<s>
In	O
statistics	O
,	O
the	B-General_Concept
Jonckheere	I-General_Concept
trend	I-General_Concept
test	I-General_Concept
(	O
sometimes	O
called	O
the	O
Jonckheere	B-General_Concept
–	I-General_Concept
Terpstra	I-General_Concept
test	I-General_Concept
)	O
is	O
a	O
test	O
for	O
an	O
ordered	O
alternative	B-General_Concept
hypothesis	I-General_Concept
within	O
an	O
independent	O
samples	O
(	O
between-participants	O
)	O
design	O
.	O
</s>
<s>
It	O
is	O
similar	O
to	O
the	O
Kruskal	B-General_Concept
–	I-General_Concept
Wallis	I-General_Concept
test	I-General_Concept
in	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
that	O
several	O
independent	O
samples	O
are	O
from	O
the	O
same	O
population	O
.	O
</s>
<s>
However	O
,	O
with	O
the	O
Kruskal	B-General_Concept
–	I-General_Concept
Wallis	I-General_Concept
test	I-General_Concept
there	O
is	O
no	O
a	O
priori	O
ordering	O
of	O
the	O
populations	O
from	O
which	O
the	O
samples	O
are	O
drawn	O
.	O
</s>
<s>
When	O
there	O
is	O
an	O
a	O
priori	O
ordering	O
,	O
the	O
Jonckheere	O
test	O
has	O
more	O
statistical	B-General_Concept
power	I-General_Concept
than	O
the	O
Kruskal	B-General_Concept
–	I-General_Concept
Wallis	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
The	O
null	O
and	O
alternative	B-General_Concept
hypotheses	I-General_Concept
can	O
be	O
conveniently	O
expressed	O
in	O
terms	O
of	O
population	O
medians	O
for	O
k	O
populations	O
(	O
where	O
k	O
>	O
2	O
)	O
.	O
</s>
<s>
Letting	O
θi	O
be	O
the	O
population	O
median	O
for	O
the	O
ith	O
population	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
:	O
</s>
<s>
The	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
that	O
the	O
population	O
medians	O
have	O
an	O
a	O
priori	O
ordering	O
e.g.	O
</s>
<s>
Cast	O
the	O
data	O
into	O
an	O
ordered	O
contingency	B-Application
table	I-Application
,	O
with	O
the	O
levels	O
of	O
the	O
independent	O
variable	O
increasing	O
from	O
left	O
to	O
right	O
,	O
and	O
values	O
of	O
the	O
dependent	O
variable	O
increasing	O
from	O
top	O
to	O
bottom	O
.	O
</s>
<s>
The	O
standard	O
normal	O
distribution	O
can	O
be	O
used	O
to	O
approximate	O
the	O
distribution	O
of	O
S	O
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
for	O
cases	O
in	O
which	O
exact	O
tables	O
are	O
not	O
available	O
.	O
</s>
<s>
where	O
ti	O
is	O
a	O
row	O
marginal	O
total	O
and	O
ui	O
a	O
column	O
marginal	O
total	O
in	O
the	O
contingency	B-Application
table	I-Application
.	O
</s>
<s>
Jonckheere	O
suggested	O
breaking	O
the	O
ties	O
against	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
and	O
then	O
using	O
exact	O
tables	O
.	O
</s>
<s>
In	O
the	O
current	O
example	O
where	O
tied	O
scores	O
only	O
appear	O
in	O
adjacent	O
groups	O
,	O
the	O
value	O
of	O
S	O
is	O
unchanged	O
if	O
the	O
ties	O
are	O
broken	O
against	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
From	O
tables	O
with	O
k	O
=	O
3	O
,	O
and	O
m	O
=	O
4	O
,	O
the	O
critical	O
S	O
value	O
for	O
α	O
=	O
0.05	O
is	O
36	O
and	O
thus	O
the	O
result	O
would	O
be	O
declared	O
statistically	B-General_Concept
significant	I-General_Concept
at	O
this	O
level	O
.	O
</s>
<s>
A	O
similar	O
test	O
for	O
trend	O
within	O
the	O
context	O
of	O
repeated	O
measures	O
(	O
within-participants	O
)	O
designs	O
and	O
based	O
on	O
Spearman	O
's	O
rank	O
correlation	O
coefficient	O
was	O
developed	O
by	O
Page	B-General_Concept
.	O
</s>
