<s>
In	O
randomized	O
statistical	O
experiments	O
,	O
generalized	B-General_Concept
randomized	I-General_Concept
block	I-General_Concept
designs	I-General_Concept
(	O
GRBDs	O
)	O
are	O
used	O
to	O
study	O
the	O
interaction	O
between	O
blocks	O
and	O
treatments	O
.	O
</s>
<s>
For	O
a	O
GRBD	O
,	O
each	O
treatment	O
is	O
replicated	O
at	O
least	O
two	O
times	O
in	O
each	O
block	O
;	O
this	O
replication	O
allows	O
the	O
estimation	O
and	O
testing	O
of	O
an	O
interaction	O
term	O
in	O
the	O
linear	B-Algorithm
model	I-Algorithm
(	O
without	O
making	O
parametric	O
assumptions	O
about	O
a	O
normal	O
distribution	O
for	O
the	O
error	O
)	O
.	O
</s>
<s>
The	O
experimental	O
design	O
guides	O
the	O
formulation	O
of	O
an	O
appropriate	O
linear	B-Algorithm
model	I-Algorithm
.	O
</s>
<s>
Without	O
replication	O
,	O
the	O
(	O
classic	O
)	O
RCBD	O
has	O
a	O
two-way	B-General_Concept
linear-model	I-General_Concept
with	O
treatment	O
-	O
and	O
block-effects	O
but	O
without	O
a	O
block-treatment	O
interaction	O
.	O
</s>
<s>
Without	O
replicates	O
,	O
this	O
two-way	B-General_Concept
linear-model	I-General_Concept
that	O
may	O
be	O
estimated	O
and	O
tested	O
without	O
making	O
parametric	O
assumptions	O
(	O
by	O
using	O
the	O
randomization	O
distribution	O
,	O
without	O
using	O
a	O
normal	O
distribution	O
for	O
the	O
error	O
)	O
.	O
</s>
<s>
randomization-based	O
)	O
test	O
for	O
the	O
block-treatment	O
interaction	O
in	O
the	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
(	O
anova	B-General_Concept
)	O
of	O
the	O
RCBD	O
.	O
</s>
<s>
With	O
replicates	O
,	O
interaction	O
can	O
be	O
tested	O
with	O
the	O
multivariate	B-General_Concept
analysis	I-General_Concept
of	I-General_Concept
variance	I-General_Concept
and	O
coefficients	O
in	O
the	O
linear	B-Algorithm
model	I-Algorithm
can	O
be	O
estimated	O
without	O
bias	O
and	O
with	O
minimum	O
variance	O
(	O
by	O
using	O
the	O
least-squares	B-Algorithm
method	I-Algorithm
)	O
.	O
</s>
