<s>
In	O
statistics	O
,	O
the	O
Page	B-General_Concept
test	I-General_Concept
for	O
multiple	O
comparisons	O
between	O
ordered	O
correlated	O
variables	O
is	O
the	O
counterpart	O
of	O
Spearman	B-General_Concept
's	I-General_Concept
rank	I-General_Concept
correlation	I-General_Concept
coefficient	I-General_Concept
which	O
summarizes	O
the	O
association	O
of	O
continuous	O
variables	O
.	O
</s>
<s>
It	O
is	O
also	O
known	O
as	O
Page	B-General_Concept
's	I-General_Concept
trend	I-General_Concept
test	I-General_Concept
or	O
Page	O
's	O
L	O
test	O
.	O
</s>
<s>
The	O
Page	B-General_Concept
test	I-General_Concept
is	O
useful	O
where	O
:	O
</s>
<s>
More	O
formally	O
,	O
the	O
test	O
considers	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
,	O
for	O
n	O
conditions	O
,	O
where	O
mi	O
is	O
a	O
measure	O
of	O
the	O
central	O
tendency	O
of	O
the	O
ith	O
condition	O
,	O
</s>
<s>
It	O
has	O
more	O
statistical	B-General_Concept
power	I-General_Concept
than	O
the	O
Friedman	B-General_Concept
test	I-General_Concept
against	O
the	O
alternative	O
that	O
there	O
is	O
a	O
difference	O
in	O
trend	O
.	O
</s>
<s>
Friedman	O
's	O
test	O
considers	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
that	O
the	O
central	O
tendencies	O
of	O
the	O
observations	O
under	O
the	O
n	O
conditions	O
are	O
different	O
without	O
specifying	O
their	O
order	O
.	O
</s>
<s>
Procedure	O
for	O
the	O
Page	B-General_Concept
test	I-General_Concept
,	O
with	O
k	O
subjects	O
each	O
exposed	O
to	O
n	O
conditions	O
:	O
</s>
<s>
Arrange	O
the	O
n	O
conditions	O
in	O
the	O
order	O
implied	O
by	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
,	O
and	O
assign	O
each	O
of	O
them	O
a	O
rank	O
Yi	O
.	O
</s>
<s>
This	O
gives	O
a	O
two-tailed	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
if	O
k	O
=	O
1	O
,	O
this	O
reduces	O
to	O
the	O
familiar	O
Spearman	B-General_Concept
coefficient	I-General_Concept
.	O
</s>
<s>
The	O
Page	B-General_Concept
test	I-General_Concept
is	O
most	O
often	O
used	O
with	O
fairly	O
small	O
numbers	O
of	O
conditions	O
and	O
subjects	O
.	O
</s>
<s>
The	O
minimum	O
values	O
of	O
L	O
for	O
significance	O
at	O
the	O
0.05	O
level	O
,	O
one-tailed	B-General_Concept
,	O
with	O
three	O
conditions	O
,	O
are	O
56	O
for	O
4	O
subjects	O
(	O
the	O
lowest	O
number	O
that	O
is	O
capable	O
of	O
giving	O
a	O
significant	O
result	O
at	O
this	O
level	O
)	O
,	O
54	O
for	O
5	O
subjects	O
,	O
91	O
for	O
7	O
subjects	O
,	O
128	O
for	O
10	O
subjects	O
,	O
190	O
for	O
15	O
subjects	O
and	O
251	O
for	O
20	O
subjects	O
..	O
</s>
<s>
A	O
corresponding	O
extension	O
of	O
Kendall	B-General_Concept
's	I-General_Concept
tau	I-General_Concept
was	O
developed	O
by	O
Jonckheere	B-General_Concept
(	O
1954	O
)	O
.	O
</s>
