Agriculture Reference
In-Depth Information
Table 8.12
Bivariate frequency distribution table for correlation ratio analysis
x
i
y
ij
y
i
1
x
1
x
2
... x
i
... x
n
f
11
f
21
... f
i1
... f
n
1
y
i
2
f
f
... f
i
2
... f
n
2
12
22
y
i
3
f
f
... f
i
3
... f
n
3
13
23
...
...
.
...
... ...
... ...
y
i
j
f
1
j
...
... f
ij
... f
nj
...
...
...
... ...
... ...
y
im
f
f
... f
im
... f
nm
1
m
2
m
n
i
¼
P
j¼
1
f
ij
P
i
P
j
f
ij
¼
P
i¼
1
n
i
¼ N
n
n
... n
i
... n
n
1
2
T
i
¼
P
j¼
1
f
ij
y
ij
T
P
i
P
j
f
ij
y
ij
¼
P
i¼
1
T
i
¼ T
T
... T
i
... T
n
1
2
P
j¼
1
f
ij
y
P
j¼
1
f
1
j
y
1
j
P
j¼
1
f
2
j
y
2
j
...
P
j¼
1
f
ij
y
ij
...
P
j¼
1
f
nj
y
P
i
P
j
f
ij
y
2
ij
2
2
2
2
nj
2
ij
We have
Example 8.27.
The following table gives the
frequency distribution of milk yield (
y
)inkg/day
X
X
2
1
N
2
S
y
¼
f
ij
y
ij
y
and the age of the cows (
)inyears.Findthe
correlation ratio of yield on the age of cows.
x
i
j
X
1
N
2
2
2
2
¼ S
ey
þ S
my
;
where
; S
my
¼
n
i
y
i
y
ð
Þ
Age of cows in year
3-4 5-6 7-8 9-10 11-12 13-14
i
Yield (kg/day)
y
2
ey
S
2
my
S
¼
S
y
þ
S
4-7
233-
-
-
2
y
¼ S
2
ey
þ S
2
my
)
2
yx
) S
1
y
) η
2
2
8-11
- 678-
-
h
i
h
i
P
n
i
y
i
y
P
T
i
2
12-15
-
6
10
15
12
2
2
2
1
N
n
i
N
ð
Þ
2
my
S
S
16-19
- 15094
¼
y
¼
¼
:
P
P
2
S
2
y
ij
T
2
N
20-23
-
-
-
10
15
10
f
ij
y
2
24-27
-
-
-
- 5 4
i
j
One can substitute the values of the above
quantities from the table to get
Solution. From the given information, we frame
the following table:
2
yx
η
.
Age of cows (years) (
x
)
3-4
5-6
7-8
9-10
11-12
13-14
Mid values (
x
)
Milk yield
(kg/day) (
y
) Mid values (
y
)
3.5
5.5
7.5
9.5
11.5
13.5
Total
4-7
5.5
2
3
3
0
0
0
8
8-11
9.5
0
3
7
8
0
0
21
12-15
13.5
0
6
10
15
12
2
45
16-19
17.5
0
1
5
10
19
4
39
20-23
21.5
0
0
0
10
15
10
35
24-27
25.5
0
0
0
0
5
4
9
n
i
¼
P
2
16
25
43
51
20
157
6
1
f
i
j
j¼
T
i
¼
P
6
j¼
1
f
ij
y
ij
11
172
305.5
668.5
944.5
414
2,515.5
60.5
1,849
3,733.21
10,392.84
17,491.769
8,569.8
42,097.122
T
2
i
n
i
P
60.5
2,032
4,076.25
11,140.75
18,190.75
8,813
44,313.25
6
j¼
1
f
ij
y
2
ij
