Agriculture Reference
In-Depth Information
For the above experiment,
the appropriate
e
ij
(error
I)
¼
error associated with the
i
th
model is
y
ijk
¼μ þ γ
i
þ α
j
þ e
ij
þ β
k
þ υ
jk
þ e
ijk
,
replication and the
j
th level of tillage and
i ¼
3,
2
m
e
ij
~ i.i.d.
N
(0,
σ
)
j ¼
3,
k ¼
4,
0
ijk
e
(error II)
¼
error associated with the
i
th repli-
cation, the
where
μ ¼
j
th level of tillage, and the
k
th level of
general effect
subplot factor (variety) and
e
ijk
~ i.i.d.
N
(0,
σ
2
s
)
γ
i
¼
additional effect due to the
i
th replication
Hypothesis to Be Tested
α
j
¼
j
additional effect due to the
th level of main
plot factor, tillage, and
P
3
j¼
1
α
j
¼
H
0
: γ
1
¼ γ
2
¼ γ
3
¼
0
;
0
α
1
¼ α
2
¼ α
3
¼
;
β
1
¼ β
2
¼ β
3
¼ β
4
¼
0
β
k
¼
additional effect due to the
k
th level of
;
υ
0
s are all equal to zero
0
subplot factor, variety, and
P
4
k¼
1
β
k
¼
0
:
υ
jk
¼
th level of
main plot factor (tillage) and the
interaction effect due to the
j
H
1
: α
's are not all equal,
k
th level
γ
's are not all equal,
β
(variety) and
P
3
j¼
1
υ
jk
¼
's are not all equal,
of
subplot
factor
υ
's are not all equal
:
4
k¼
1
υ
jk
¼
P
0
Let the level of significance be 0.05.
X
3
X
3
X
4
k¼
1
y
ijk
¼
Grand total
¼
GT
¼
8
:
7
þ
9
:
1
þþ
8
:
5
þ
8
:
1
¼
328
:
20
i¼
1
j¼
1
GT
2
mnr
¼
20
2
3
:
4
:
3
¼
328
:
ð
Þ¼
:
Correction factor
CF
2992
09
X
X
X
3
3
4
k¼
1
y
2
7
2
1
2
5
2
1
2
¼
ijk
¼
:
þ
:
þþþ
:
þ
:
:
¼
:
Total SS
CF
8
9
8
8
2992
09
75
87
i¼
1
j¼
1
X
r
i¼
1
y
1
mn
2
i
00
Replication SS
¼
CF
Table I
Table of totals for tillage
replication
3
:
4
X
Replication
R
1
3
1
2
i
¼
1
y
CF
Tillage
R
2
R
3
Total
00
i¼
T
1
32.800
33.000
33.400
99.20
109
2
þ
109
:
3
2
þ
109
:
9
2
¼
2992
:
09
T
2
43.100
42.500
42.800
128.40
12
T
3
33.100
33.800
33.700
100.60
¼
0
:
035
Total
109.000
109.300
109.900
328.20
Average
36.3333
36.43333
36.6333
m
1
nr
2
0
SS
ð
tillage
Þ¼
1
y
CF
X
r
m
j¼
1
y
j
0
1
n
j¼
2
TSS Table 1
ð
Þ ¼
ij
0
CF
4
:
3
X
3
1
i¼
1
2
0
¼
1
y
CF
j
0
¼
45
:
37
j¼
99
:
2
2
þ
128
:
4
2
þ
100
:
6
2
¼
2992
:
09
SS
ð
Error I
Þ¼
TSS
ð
Table I
Þ
RSS
SS
ð
P
Þ
12
¼
45
:
37
45
:
207
0
:
035
¼
0
:
128
:
¼
45
:
207
