Agriculture Reference
In-Depth Information
whole experimental area is divided into a number
of homogeneous blocks, each having a number of
experimental units as the number of treatments.
Blocking is done in such a way that the variations
among the experimental units within the block
are minimum (homogeneous). In doing so,
blocking is done perpendicular to the direction
of the variability of the experimental area. Thus,
if the variability (may be fertility gradient) is in
east-west direction, then blocking should be
done in north-west direction.
10.8
Randomized Block Design
(RBD)
Randomized block design uses all the three basic
principles of experimental design, namely, (1)
replication, (2) randomization, and (3) local con-
trol. Randomized complete block design
(RCBD) or simply randomized block design
(RBD) takes into account the variability among
the experimental units in one direction. The
Gradient
Gradient Blocking
Let there be
t
number of treatments, each to be
y
ij
¼
j
response corresponding to
th replication/
replicated
number of times. So according to
randomized block design, we should have
r
block of the
i
th treatment
r
num-
μ ¼
general effect
ber of blocks each having
number of experi-
mental units as follows (Table
10.9
):
Thus, the total number of experimental units
(plots) in randomized block design is “number of
treatments
t
α
i
¼
additional effect due to the
i
th treatment
and
P
α
i
¼
0
β
j
¼
additional effect due to the
j
th replication/
block and
P
β
j
¼
0
(
t
)” multiplied by “number of
e
ij
¼
errors associated with
j
th replication/block
replications (
r
),” that is,
rt ¼ n
.
2
)
The above model is based on the assumptions
that the effects are additive in nature and the
error components are identically, independently
distributed as normal variate with mean zero and
constant variance.
Let the level of significance be
of
i
th treatment and are i.i.d.
N
(0,
σ
Analysis
Let us suppose that we have
t
number of
r
treatments, each being replicated
number of
times. The appropriate statistical model
for
RBD will be
α
.
y
ij
¼ μ þ α
i
þ β
j
þ e
ij
; i ¼
1
;
2
;
3
; ; t;
Hypothesis to Be Tested
The null hypotheses to be tested are
j ¼
;
; ; r
1
2
where
Table 10.9
Treatments and blocks in RBD
Replication/blocks
Experimental unit
...
.
r
1
r
1
2
1
t
+1
...
.
(
r
2)
t
+1
(
r
1)
t
+1
2
t
+2
...
.
(
r
2)
t
+2
(
r
1)
t
+2
:
:
...
.
:
:
:
:
...
.
:
:
t
2
t
...
.
(
r
1)
t
rt
