Agriculture Reference
In-Depth Information
Similarly,
8.4
Correlation Ratio
m
j¼
1
f
:j
:y
1
m
2
2
2
S
y
¼
j
y
Generally, in a real-life situation, we come across
a nonlinear type of relationships among the vari-
ables. For example, when the varying doses of
nitrogenous fertilizer to respond nonlinearly with
the yield, it will be unwise to assume that as we go
on increasing the dose of nitrogen, the yield will
increase linearly. The yield will increase initially as
we go on increasing the doses of fertilizer, reaches
to maximum and then decreases. So a curvilinear
relationship will be appropriate, and the use of
correlation coefficient (
1
f
:j
j¼
2
¼
=
ð
:
Þ
¼
:
2280
53
6
113
5
405
X
1
N
Cov
x; ðÞ¼S
xy
¼
f
ij
x
i
y
j
x:y
i;j
¼
20520
=
53
59
:
716
6
:
113
¼
22
:
126
Cov
ðX
,
YÞ
S
X
S
y
22
:
126
ð
) to measure the degree
of association will be misleading.
r
;
r
xy
¼
¼
p
387
:
301
Þð
5
:
405
Þ
¼
0
:
484
Yield
Limitations:
1. Correlation coefficient assumes linear rela-
tionship between two variables.
2. High correlation coefficient does not mean
high direct association between the variables
under a multiple variables consideration prob-
lem. The high correlation coefficient between
the two variables may be due to the influence
of the third and/or fourth variable influencing
both the variables. Unless and otherwise the
effect of the third and/or fourth variable on
the two variables is eliminated, the correlation
between the variables may be misleading.
To counter this problem, path coefficient anal-
ysis discussed in the 2nd volume of this topic
is useful.
3. If the data are not homogeneous to some
extent, correlation coefficient may give rise
to misleading conclusions.
4. For any two series of values, the correlation
coefficient between the variables can be
worked out, but there should be logical
basis for any correlation coefficient; one
should be sure about the significance of cor-
relation coefficient; otherwise, the correla-
tion is known as
Doses of Nitrogen
is the appropriate
measure of degree of nonlinear relationship
between
“Correlation ratio” “
η
”
. Correlation ratio
measures the concentration of points about the
curve fitted to exhibit the nonlinear relationship
between the two variables.
Correlation ratio ðÞ
two
variables
of
Y
on
X
is defined as
S
2
ey
2
η
yx
¼
1
S
2
y
where
X
X
2
and
1
N
2
S
ey
¼
f
ij
y
ij
y
i
i
j
X
X
2
1
N
2
y
¼
f
ij
y
ij
y
S
i
j
(Table
8.12
).
Let the value
f
ij
.
Thus, the frequency distribution of two variables
X
y
ij
occur with the frequency
Y
and
can be arranged as given in Table
8.11
.
y
i
¼
T
i
y ¼
N
Further,
and
are the means of
i
th
nonsense correlation or
n
i
spurious
correlation.
array and the overall mean, respectively.
