Agriculture Reference
In-Depth Information
where
y
(
i
)
are the ordered values of the
two samples, respectively. In a combined
ordered arrangements of
x
(
i
)
and
parent distributions are not identical.
Table
A.11
given in the
Appendix
gives the
critical values of
mx
's and
ny
's,
F
m
D
for different sample sizes
and
G
n
represent the respective proportions of
(
n
2
) at different level of significance. If the
calculated value of
n
1
,
x
values that do not exceed x. Thus, we
are interested to test whether the two distribu-
tion functions are identical or not, that is, to
test
and
y
D <
critical value
D
m
,
n
;
α
we accept
H
0
, that is, the parent distributions
are identical.
H
0
:
F
(
x
)
¼ G
(
x
) against the alternative
H
1
:
FðxÞ 6¼ GðxÞ
Example 9.42.
hypothesis
; the test statistic
Two samples of ten each are
taken independently at random for the number
of grains per panicle in wheat. Test whether the
two samples belong to the identical parent popu-
lation distribution or not.
is
D
m;n
¼
Sup
x
½
j
F
m
ðxÞG
n
ðxÞ
j
. Now if the
null hypothesis is true, then one would expect
very small value of
D
m
,
n
; on the other hand, a
large value of
D
m
,
n
is an indication that the
Sample
1
2
3
4
5
6
7
8
9
10
S1
70
80
75
85
100
110
90
115
120
95
S2
73
82
78
83
98
102
97
114
118
116
Solution.
Here the problem is to test whether
the two samples have come from the same parent
population or not, that is,
Frequency
Sample 1
Class interval
Sample 2
H
0
:
Fm ¼ Gn
against
70-75
2
1
the alternative hypothesis
H
1
:
Fm 6¼ Gn
where
76-81
1
1
Fm
are the two distributions from which
the above two samples have been drawn inde-
pendently at random. For this example,
and
Gn
82-87
1
2
88-93
1
0
.
Under the given null hypothesis, we apply K-S
two-sample
m ¼ n
94-99
1
2
100-105
1
1
test
having
the
statistic
106-111
1
0
D
m;n
¼
Sup
x
F
m
ðxÞG
n
ðxÞ
½
j
j
. Let the level of
112-117
1
2
significance be
α ¼
0
:
05. We make the following
118-123
1
1
table:
We make a cumulative frequency distribution
for each sample of observations using the same
intervals for both distributions.
For the calculation of
D
m
,
n
, we make the fol-
lowing table:
70-75
76-81
82-87
88-93
94-99
100-105
106-111
112-117
118-123
F
10
ðxÞ
2/10
3/10
4/10
5/10
6/10
7/10
8/10
9/10
10/10
F
10
ðxÞ
1/10
2/10
4/10
4/10
6/10
7/10
7/10
9/10
10/10
F
10
ðxÞF
10
ðxÞ
1/10
1/10
0
1/10
0
0
1/10
0
0
