Agriculture Reference
In-Depth Information
Fig 8.20
Graphical presentation of correlation coefficient and correlation ratio
2
ey
S
2
my
S
relationship between
y
and
x
which of course
S
S
η
2
yx
¼
η
2
yx
¼
One can get the
1
or
.
2
y
2
y
need not be linear.
We have
2
2
5.
η
y
i
¼ y
ij
¼ Y
i
; that is, array means
lie on a straight line. Thus,
yx
¼ r
if
X
X
X
X
2
2
η
yx
r
is the
2
y
¼
2
2
ij
Ny
2
NS
f
ij
ðy
ij
yÞ
¼
f
ij
y
departure of regression from linearity.
6. If
r
i
j
i
j
2
¼
1, that is, the relationship between y
and is linear, then
X
X
2
2
ij
T
N
¼
44313
:
25
ð
2515
:
5
Þ
2
¼
f
ij
y
2
yx
must be unity and the
relationship is to be linear.
η
157
i
j
¼
44
;
313
:
25
40
;
304
:
077
¼
4
;
009
:
173
:
7.
η
yx
¼
; that is, all the array means
are equal to a constant, that is, the overall
mean, then r must be zero and there is no
relationship (Fig.
8.20
).
0if
y
i
¼ y
Again
;
X
X
T
2
i
2
N
n
i
T
2
2
NS
my
¼
n
i
ðy
i
yÞ
¼
i
¼
42
;
097
:
122
40
;
304
:
077
¼
1
;
793
:
045
:
8.5
Association of Attributes
2
my
S
S
1
;
793
:
045
2
So,
η
yx
¼
y
¼
173
¼
0
:
447.
2
4
;
009
:
Qualitative characters like gender, religion, color,
aroma, taste, education standard, and economic
status cannot be measured as such in any numeric
scale; rather, these could be grouped or categorized.
Thus, the above-discussed measures of association
may not be applicable. To have an association
between the two attributes grouped into different
categories, one can use Spearman's rank correla-
tion coefficient and Yule's coefficient of attributes.
Properties of Correlation Ratio:
1.
2
2
r
η
yx
1.
2
yx
2.
η
is independent of change of origin and scale.
2
yx
2
xy
3.
r
xy
¼ r
yx
,but
η
may or may not be equal to
η
.
η
: y
ij
¼ y
i
.
That means all observations in any array coin-
cide with their mean, and there is a functional
2
yx
¼
;
S
2
ey
¼
:
4.
1
if
0i
e
