<s>
Compact	B-Application
Letter	I-Application
Display	I-Application
(	O
CLD	O
)	O
is	O
a	O
statistical	O
method	O
to	O
clarify	O
the	O
output	O
of	O
multiple	O
hypothesis	O
testing	O
when	O
using	O
the	O
ANOVA	B-General_Concept
and	O
Tukey	B-General_Concept
's	I-General_Concept
range	I-General_Concept
tests	I-General_Concept
.	O
</s>
<s>
CLD	O
can	O
also	O
be	O
applied	O
following	O
the	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
which	O
is	O
similar	O
to	O
Tukey	B-General_Concept
's	I-General_Concept
range	I-General_Concept
test	I-General_Concept
)	O
.	O
</s>
<s>
The	O
basic	O
technique	O
of	O
compact	B-Application
letter	I-Application
display	I-Application
is	O
to	O
label	O
variables	O
by	O
one	O
or	O
more	O
letters	O
,	O
so	O
that	O
variables	O
are	O
statistically	O
indistinguishable	O
if	O
and	O
only	O
if	O
they	O
share	O
at	O
least	O
one	O
letter	O
.	O
</s>
<s>
The	O
CLD	O
methodology	O
can	O
be	O
applied	O
to	O
tabular	O
data	O
(	O
spreadsheet	B-Application
,	O
data	O
frame	O
)	O
or	O
visual	O
data	O
(	O
box	B-Application
plot	I-Application
and	O
bar	B-Application
chart	I-Application
)	O
.	O
</s>
<s>
This	O
constraint	O
is	O
typically	O
much	O
higher	O
than	O
the	O
vast	O
majority	O
of	O
multiple	O
hypothesis	O
testing	O
conducted	O
using	O
ANOVA	B-General_Concept
and	O
Tukey	B-General_Concept
's	I-General_Concept
range	I-General_Concept
tests	I-General_Concept
.	O
</s>
<s>
Next	O
,	O
we	O
reproduce	O
the	O
same	O
table	O
but	O
we	O
sort	O
the	O
cities	O
using	O
the	O
CLD	O
methodology	O
after	O
we	O
would	O
have	O
conducted	O
a	O
Tukey	B-General_Concept
's	I-General_Concept
range	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
Here	O
is	O
a	O
first	O
box	B-Application
plot	I-Application
with	O
cities	O
just	O
sorted	O
in	O
alphabetical	O
order	O
from	O
left	O
to	O
right	O
.	O
</s>
<s>
The	O
box	B-Application
plot	I-Application
above	O
is	O
not	O
entirely	O
clear	O
.	O
</s>
<s>
Now	O
,	O
let	O
's	O
view	O
the	O
same	O
boxplot	B-Application
using	O
the	O
CLD	O
methodology	O
.	O
</s>
<s>
The	O
box	B-Application
plot	I-Application
above	O
,	O
using	O
the	O
CLD	O
methodology	O
,	O
is	O
now	O
far	O
more	O
informative	O
.	O
</s>
<s>
In	O
the	O
absence	O
of	O
the	O
CLD	O
methodology	O
,	O
the	O
main	O
underlying	O
way	O
of	O
identifying	O
statistical	O
difference	O
in	O
means	O
between	O
paired	O
variables	O
is	O
the	O
mentioned	O
Tukey	B-General_Concept
's	I-General_Concept
range	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
The	O
Tukey	B-General_Concept
's	I-General_Concept
range	I-General_Concept
test	I-General_Concept
uncovered	O
that	O
San	O
Francisco	O
&	O
Spokane	O
did	O
not	O
have	O
statistically	O
different	O
rainfall	O
mean	O
(	O
at	O
the	O
alpha	O
=	O
0.05	O
level	O
)	O
with	O
a	O
p-value	O
of	O
0.08	O
.	O
</s>
<s>
And	O
,	O
the	O
CLD	O
enhanced	O
information	O
can	O
be	O
readily	O
interpreted	O
by	O
a	O
far	O
wider	O
audience	O
than	O
doing	O
otherwise	O
(	O
communicating	O
the	O
results	O
without	O
using	O
the	O
CLD	O
methodology	O
,	O
including	O
communicating	O
the	O
result	O
of	O
the	O
Tukey	B-General_Concept
's	I-General_Concept
range	I-General_Concept
test	I-General_Concept
directly	O
)	O
.	O
</s>
