Agriculture Reference
In-Depth Information
mean having missing value using the formula
for standard error of difference as
α
i
¼
additional effect due to the
i
th variety
P
α
i
¼
0
i
s
ErMS
t
β
j
¼
additional effect due to the
j
th row
t
ðt
1
Þðt
2
Þ
P
SE
d
¼
2
þ
:
β
j
¼
0
j
γ
k
¼
additional effect due to the
k
th column
P
Example 10.14.
Five varieties of paddy were
tested in LSD for yield. The following is the
layout and responses due to different treatments
with a missing value in variety 3. Estimate the
missing yield and find out which variety is the
best yielder among the varieties of paddy.
γ
k
¼
0
k
e
ijk
¼
errors that are associated with the
i
th vari-
ety in the
j
th row and the
k
th column and are
2
).
The hypotheses to be tested are
N
σ
i.i.d.
(0,
H
0
: α
1
¼ α
2
¼ α
3
¼ α
4
¼ α
5
,
β
1
¼ β
2
¼ β
3
¼ β
4
¼ β
5
;
γ
1
¼ γ
2
¼ γ
3
¼ γ
4
¼ γ
5
against
H
1
: α
i
's are not all equal,
β
j
's are not all equal,
γ
k
's are not all equal
V1 10.5
V4 9.5
V5 13.0
V3 14.5
V2 17.5
V4 10.0
V2 16.5
V1 11.0
V5 12.5
V3 13.5
V5 13.5
V3
V4 9.0 V2 17.0
V1 12.0
V3 14.0
V5 12.75
V2 17.6
V1 10.0
V4 10.0
V2 17.9
V1 11.5
V3 14.5
V4 10.5
V5 12.25
Solution. The
model
for
LSD
is
:
y
ijk
¼ μ þ α
i
þ β
j
þ γ
k
þ e
ijk
where
i ¼ j ¼ k ¼
5
0.05.
We shall analyze the data in the following steps:
Make the following two tables from the given
information.
Let the level of significance be
α ¼
y
ijk
¼
i
j
effect due to the
th variety in the
th row
and the
k
th column
μ ¼
general effect
C1
C2
C3
C4
C5
Total
ðy
0
j
0
Þ
Average
ðy
0
j
0
Þ
R1
10.5
9.5
13.0
14.5
17.5
65.0
13.0
R2
10.0
16.5
11.0
12.5
13.5
63.5
12.7
R3
13.5
V3
9.0
17.0
12.0
51.5
12.9
R4
14.0
12.75
17.6
10.0
10.0
64.35
12.9
R5
17.9
11.5
14.5
10.5
12.25
66.65
13.3
Total
y
00
ðÞ
65.9
50.25
65.1
64.5
65.25
311
y
00
ðÞ
13.18
Average
12.563
13.02
12.9
13.05
Varieties
V1
V2
V3
V4
V5
10.5
17.5
14.5
9.5
13
11
16.5
13.5
10
12.5
12
17
y
9
13.5
10
17.6
14
10
12.75
11.5
17.9
14.5
10.5
12.25
Total
ðy
i
00
Þ
55
86.5
56.5
49
64
Average
ðy
i
00
Þ
11
17.3
14.125
9.8
12.8
