<s>
The	O
Cochran	B-General_Concept
–	I-General_Concept
Armitage	I-General_Concept
test	I-General_Concept
for	I-General_Concept
trend	I-General_Concept
,	O
named	O
for	O
William	O
Cochran	O
and	O
Peter	O
Armitage	O
,	O
is	O
used	O
in	O
categorical	O
data	O
analysis	O
when	O
the	O
aim	O
is	O
to	O
assess	O
for	O
the	O
presence	O
of	O
an	O
association	O
between	O
a	O
variable	O
with	O
two	O
categories	O
and	O
an	O
ordinal	O
variable	O
with	O
k	O
categories	O
.	O
</s>
<s>
It	O
modifies	O
the	O
Pearson	B-General_Concept
chi-squared	I-General_Concept
test	I-General_Concept
to	O
incorporate	O
a	O
suspected	O
ordering	O
in	O
the	O
effects	O
of	O
the	O
k	O
categories	O
of	O
the	O
second	O
variable	O
.	O
</s>
<s>
The	O
trend	O
test	O
is	O
applied	O
when	O
the	O
data	O
take	O
the	O
form	O
of	O
a	O
2×k	O
contingency	B-Application
table	I-Application
.	O
</s>
<s>
The	O
hypothesis	O
of	O
no	O
association	O
(	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
)	O
can	O
be	O
expressed	O
as	O
:	O
</s>
<s>
The	O
weights	O
ti	O
can	O
be	O
chosen	O
such	O
that	O
the	O
trend	O
test	O
becomes	O
locally	O
most	O
powerful	B-General_Concept
for	O
detecting	O
particular	O
types	O
of	O
associations	O
.	O
</s>
<s>
The	O
trend	O
test	O
will	O
have	O
higher	O
power	B-General_Concept
than	O
the	O
chi-squared	O
test	O
when	O
the	O
suspected	O
trend	O
is	O
correct	O
,	O
but	O
the	O
ability	O
to	O
detect	O
unsuspected	O
trends	O
is	O
sacrificed	O
.	O
</s>
<s>
This	O
is	O
an	O
example	O
of	O
a	O
general	O
technique	O
of	O
directing	O
hypothesis	O
tests	O
toward	O
narrow	O
alternatives	B-General_Concept
.	O
</s>
<s>
The	O
trend	O
test	O
exploits	O
the	O
suspected	O
effect	O
direction	O
to	O
increase	O
power	B-General_Concept
,	O
but	O
this	O
does	O
not	O
affect	O
the	O
sampling	O
distribution	O
of	O
the	O
test	B-General_Concept
statistic	I-General_Concept
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
The	O
distribution	O
of	O
genotype	O
counts	O
can	O
be	O
put	O
in	O
a	O
2×3	O
contingency	B-Application
table	I-Application
.	O
</s>
<s>
and	O
the	O
Pearson	B-General_Concept
chi-squared	I-General_Concept
test	I-General_Concept
gives	O
a	O
standardized	O
test	B-General_Concept
statistic	I-General_Concept
of	O
2	O
.	O
</s>
<s>
Note	O
that	O
for	O
the	O
significance	O
level	O
to	O
give	O
a	O
p-value	B-General_Concept
with	O
the	O
usual	O
probabilistic	O
interpretation	O
,	O
the	O
weights	O
must	O
be	O
specified	O
before	O
examining	O
the	O
data	O
,	O
and	O
only	O
one	O
set	O
of	O
weights	O
may	O
be	O
used	O
.	O
</s>
