Agriculture Reference
In-Depth Information
Example 10.10.
Seven varieties of wheat were
tested for yield using CRD with 5 plots per
variety. The following table gives the yields of
grain in quintal per acre. Test whether the 7
varieties differ significantly with respect
to
yield or not.
Variety A
Variety B
Variety C
Variety D
Variety E
Variety F
Variety G
18
19
17
18
21
20
19
14
19.5
15
14
21.5
16
13
16
20
14
19
22
17
17
17
22
20
21
23
19
18
15
18
16
14
22
15
14
Solution. The statement shows that the experi-
ment was laid out in completely randomized design
with seven varieties each replicated five times.
The model for the purpose is
Let
the level of significance be
α ¼
0.05.
Let us construct the following table:
AB C D E F G
18 19
y
ij
¼ μ þ α
i
þ e
ij
,
17
18
21
20
19
i ¼
7, j
¼
5
14 19.5 15
14
21.5
16
13
where
y
ij
¼ j
16 20
14
19
22
17
17
th observation for the
i
th variety
17 22
20
21
23
19
18
μ ¼
general effect
15 18
16
14
22
15
14
α
i
¼
th variety
e
ij
¼
errors that are associated with
j
th obser-
vation in the
additional effect due to the
i
Total (
y
i
0
)
80 98.5 82
86
109.5 87
81
Average (
y
i
0
) 16 19.7 16.4 17.2 21.9
17.4 16.2
2
)
i
th variety and are i.i.d.
N
(0,
σ
So the problem is to test
H
0
: α
1
¼ α
2
¼ α
3
¼ α
4
¼ α
5
¼ α
6
¼ α
7
against
H
1
: α
i
's are not all equal
:
Grand total G
ðÞ¼
18
þ
14
þ
16
þþ
17
þ
18
þ
14
¼
624
:
00
GT
2
n
624
2
35
¼
11125
:
03
Correction factor C
ðÞ¼
¼
18
2
14
2
16
2
17
2
18
2
14
2
Total sum of squares TSS
ð
Þ¼
þ
þ
þþ
þ
þ
CF
¼
268
:
471
80
2
5
þ
5
2
5
þ
82
2
5
þ
86
2
5
þ
5
2
5
þ
00
2
5
þ
00
2
5
CF
¼
143
:
471
98
:
109
:
87
:
81
:
ð
Þ¼
Variety sum of squares VSS
Error sum of squares ErSS
ð
Þ¼
TSS
VSS
¼
268
:
471
143
:
471
¼
125
:
00
The table value of
F
0.05;6,28
¼
2.45.
ANOVA
SOV
(tab)
0.05;6,28
, so the test is
significant and we reject the null hypothesis of
equality of yields.
Thus,
F
(cal)
> F
d.f.
SS
MS
F
Variety
6
143.471
23.912
5.356
Error
28
125.000
4.464
Total
34
268.471
