Agriculture Reference
In-Depth Information
Solution. From the given information it is clear
that the experiment is an asymmetrical (4
3)
factorial experiment conducted in randomized
block design, so the appropriate statistical
model for the analysis will be
y
ijk
¼ μ þ α
i
þ β
j
þ γ
k
þ αð
ij
þ e
ijk
,
γ
's are not all equal
;
All αð
ij
's are not equal
:
Let the level of significance be 0.05.
From the given data table, let us calculate the
following quantities:
where
i ¼
4;
j ¼
3;
k ¼
3
y
ijk
¼
response in the
k
th replicate due to the
X
X
X
4
3
3
k¼
1
y
ijk
¼
i
th level of the first factor (variety) and the
Grand total GT
ðÞ¼
541
:
300
th level of the second factor (seed rate)
μ ¼
j
i¼
1
j¼
1
general effect
α
i
¼
additional effect due to the
i
th level of the
GT
2
4
:
3
:
3
¼
3
2
36
¼
8139
:
047
541
:
first factor (nitrogen),
P
α
i
¼
Correction factor C
ðÞ¼
0
β
j
¼
th level of the
second factor (spacing),
P
β
j
¼
additional effect due to the
j
X
X
X
4
3
3
0
2
ijk
TSS
¼
1
y
CF
γ
k
¼
k
additional effect due to the
th replicate,
P
γ
k
¼
i¼
1
j¼
1
k¼
0
¼
8162
:
810
8139
:
047
¼
23
:
763
αð
ij
¼
th level of the
first factor (nitrogen) and the
interaction effect of the
i
j
th level of
(spacing),
P
i
X
3
k¼
1
y
1
v:s
the second factor
αð
ij
¼
2
RSS
¼
ijk
CF
P
αð
ij
¼
0
j
:
3
2
þ
:
8
2
þ
:
2
2
180
180
180
¼
8139
:
047
e
ijk
¼
error component associated with the
i
th
12
level of the first factor (nitrogen),
th
level of the second factor (spacing), and the
k
the
j
¼
0
:
017
2
)
th replicates and
e
ijk
~
N
(0,
σ
From the above table first let us form the
following table and from the table get
Hypothesis to Be Tested
the
following quantities:
H
0
: α
1
¼ α
2
¼ α
3
¼ α
4
¼
0
;
β
1
¼ β
2
¼ β
3
¼
0
;
3
X
X
4
3
j¼
1
y
1
2
TrSS
¼
ij
0
CF
γ
1
¼ γ
2
¼ γ
3
¼
;
0
i¼
1
All
αð
ij
's are equal
42
2
5
2
0
2
5
2
6
2
þ
47
:
þ
45
:
þþ
45
:
þ
43
:
¼
3
against
8139
:
047
;
β
j
's are not all equal
α
's are not all equal
¼
20
:
296
;
Table of totals
Nitrogen
N1
Spacing
N2
N3
N4
Total
Average
S1
42.0
46.0
41.3
43.2
172.5
14.4
S2
47.5
49.5
45.5
46.7
189.2
15.8
S3
45.0
46.5
43.6
44.5
179.6
15.0
Total
134.5
142.0
130.4
134.4
Average
14.9
15.8
14.5
14.9
