<s>
In	O
statistics	O
,	O
Mood	B-General_Concept
's	I-General_Concept
median	I-General_Concept
test	I-General_Concept
is	O
a	O
special	O
case	O
of	O
Pearson	B-General_Concept
's	I-General_Concept
chi-squared	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
It	O
is	O
a	O
nonparametric	B-General_Concept
test	I-General_Concept
that	O
tests	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
the	O
medians	O
of	O
the	O
populations	O
from	O
which	O
two	O
or	O
more	O
samples	O
are	O
drawn	O
are	O
identical	O
.	O
</s>
<s>
A	O
Pearson	B-General_Concept
's	I-General_Concept
chi-squared	I-General_Concept
test	I-General_Concept
is	O
then	O
used	O
to	O
determine	O
whether	O
the	O
observed	O
frequencies	O
in	O
each	O
sample	O
differ	O
from	O
expected	O
frequencies	O
derived	O
from	O
a	O
distribution	O
combining	O
the	O
two	O
groups	O
.	O
</s>
<s>
The	O
test	O
has	O
low	O
power	B-General_Concept
(	O
efficiency	O
)	O
for	O
moderate	O
to	O
large	O
sample	O
sizes	O
.	O
</s>
<s>
The	O
Wilcoxon	O
–	O
Mann	B-General_Concept
–	I-General_Concept
Whitney	I-General_Concept
U	I-General_Concept
two-sample	O
test	O
or	O
its	O
generalisation	O
for	O
more	O
samples	O
,	O
the	O
Kruskal	B-General_Concept
–	I-General_Concept
Wallis	I-General_Concept
test	I-General_Concept
,	O
can	O
often	O
be	O
considered	O
instead	O
.	O
</s>
<s>
The	O
relevant	O
aspect	O
of	O
the	O
median	B-General_Concept
test	I-General_Concept
is	O
that	O
it	O
only	O
considers	O
the	O
position	O
of	O
each	O
observation	O
relative	O
to	O
the	O
overall	O
median	O
,	O
whereas	O
the	O
Wilcoxon	O
–	O
Mann	B-General_Concept
–	I-General_Concept
Whitney	I-General_Concept
test	I-General_Concept
takes	O
the	O
ranks	O
of	O
each	O
observation	O
into	O
account	O
.	O
</s>
<s>
Thus	O
the	O
other	O
mentioned	O
tests	O
are	O
usually	O
more	O
powerful	O
than	O
the	O
median	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
Moreover	O
,	O
the	O
median	B-General_Concept
test	I-General_Concept
can	O
only	O
be	O
used	O
for	O
quantitative	O
data	O
.	O
</s>
<s>
It	O
is	O
crucial	O
to	O
note	O
,	O
however	O
,	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
verified	O
by	O
the	O
Wilcoxon	O
–	O
Mann	B-General_Concept
–	I-General_Concept
Whitney	I-General_Concept
U	I-General_Concept
(	O
and	O
so	O
the	O
Kruskal	B-General_Concept
–	I-General_Concept
Wallis	I-General_Concept
test	I-General_Concept
)	O
is	O
not	O
about	O
medians	O
.	O
</s>
<s>
As	O
a	O
consequence	O
,	O
if	O
the	O
Wilcoxon	O
–	O
Mann	B-General_Concept
–	I-General_Concept
Whitney	I-General_Concept
U	I-General_Concept
test	I-General_Concept
rejects	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
one	O
cannot	O
say	O
that	O
the	O
rejection	O
was	O
caused	O
only	O
by	O
the	O
shift	O
in	O
medians	O
.	O
</s>
<s>
It	O
is	O
easy	O
to	O
prove	O
by	O
simulations	O
,	O
where	O
samples	O
with	O
equal	O
medians	O
,	O
yet	O
different	O
scales	O
and	O
shapes	O
,	O
lead	O
the	O
Wilcoxon	O
–	O
Mann	B-General_Concept
–	I-General_Concept
Whitney	I-General_Concept
U	I-General_Concept
test	I-General_Concept
to	O
fail	O
completely	O
.	O
</s>
<s>
However	O
,	O
although	O
the	O
alternative	O
Kruskal-Wallis	B-General_Concept
test	I-General_Concept
does	O
not	O
assume	O
normal	O
distributions	O
,	O
it	O
does	O
assume	O
that	O
the	O
variance	O
is	O
approximately	O
equal	O
across	O
samples	O
.	O
</s>
<s>
Hence	O
,	O
in	O
situations	O
where	O
that	O
assumption	O
does	O
not	O
hold	O
,	O
the	O
median	B-General_Concept
test	I-General_Concept
is	O
an	O
appropriate	O
test	O
.	O
</s>
<s>
Moreover	O
,	O
Siegel	O
&	O
Castellan	O
(	O
1988	O
,	O
p.124	O
)	O
suggest	O
that	O
there	O
is	O
no	O
alternative	O
to	O
the	O
median	B-General_Concept
test	I-General_Concept
when	O
one	O
or	O
more	O
observations	O
are	O
"	O
off	O
the	O
scale.	O
"	O
</s>
