<s>
In	O
statistics	O
,	O
the	O
Siegel	B-General_Concept
–	I-General_Concept
Tukey	I-General_Concept
test	I-General_Concept
,	O
named	O
after	O
Sidney	O
Siegel	O
and	O
John	O
Tukey	O
,	O
is	O
a	O
non-parametric	B-General_Concept
test	I-General_Concept
which	O
may	O
be	O
applied	O
to	O
data	O
measured	O
at	O
least	O
on	O
an	O
ordinal	O
scale	O
.	O
</s>
<s>
The	O
test	O
was	O
published	O
in	O
1960	O
by	O
Sidney	O
Siegel	O
and	O
John	O
Wilder	O
Tukey	O
in	O
the	O
Journal	O
of	O
the	O
American	O
Statistical	O
Association	O
,	O
in	O
the	O
article	O
"	O
A	O
Nonparametric	B-General_Concept
Sum	O
of	O
Ranks	O
Procedure	O
for	O
Relative	O
Spread	O
in	O
Unpaired	O
Samples.	O
"	O
</s>
<s>
If	O
all	O
N	O
observations	O
are	O
arranged	O
in	O
ascending	O
order	O
,	O
it	O
can	O
be	O
expected	O
that	O
the	O
values	O
of	O
the	O
two	O
groups	O
will	O
be	O
mixed	O
or	O
sorted	O
randomly	O
,	O
if	O
there	O
are	O
no	O
differences	O
between	O
the	O
two	O
groups	O
(	O
following	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
H0	O
)	O
.	O
</s>
<s>
If	O
,	O
say	O
,	O
Group	O
A	O
were	O
more	O
inclined	O
to	O
extreme	O
values	O
(	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
H1	O
)	O
,	O
then	O
there	O
will	O
be	O
a	O
higher	O
proportion	O
of	O
observations	O
from	O
group	O
A	O
with	O
low	O
or	O
high	O
values	O
,	O
and	O
a	O
reduced	O
proportion	O
of	O
values	O
at	O
the	O
center	O
.	O
</s>
<s>
If	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
,	O
it	O
is	O
expected	O
that	O
the	O
average	O
ranks	O
of	O
the	O
two	O
groups	O
will	O
be	O
similar	O
.	O
</s>
<s>
To	O
test	O
the	O
difference	O
between	O
groups	O
for	O
significance	O
a	O
Wilcoxon	B-General_Concept
rank	I-General_Concept
sum	I-General_Concept
test	I-General_Concept
is	O
used	O
,	O
which	O
also	O
justifies	O
the	O
notation	O
WA	O
and	O
WB	O
in	O
calculating	O
the	O
rank	O
sums	O
.	O
</s>
<s>
According	O
to	O
the	O
minimum	O
of	O
these	O
two	O
values	O
is	O
distributed	O
according	O
to	O
a	O
Wilcoxon	B-General_Concept
rank-sum	I-General_Concept
distribution	O
with	O
parameters	O
given	O
by	O
the	O
two	O
group	O
sizes	O
:	O
</s>
<s>
a	O
table	O
of	O
the	O
Wilcoxon	B-General_Concept
rank-sum	I-General_Concept
distribution	O
can	O
be	O
used	O
to	O
find	O
the	O
statistical	O
significance	O
of	O
the	O
results	O
(	O
see	O
Mann	O
–	O
Whitney_U_test	O
for	O
more	O
explanations	O
on	O
these	O
tables	O
)	O
.	O
</s>
<s>
indicating	O
little	O
or	O
no	O
reason	O
to	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
the	O
dispersion	O
of	O
the	O
two	O
groups	O
is	O
the	O
same	O
.	O
</s>
