Agriculture Reference
In-Depth Information
Table 10.4
ANOVA table for two-way classification of data
SOV
d.f.
SS
MS
F
Factor A
m
1
SS(A)
AMS
¼
SS(A)/(
m
1)
AMS/ErMS
Factor B
n
1
SS(B)
BMS
¼
SS(B)/(
n
1)
BMS/ErMS
Error
(
m
1)(
n
1)
ErSS
ErMS
¼
ErSS/(
m
1)(
n
1)
Total
mn
1
TSS
Example 10.2.
The following table gives the
milk produced (liter/day) by four breeds of
cows under five different feeds. Analyze the
data to find out the best feed and best breed of
cow with respect to production of milk.
H
01
:α
1
¼ α
2
¼ α
3
¼ α
4
¼ α
5
¼
0 against
H
11
:α
's are not all equal and
H
02
:β
1
¼ β
2
¼ β
3
¼ β
4
¼
0 against
H
12
:β
's are not all equal
:
The appropriate model to test the above is
y
ij
¼ μ þ α
i
þ β
j
þ e
ij
, where
Breed
Breed A
i ¼
5,
j ¼
4
Feed
Breed B
Breed C
Breed D
y
ij
¼
value of the observation corresponding to
the
Feed 1
17
10.6
47
30
i
th feed and
j
th breed
Feed 2
19
10.8
46
28
μ ¼
general mean effect
Feed 3
21
10.9
45.5
29
α
i
¼
additional effect due to the
i
th feed
Feed 4
23
11.2
48
25
β
j
¼
additional effect due to the
j
th breed
Feed 5
25
11.3
45
26
e
ij
¼
errors associated with the
i
th feed and
j
th
Solution. Under the given condition we are to
analyze the data per the two-way ANOVA with
one observation per cell
breed
For the purpose let us frame the following
table:
to test
the null
hypotheses:
Total number of observations
¼ N ¼ mn ¼
20,
Breed
Feed
Breed A
Breed B
Breed C
Breed D
Total
Mean
Feed 1
17
10.6
47
30
104.6
26.15
Feed 2
19
10.8
46
28
103.8
25.95
Feed 3
21
10.9
45.5
29
106.4
26.6
Feed 4
23
11.2
48
25
107.2
26.8
Feed 5
25
11.3
45
26
107.3
26.825
Total (
y
0
j
)
105
54.8
231.5
138
529.3
26.465
21
10.96
46.3
27.6
Mean
y
0
j
G ¼
17
:
0
þ
10
:
6
þ
47
:
0
þþ
11
:
3
þ
45
þ
26
¼
529
:
3
2
N
3
2
CF
¼ G
= ¼
529
:
= ¼
20
14007
:
92
0
2
6
2
0
2
3
2
45
2
26
2
TSS
¼
17
:
þ
10
:
þ
47
:
þþ
11
:
þ
þ
CF
¼
3388
:
27
6
2
4
þ
8
2
4
þ
2
2
2
104
:
103
:
106
:
4
107
:
2
107
:
3
FSS
¼
SS Feed
ð
Þ¼
þ
þ
14007
:
92
¼
2
:
498
4
4
4
105
2
5
þ
8
2
5
þ
2
2
54
:
231
:
5
138
5
BrSS
¼
SS Breed
ð
Þ¼
þ
14007
:
92
¼
3324
:
934
5
ErSS
¼
TSS
FSS
BrSS
¼
60
:
834
