<s>
In	O
statistics	O
,	O
Duncan	B-General_Concept
's	I-General_Concept
new	I-General_Concept
multiple	I-General_Concept
range	I-General_Concept
test	I-General_Concept
(	O
MRT	O
)	O
is	O
a	O
multiple	B-General_Concept
comparison	I-General_Concept
procedure	O
developed	O
by	O
David	O
B	O
.	O
Duncan	O
in	O
1955	O
.	O
</s>
<s>
Duncan	O
's	O
MRT	O
belongs	O
to	O
the	O
general	O
class	O
of	O
multiple	B-General_Concept
comparison	I-General_Concept
procedures	O
that	O
use	O
the	O
studentized	O
range	O
statistic	O
qr	O
to	O
compare	O
sets	O
of	O
means	O
.	O
</s>
<s>
David	O
B	O
.	O
Duncan	O
developed	O
this	O
test	O
as	O
a	O
modification	O
of	O
the	O
Student	O
–	O
Newman	O
–	O
Keuls	O
method	O
that	O
would	O
have	O
greater	O
power	B-General_Concept
.	O
</s>
<s>
This	O
test	O
is	O
often	O
followed	O
by	O
the	O
Compact	B-Application
Letter	I-Application
Display	I-Application
(	O
CLD	O
)	O
methodology	O
that	O
renders	O
the	O
output	O
of	O
such	O
test	O
much	O
more	O
accessible	O
to	O
non-statistician	O
audiences	O
.	O
</s>
<s>
2.A	O
common	O
standard	B-General_Concept
error	I-General_Concept
.	O
</s>
<s>
This	O
standard	B-General_Concept
error	I-General_Concept
is	O
unknown	O
,	O
but	O
there	O
is	O
available	O
the	O
usual	O
estimate	O
,	O
which	O
is	O
independent	O
of	O
the	O
observed	O
means	O
and	O
is	O
based	O
on	O
a	O
number	O
of	O
degrees	O
of	O
freedom	O
,	O
denoted	O
by	O
.	O
</s>
<s>
Where	O
the	O
shortest	O
significant	O
range	O
is	O
the	O
significant	O
studentized	O
range	O
,	O
multiplied	O
by	O
the	O
standard	B-General_Concept
error	I-General_Concept
.	O
</s>
<s>
With	O
a	O
standard	B-General_Concept
error	I-General_Concept
of	O
,	O
and	O
(	O
degrees	O
of	O
freedom	O
for	O
estimating	O
the	O
standard	B-General_Concept
error	I-General_Concept
)	O
.	O
</s>
<s>
Duncan	O
(	O
1965	O
)	O
also	O
gave	O
the	O
first	O
Bayesian	O
multiple	B-General_Concept
comparison	I-General_Concept
procedure	O
,	O
for	O
the	O
pairwise	O
comparisons	O
among	O
the	O
means	O
in	O
a	O
one-way	O
layout	O
.	O
</s>
<s>
This	O
multiple	B-General_Concept
comparison	I-General_Concept
procedure	O
is	O
different	O
for	O
the	O
one	O
discussed	O
above	O
.	O
</s>
<s>
A	O
study	O
,	O
which	O
performed	O
by	O
Juliet	O
Popper	O
Shaffer	O
(	O
1998	O
)	O
,	O
has	O
shown	O
that	O
the	O
method	O
proposed	O
by	O
Duncan	O
,	O
modified	O
to	O
provide	O
weak	O
control	O
of	O
FWE	O
and	O
using	O
an	O
empirical	O
estimate	O
of	O
the	O
variance	O
of	O
the	O
population	O
means	O
,	O
has	O
good	O
properties	O
both	O
from	O
the	O
Bayesian	O
point	O
of	O
view	O
,	O
as	O
a	O
minimum	O
-	O
risk	O
method	O
,	O
and	O
from	O
the	O
frequentist	O
point	O
of	O
view	O
,	O
with	O
good	O
average	O
power	B-General_Concept
.	O
</s>
<s>
In	O
addition	O
,	O
results	O
indicate	O
considerable	O
similarity	O
in	O
both	O
risk	O
and	O
average	O
power	B-General_Concept
between	O
Duncan	O
's	O
modified	O
procedure	O
and	O
the	O
Benjamini	O
and	O
Hochberg	O
(	O
1995	O
)	O
False	B-General_Concept
discovery	I-General_Concept
rate	I-General_Concept
-controlling	O
procedure	O
,	O
with	O
the	O
same	O
weak	O
family-wise	O
error	O
control	O
.	O
</s>
<s>
Duncan	O
argued	O
that	O
a	O
more	O
liberal	O
procedure	O
was	O
appropriate	O
because	O
in	O
real	O
world	O
practice	O
the	O
global	O
null	B-General_Concept
hypothesis	I-General_Concept
H0	O
=	O
"	O
All	O
means	O
are	O
equal	O
"	O
is	O
often	O
false	O
and	O
thus	O
traditional	O
statisticians	O
overprotect	O
a	O
probably	O
false	O
null	B-General_Concept
hypothesis	I-General_Concept
against	O
type	O
I	O
errors	O
.	O
</s>
<s>
Given	O
an	O
overall	O
set	O
of	O
100	O
means	O
,	O
let	O
us	O
look	O
at	O
the	O
null	B-General_Concept
hypotheses	I-General_Concept
of	O
the	O
test	O
:	O
</s>
<s>
There	O
are	O
null	B-General_Concept
hypotheses	I-General_Concept
for	O
the	O
correct	O
ranking	O
of	O
each	O
2	O
means	O
.	O
</s>
<s>
There	O
are	O
null	B-General_Concept
hypotheses	I-General_Concept
for	O
the	O
correct	O
ranking	O
of	O
each	O
3	O
means	O
.	O
</s>
<s>
There	O
are	O
null	B-General_Concept
hypotheses	I-General_Concept
for	O
the	O
correct	O
ranking	O
of	O
each	O
4	O
means	O
.	O
</s>
<s>
It	O
uses	O
the	O
obtained	O
value	O
of	O
F	O
to	O
estimate	O
the	O
prior	O
probability	O
of	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
being	O
true	O
.	O
</s>
<s>
Tukey	B-General_Concept
's	I-General_Concept
range	I-General_Concept
test	I-General_Concept
is	O
commonly	O
used	O
to	O
compare	O
pairs	O
of	O
means	O
,	O
this	O
procedure	O
controls	O
the	O
family-wise	O
error	O
rate	O
in	O
the	O
strong	O
sense	O
.	O
</s>
<s>
Another	O
solution	O
is	O
to	O
perform	O
Student	B-General_Concept
's	I-General_Concept
t-test	I-General_Concept
of	O
all	O
pairs	O
of	O
means	O
,	O
and	O
then	O
to	O
use	O
FDR	O
Controlling	O
procedure	O
(	O
to	O
control	O
the	O
expected	O
proportion	O
of	O
incorrectly	O
rejected	O
null	B-General_Concept
hypotheses	I-General_Concept
)	O
.	O
</s>
<s>
Other	O
possible	O
solutions	O
,	O
which	O
do	O
not	O
include	O
hypothesis	O
testing	O
,	O
but	O
result	O
in	O
a	O
partition	O
of	O
subsets	O
include	O
Clustering	B-Algorithm
&	O
Hierarchical	B-Algorithm
Clustering	I-Algorithm
.	O
</s>
