
,	O
with	O
differences	O
ranging	O
from	O
1	O
to	O
5	O
percentage	O
points	O
.	O
</s>
<s>
However	O
,	O
in	O
some	O
other	O
cases	O
,	O
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
has	O
noticeably	O
greater	O
power	B-General_Concept
,	O
with	O
differences	O
up	O
to	O
68	O
percentage	O
points	O
.	O
</s>
<s>
The	O
resulting	O
test	O
has	O
similar	O
power	B-General_Concept
to	O
the	O
unmodified	O
test	O
in	O
most	O
scenarios	O
.	O
</s>
<s>
In	O
some	O
cases	O
,	O
the	O
power	B-General_Concept
is	O
considerably	O
improved	O
by	O
the	O
modification	O
but	O
the	O
overall	O
power	B-General_Concept
comparison	O
to	O
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
remains	O
unchanged	O
.	O
</s>
<s>
The	O
calculation	O
of	O
Boschloo	B-General_Concept
's	I-General_Concept
test	I-General_Concept
can	O
be	O
performed	O
in	O
following	O
software	O
:	O
</s>
