Agriculture Reference
In-Depth Information
Table 10.14
Plot-wise observations from factorial RBD experiment
B
Replication 1
Replication 2
Replication
r
A
b
1
b
2
...
b
j
...
b
n
b
1
b
2
...
b
j
...
b
n
...
b
1
b
2
...
b
j
...
b
n
a
1
y
111
y
121
y
1
j
1
y
1
n
1
y
112
y
122
y
1
j
2
y
1
n
2
...
y
11
r
y
12
r
y
1
jr
y
1
nr
a
2
y
y
221
y
y
2
n
1
y
y
y
y
...
y
21
r
y
y
2
jr
y
211
2
j
1
212
222
2
j
2
2
n
2
22
r
2
nr
.
.
.
......
:
:
:
......
:
:
:
......
y
i
11
y
i
21
y
ij
1
y
in
1
y
i
12
y
i
22
y
ij
2
y
in
2
y
i
1
r
y
i
2
r
y
ijr
y
inr
a
i
:
:
:
:
:
:
:
:
a
m
y
m
11
y
m
21
y
mj
1
y
mn
1
y
m
12
y
m
22
y
mj
2
y
mn
2
y
m
1
r
y
m
2
r
y
mjr
y
mnr
m
X
n
X
r
k¼
1
y
ijk
β
j
¼
additional effect due to the
j
th level of B,
Grand total
ðGÞ¼
P
β
j
¼
0
i¼
1
j¼
1
2
mnr
ðÞ¼
G
αð
ij
¼
i
interaction effect of the
th level of
Correction factor CF
the first
factor and the
j
th level of B,
P
αð
ij
¼
P
j
m
X
n
X
r
k¼
1
y
αð
ij
¼
0
2
TSS
¼
ijk
CF
i
i¼
1
j¼
1
γ
k
¼
additional effect due to the
k
th replicate,
P
γ
k
¼
X
r
1
mn
0
2
ook
RSS
¼
1
y
CF
;
e
ijk
¼
error component associated with the
k¼
i
th level of the first factor and the
j
th level of
m
X
n
where
y
00
k
¼
y
ijk
¼ k
th replication total
:
2
)
We have the following hypotheses for m n
factorial experiment in RBD to be tested:
Bin
k
th replicate and
e
ijk
~ i.i.d.
N
(0,
σ
i
j
Let us make the following table for calculating
other sums of squares (Tables
10.15
and
10.16
).
H
01
: α
1
¼ α
2
¼ ...¼ α
i
¼ ...¼ α
m
¼
0
;
m
X
n
j¼
1
y
1
r
H
02
: β
1
¼ β
2
¼ ...¼ β
j
¼ ...¼ β
n
¼
0
;
2
TrSS
¼
ij
0
CF
;
i¼
1
H
03
: γ
1
¼ γ
2
¼ ...¼ γ
k
¼ ...¼ γ
r
¼
0
;
X
r
H
04
:
All
αð
ij
s are equal
where
y
ij
0
¼
1
y
ijk
k¼
ErSS
¼
TSS
RSS
TrSS
;
against the alternative hypotheses
m
i¼
1
y
1
nr
2
SS A
ðÞ¼
i
00
CF
H
11
:
All
α
's are not equal,
H
12
:
All
β
's are not equal,
X
n
j¼
1
y
1
mr
2
0
j
0
SS B
ðÞ¼
CF
;
H
13
:
All
γ
's are not equal,
H
14
:
All
ðαβÞ
's are not equal
:
SS AB
ðÞ¼
TrSS
SS
ð
A
Þ
SS
ð
B
Þ
Let the level of significance be 0.05.
We calculate the following quantities from the
table:
F
> F
0.05;(
m
1),
If the cal.
(for A)
(
r
1)(
mn
1)
then
H
01
is rejected. This means the main effects
