<s>
The	O
Friedman	B-General_Concept
test	I-General_Concept
is	O
a	O
non-parametric	B-General_Concept
statistical	O
test	O
developed	O
by	O
Milton	O
Friedman	O
.	O
</s>
<s>
Similar	O
to	O
the	O
parametric	B-General_Concept
repeated	O
measures	O
ANOVA	B-General_Concept
,	O
it	O
is	O
used	O
to	O
detect	O
differences	O
in	O
treatments	O
across	O
multiple	O
test	O
attempts	O
.	O
</s>
<s>
Applicable	O
to	O
complete	O
block	O
designs	O
,	O
it	O
is	O
thus	O
a	O
special	O
case	O
of	O
the	O
Durbin	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
The	O
Friedman	B-General_Concept
test	I-General_Concept
is	O
used	O
for	O
one-way	O
repeated	O
measures	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
by	O
ranks	O
.	O
</s>
<s>
In	O
its	O
use	O
of	O
ranks	O
it	O
is	O
similar	O
to	O
the	O
Kruskal	B-General_Concept
–	I-General_Concept
Wallis	I-General_Concept
one-way	I-General_Concept
analysis	I-General_Concept
of	I-General_Concept
variance	I-General_Concept
by	O
ranks	O
.	O
</s>
<s>
The	O
Friedman	B-General_Concept
test	I-General_Concept
is	O
widely	O
supported	O
by	O
many	O
statistical	O
software	O
packages	O
.	O
</s>
<s>
Given	O
data	O
,	O
that	O
is	O
,	O
a	O
matrix	B-Architecture
with	O
rows	O
(	O
the	O
blocks	O
)	O
,	O
columns	O
(	O
the	O
treatments	O
)	O
and	O
a	O
single	O
observation	O
at	O
the	O
intersection	O
of	O
each	O
block	O
and	O
treatment	O
,	O
calculate	O
the	O
ranks	O
within	O
each	O
block	O
.	O
</s>
<s>
Replace	O
the	O
data	O
with	O
a	O
new	O
matrix	B-Architecture
where	O
the	O
entry	O
is	O
the	O
rank	O
of	O
within	O
block	O
.	O
</s>
<s>
In	O
this	O
case	O
the	O
p-value	B-General_Concept
is	O
given	O
by	O
.	O
</s>
<s>
If	O
n	O
or	O
k	O
is	O
small	O
,	O
the	O
approximation	O
to	O
chi-square	O
becomes	O
poor	O
and	O
the	O
p-value	B-General_Concept
should	O
be	O
obtained	O
from	O
tables	O
of	O
Q	O
specially	O
prepared	O
for	O
the	O
Friedman	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
If	O
the	O
p-value	B-General_Concept
is	O
significant	B-General_Concept
,	O
appropriate	O
post-hoc	O
multiple	B-General_Concept
comparisons	I-General_Concept
tests	O
would	O
be	O
performed	O
.	O
</s>
<s>
When	O
using	O
this	O
kind	O
of	O
design	O
for	O
a	O
binary	O
response	O
,	O
one	O
instead	O
uses	O
the	O
Cochran	B-General_Concept
's	I-General_Concept
Q	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
The	O
Sign	B-General_Concept
test	I-General_Concept
(	O
with	O
a	O
two-sided	O
alternative	O
)	O
is	O
equivalent	O
to	O
a	O
Friedman	B-General_Concept
test	I-General_Concept
on	O
two	O
groups	O
.	O
</s>
<s>
The	O
Wilcoxon	B-General_Concept
signed-rank	I-General_Concept
test	I-General_Concept
is	O
a	O
nonparametric	B-General_Concept
test	I-General_Concept
of	O
nonindependent	O
data	O
from	O
only	O
two	O
groups	O
.	O
</s>
<s>
When	O
the	O
data	O
do	O
not	O
contain	O
any	O
missing	O
value	O
,	O
it	O
gives	O
the	O
same	O
result	O
as	O
Friedman	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
An	O
implementation	O
of	O
the	O
test	O
exists	O
in	O
R	B-Language
.	O
</s>
<s>
Eisinga	O
,	O
Heskes	O
,	O
Pelzer	O
and	O
Te	O
Grotenhuis	O
(	O
2017	O
)	O
provide	O
an	O
exact	O
test	O
for	O
pairwise	O
comparison	O
of	O
Friedman	O
rank	O
sums	O
,	O
implemented	O
in	O
R	B-Language
.	O
The	O
Eisinga	O
c.s.	O
</s>
<s>
Not	O
all	O
statistical	O
packages	O
support	O
post-hoc	O
analysis	O
for	O
Friedman	O
's	O
test	O
,	O
but	O
user-contributed	O
code	O
exists	O
that	O
provides	O
these	O
facilities	O
(	O
for	O
example	O
in	O
SPSS	B-Algorithm
,	O
and	O
in	O
R	B-Language
.	O
)	O
.	O
</s>
<s>
Also	O
,	O
there	O
is	O
a	O
specialized	O
package	O
available	O
in	O
R	B-Language
containing	O
numerous	O
non-parametric	B-General_Concept
methods	I-General_Concept
for	O
post-hoc	O
analysis	O
after	O
Friedman	O
.	O
</s>
