<s>
In	O
the	O
analysis	O
of	O
designed	O
experiments	O
,	O
the	O
Friedman	B-General_Concept
test	I-General_Concept
is	O
the	O
most	O
common	O
non-parametric	B-General_Concept
test	I-General_Concept
for	O
complete	O
block	O
designs	O
.	O
</s>
<s>
The	O
Durbin	B-General_Concept
test	I-General_Concept
is	O
a	O
nonparametric	B-General_Concept
test	I-General_Concept
for	O
balanced	O
incomplete	O
designs	O
that	O
reduces	O
to	O
the	O
Friedman	B-General_Concept
test	I-General_Concept
in	O
the	O
case	O
of	O
a	O
complete	O
block	O
design	O
.	O
</s>
<s>
The	O
Durbin	B-General_Concept
test	I-General_Concept
is	O
based	O
on	O
the	O
following	O
assumptions	O
:	O
</s>
<s>
where	O
Fα	O
,	O
k	O
−	O
1	O
,	O
bk	O
−	O
b	O
−	O
t	O
+	O
1	O
denotes	O
the	O
α-quantile	O
of	O
the	O
F	B-General_Concept
distribution	I-General_Concept
with	O
k	O
−	O
1	O
numerator	O
degrees	O
of	O
freedom	O
and	O
bk	O
−	O
b	O
−	O
t	O
+	O
1	O
denominator	O
degrees	O
of	O
freedom	O
.	O
</s>
<s>
If	O
the	O
hypothesis	O
of	O
identical	O
treatment	O
effects	O
is	O
rejected	O
,	O
it	O
is	O
often	O
desirable	O
to	O
determine	O
which	O
treatments	O
are	O
different	O
(	O
i.e.	O
,	O
multiple	B-General_Concept
comparisons	I-General_Concept
)	O
.	O
</s>
<s>
The	O
T2	O
statistic	O
is	O
the	O
two-way	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
statistic	O
computed	O
on	O
the	O
ranks	O
R(Xij )	O
.	O
</s>
<s>
Cochran	B-General_Concept
's	I-General_Concept
Q	I-General_Concept
test	I-General_Concept
is	O
applied	O
for	O
the	O
special	O
case	O
of	O
a	O
binary	O
response	O
variable	O
(	O
i.e.	O
,	O
one	O
that	O
can	O
have	O
only	O
one	O
of	O
two	O
possible	O
outcomes	O
)	O
.	O
</s>
<s>
Cochran	B-General_Concept
's	I-General_Concept
Q	I-General_Concept
test	I-General_Concept
is	O
valid	O
for	O
complete	O
block	O
designs	O
only	O
.	O
</s>
