<s>
The	O
Mantel	B-General_Concept
test	I-General_Concept
,	O
named	O
after	O
Nathan	O
Mantel	O
,	O
is	O
a	O
statistical	O
test	O
of	O
the	O
correlation	O
between	O
two	O
matrices	B-Architecture
.	O
</s>
<s>
The	O
matrices	B-Architecture
must	O
be	O
of	O
the	O
same	O
dimension	O
;	O
in	O
most	O
applications	O
,	O
they	O
are	O
matrices	B-Architecture
of	O
interrelations	O
between	O
the	O
same	O
vectors	O
of	O
objects	O
.	O
</s>
<s>
Because	O
distances	O
are	O
not	O
independent	O
of	O
each	O
other	O
since	O
changing	O
the	O
"	O
position	O
"	O
of	O
one	O
object	O
would	O
change	O
of	O
these	O
distances	O
(	O
the	O
distance	O
from	O
that	O
object	O
to	O
each	O
of	O
the	O
others	O
)	O
we	O
can	O
not	O
assess	O
the	O
relationship	O
between	O
the	O
two	O
matrices	B-Architecture
by	O
simply	O
evaluating	O
the	O
correlation	O
coefficient	O
between	O
the	O
two	O
sets	O
of	O
distances	O
and	O
testing	O
its	O
statistical	B-General_Concept
significance	I-General_Concept
.	O
</s>
<s>
The	O
Mantel	B-General_Concept
test	I-General_Concept
deals	O
with	O
this	O
problem	O
.	O
</s>
<s>
The	O
correlation	O
between	O
the	O
two	O
sets	O
of	O
distances	O
is	O
calculated	O
,	O
and	O
this	O
is	O
both	O
the	O
measure	O
of	O
correlation	O
reported	O
and	O
the	O
test	B-General_Concept
statistic	I-General_Concept
on	O
which	O
the	O
test	O
is	O
based	O
.	O
</s>
<s>
In	O
contrast	O
to	O
the	O
ordinary	O
use	O
of	O
the	O
correlation	O
coefficient	O
,	O
to	O
assess	O
significance	O
of	O
any	O
apparent	O
departure	O
from	O
a	O
zero	O
correlation	O
,	O
the	O
rows	O
and	O
columns	O
of	O
one	O
of	O
the	O
matrices	B-Architecture
are	O
subjected	O
to	O
random	B-Algorithm
permutations	I-Algorithm
many	O
times	O
,	O
with	O
the	O
correlation	O
being	O
recalculated	O
after	O
each	O
permutation	O
.	O
</s>
<s>
The	O
reasoning	O
is	O
that	O
if	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
there	O
being	O
no	O
relation	O
between	O
the	O
two	O
matrices	B-Architecture
is	O
true	O
,	O
then	O
permuting	O
the	O
rows	O
and	O
columns	O
of	O
the	O
matrix	O
should	O
be	O
equally	O
likely	O
to	O
produce	O
a	O
larger	O
or	O
a	O
smaller	O
coefficient	O
.	O
</s>
<s>
In	O
addition	O
to	O
overcoming	O
the	O
problems	O
arising	O
from	O
the	O
statistical	O
dependence	O
of	O
elements	O
within	O
each	O
of	O
the	O
two	O
matrices	B-Architecture
,	O
use	O
of	O
the	O
permutation	O
test	O
means	O
that	O
no	O
reliance	O
is	O
being	O
placed	O
on	O
assumptions	O
about	O
the	O
statistical	O
distributions	O
of	O
elements	O
in	O
the	O
matrices	B-Architecture
.	O
</s>
<s>
Many	O
statistical	B-Algorithm
packages	I-Algorithm
include	O
routines	O
for	O
carrying	O
out	O
the	O
Mantel	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
The	O
various	O
papers	O
introducing	O
the	O
Mantel	B-General_Concept
test	I-General_Concept
(	O
and	O
its	O
extension	O
,	O
the	O
partial	O
Mantel	B-General_Concept
test	I-General_Concept
)	O
lack	O
a	O
clear	O
statistical	O
framework	O
specifying	O
fully	O
the	O
null	O
and	O
alternative	O
hypotheses	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
Mantel	O
and	O
partial	O
Mantel	B-General_Concept
tests	I-General_Concept
can	O
be	O
flawed	O
in	O
the	O
presence	O
of	O
spatial	O
auto-correlation	O
and	O
return	O
erroneously	O
low	O
p-values	O
.	O
</s>
