Agriculture Reference
In-Depth Information
y
y
y
(
r
xy
<
0,
say -
0.6
)
(
r
xy
=
0
)
0
(
r
xy
> 0,
say
0.8)
0
x
0
x
y
y
0
(
r
xy
= +1)
x
0
(
r
xy
= −1)
x
Fig. 8.19
Graphical presentation of different types of correlation coefficient
Table 8.11
Bivariate frequency distribution table
Mid value
Mid value (
y
)
(
x
)
y
1
y
2
y
3
...
y
j
...
y
m
Total
x
1
f
11
f
12
f
13
...
...
...
f
1
m
f
1.
x
2
f
f
f
...
...
...
f
f
21
22
23
2
m
2.
x
3
f
f
f
...
...
...
f
f
31
32
33
3
m
3.
...
...
...
...
...
...
...
...
...
x
i
...
...
...
f
ij
...
f
1
m
f
1.
...
...
...
...
...
...
...
...
...
x
n
f
n
1
f
n
2
f
n
3
...
...
...
f
nm
f
n
.
P
i
P
j
f
ij
¼ N
Total
f
f
f
...
f
f
.1
.2
.3
.
j
.
m
Significance of the Values of Correlation
Coefficients:
1. A positive correlation coefficient between any
two variables means both the variables move
in the same direction.
2. A negative correlation between any two
variables means if there is an increase or
decrease in one variable, then there will be a
decrease/increase, respectively, in the other
variables.
3. As the numerical value of correlation coeffi-
cient approaches 1, the degree of linear asso-
ciation becomes more and more intense
(Fig.
8.19
).
Correlation Coefficient of Bivariate Frequency
Distribution
:
Let the two variables
X
Y
have a joint fre-
quency distribution as follows (Table
8.11
):where
and
X
n
m
X
n
m
1
f
ij
¼
1
f
i:
¼
1
f
:j
¼ N:
i¼
j¼
i¼
j¼
From the data given in Table
8.11
, we shall
calculate the means and variances using the mar-
ginal frequencies and the corresponding mid
values of the classes. The covariance between
the variables will be calculated by taking cell
frequencies and the corresponding mid values
