Agriculture Reference
In-Depth Information
h
i
2
Variety Rep-1
Rep-2
Rep-3
Rep-4
Total
0
0
j
t
y
ð
1
Þy
V1
17.8
17.3
18.5
18.5
72.10
B ¼
:
tt
ð
1
Þ
V2
23.6
23.8
23.5
24
94.90
V3
27.7
26.7
27.9
26.8
109.10
The degrees of freedom for both total and error
sum of squares are reduced by one in each case.
The treatment means are compared with the mean
having missing value and no missing value using
the formula for standard error of difference as
V4
16.2
16
15
15.5
62.70
V5
19.2
X
19.7
19.4
58.30
V6
22.3
22.5
22.8
23.5
91.10
Total
126.80
106.30
127.40
127.70
488.20
s
ErMS
r
The estimate of the missing value is given by
t
SE
d
¼
2
þ
:
ðr
1
Þðt
1
Þ
y
ij
¼ X ¼
rR
0
þ tT
0
G
0
ðr
1
Þðt
1
Þ
Example
An experiment with six
varieties of onion was conducted using RBD
with four replications. The following table gives
the layout and data pertaining to yield (t/ha) from
the experiment. Analyze the data and find out the
best variety of onion.
10.13.
where
X ¼
estimate of the missing value
R
0
¼
total of available entries of the replication
having the missing observation
T
0
¼
total of available entries of the treatment
having the missing observation
G
0
¼
total of available entries in the whole
design
Rep-1
Rep-2
Rep-3
Rep-4
V1 17.8
V2 23.8
V3 27.9
V4 15.5
X ¼
rR
0
þ tT
0
G
0
ðr
For
this
problem
Þ
¼
V5 19.2
V3 26.7
V5 19.7
V6 23.5
1
Þðt
1
V2 23.6
V5
V2 23.5
V3 26.8
4
106
:
3
þ
6
58
:
3
488
:
2
V4 16.2
V6 22.5
V4 15.0
V2 24.0
¼
19
:
12.
ð
4
1
Þð
6
1
Þ
V6 22.3
V4 16
V1 18.5
V5 19.4
G ¼ G
0
+
Now,
X ¼
488.2 + 19.12
¼
507.32
V3 27.7
V1 17.3
V6 22.8
V1 18.5
Total of variety five
¼
58.30 +
X ¼
77.42
As per the given information, the appropriate
model is given by
Total of replication four
125.42
Now we proceed for usual analysis of vari-
ance is taken up with the estimated values of the
missing observation.
¼
106.30 +
X ¼
y
ij
¼ μ þ α
i
þ β
j
þ e
ij
where
i ¼
6,
j ¼
4
y
ij
¼
effect due to the
i
th variety in
j
th replicates
μ ¼
general effect
GT
2
n
32
2
507
:
α
i
¼
additional effect due to the
i
th variety
CF
¼
¼
4
¼
10723.90,
β
j
¼
additional effect due to the
j
th replicate
6
X
Obs
2
5
2
7
2
TSS
¼
:
CF
¼
18
:
þ
19
:
þ
e
ij
¼
errors that are associated with the
i
th vari-
2
)
ety in the
j
th replicate and are i.i.d.
N
(0,
σ
12
2
3
2
þ
19
:
þ
17
:
10723
:
90
¼
363
:
20
;
The hypotheses to be tested are
6
X
4
1
1
6
2
j
4
2
7
2
RSS
¼
1
R
CF
¼
127
:
þ
127
:
H
0
: α
1
¼ α
2
¼ α
3
¼ α
4
¼ α
5
¼ α
6
;
β
1
¼ β
2
¼ β
3
¼ β
4
against
H
1
: α
i
's are not all equal,
β
j
's are not all equal
j¼
3
2
8
2
þ
126
:
þ
106
:
10723
:
90
¼
0.51,
4
X
6
i¼
1
V
1
1
4
2
72
:
1
2
þ
94
:
9
2
TrSS
¼
i
CF
¼
:
1
2
1
2
7
2
42
2
þ
109
:
þ
62
:
þ
77
:
þ
91
:
0.05.
We shall analyze the data in the following steps:
Make the following table from the given
information.
Let the level of significance be
α ¼
10723
:
90
¼
359
:
00
:
The TrSS is an overestimate and has to be
corrected by subtracting from a quantity (bias)
