Agriculture Reference
In-Depth Information
Table 9.5 N K
table for Kendall's coefficient of concordance test
Individuals/objects
1
Judges
2
.......................
j
.......................
N
1
N
Judge1
2
4
..............................................
1
3
Judge2
N
2
N
..............................................
4
2
:
:
:
..............................................
:
:
:
:
:
..............................................
:
:
Judge (
K
1)
:
:
..............................................
:
:
Judge
K
:
:
..............................................
:
:
Total rank (
R
j
)
R
R
.......................
R
j
....................
R
N
1
R
N
1
2
2
2
2
2
...........
2
2
R
j
R
j
R
1
R
j
R
2
R
j
.................
R
j
R
j
R
N
1
R
j
R
N
R
j
2
2
Kendall'
coefficient
of
concordance
is
84, so the
test is significant and the null hypothesis of
equality of probabilities is rejected. So one can
conclude safely that there has been significant
change in the attitude of the farmers towards
SRI after demonstration.
8.
The calculated value of
χ
> χ
1
¼
3
:
given by
S
W ¼
1
12
K
2
NN
ð
2
1
Þ
R
j
j
where
is the total rank of
th object/
The Kendall's Coefficient of Concordance
In social/sports or other branches of sciences,
frequently a set of objects are required to be
assessed by a group of experts based on both
quantitative and qualitative characters. In
these cases, for unbiased judgment, it is
assumed that there is no association among
several sets of ranking and the individuals or
objects under consideration. In this aspect,
Kendall's coefficient of concordance plays
vital role, the special case of this test is
being the Spearman's rank correlation coeffi-
Let us suppose
individual.
For Tied Ranks
Just like to that of Spearman's rank correla-
tion coefficient, in Kendall's coefficient of
concordance, if there exists tied ranks, then a
correction factor is computed for each of the
K
. Judges as follows:
N
3
t
j
t
j
j¼
1
T ¼
where
t
is no of ties in
j
th
12
=
;
t <N:
object
individual
0
N
no. of individuals has been
Next totals of all Ts from each of the judges
are obtained, and the Kendall's coefficient of
concordance W is calculated as follows:
ranked by
K
no. of
judges. Thus,
these
rankings can be put into
N K
matrix form
as follows (Table
9.5
):
S
R
j
¼
R
1
þ R
2
þ :::: þ R
j
þ :::: þ R
N
N
W ¼
:
X
K
1
12
K
2
2
NN
T
1
N
j¼
1
R
j
;
1
N
¼
and
This correction is generally used when there
are large number of ties.
To test the null hypothesis that Kendall's
coefficient of concordance
2
2
S ¼ R
1
R
j
þ R
2
R
j
þ
is equal to zero
or not, the no. of objects/individuals (
W
2
2
N
) plays
þ R
j
R
j
þþ R
N
R
j
a vital role. If
N >
7, then W is distributed as
N
j¼
1
R
j
R
j
2
¼
:
2
χ
¼ KðN
1
ÞW
with
ðN
1
Þ
d
:
f
:;
