Agriculture Reference
In-Depth Information
Original score
Ordered score
Rank
Group
Score
Group
Score
Unified rank
Group A
Group B
A
59
A
32
1
1
A
48
B
36
2
2
A
52
B
38
3
3
A
45
B
39
4
4
A
32
A
43
5
5
A
56
A
45
6.5
6.5
A
98
B
45
6.5
6.5
A
78
A
48
8
8
A
70
A
52
9
9
A
85
B
55
10
10
A
43
A
56
11
11
A
80
A
59
12
12
B
39
B
65
13
13
B
45
B
67
14
14
B
55
A
70
15
15
B
87
B
75
16
16
B
36
A
78
17
17
B
67
A
80
18
18
B
96
A
85
19
19
B
75
B
87
20
20
B
65
B
96
21
21
B
38
A
98
22
22
Total
253
143.5
109.5
At 5% level of significance, the critical value
6.
The Kruskal-Wallis Test
The Kruskal-Wallis test is used to compare
the average performance of many groups,
analogous to the one-way analysis of variance
in parametric method. But unlike the para-
metric method, it does not require the assump-
tion that the samples have come from normal
populations. This test is mostly an extension
of the Mann-Whitney
of
Z
the standard normal variate is 1.96.
So the upper and lower confidential limits are
μ
U
þ
:
σ
U
¼
þ
:
:
1
96
60
1
96
11
958
¼
:
μ
U
:
σ
U
83
438 and
1
96
¼
60
1
:
96
11
:
958
¼
36
:
562
:
As the observed value is within the accep-
tance zone, one can accept the null hypothesis
to conclude that the two groups of students have
come from the same population.
By calculating
-test; difference is
that here more than two groups are compared,
and the test statistic is approximated to
U
2
with
the stipulation that none of the groups should
have less than five observations. The steps for
this test are given below:
(a) Rank the data of all the samples taking them
as one sample from low to high (generally
low ranking is given to low value and so on).
(b) For tied ranks take the average of
the ranks for each of the tied values
(e.g., if 4th, 5th, 6th, and 7th places are
having the same value then each of
these identical values would be assigned
χ
U
using
R
2
, one get the value
of
U
as
U ¼ n
1
n
2
þ
n
2
ðn
2
þ
1
Þ
R
2
2
10
ð
10
þ
1
Þ
¼
12
:
10
þ
109
:
5
2
¼
120
þ
55
109
:
5
¼
65
:
5
which is also within the zone of acceptance. So it
does not matter how we are calculating the U
