Agriculture Reference
In-Depth Information
of
arranged
observations be
r
. Number of runs
r
is
expected to be very high if the two samples
are thoroughly mixed; that means the two
samples are coming from the identical
distributions, otherwise the number of runs
will be very small. Table for critical values
of
runs
in total
n
1
+
n
2
¼ N
2
n
1
n
2
N
EðrÞ¼
þ
1 and Var
ðrÞ
2
n
1
n
2
ð
2
n
1
n
2
NÞ
¼
;
N
2
ðN
1
Þ
and we can perform an approximate test sta-
tistic as
n
2
are provided
in Table
A.10
(
Appendix
) for both
r
for given values of
n
1
and
n
1
and
n
2
τ ¼
r EðrÞ
p
Var
Nð
0
;
1
Þ:
less than 20. If the calculated
value is greater
than the critical value of run for a given set of
n
1
and
r
ðrÞ
n
2
, then we cannot reject the null
hypothesis; otherwise any value of calculated
r
Example 9.40.
Two independent samples of 9
and 8 plants of coconuts were selected randomly,
and the number of nuts per plant was recorded.
On the basis of nut characters, we are to decide
whether the two samples came from the same
coconut population or not.
is less than or equal to the critical value of
r
for a given set
n
2
, the test is significant
and the null hypothesis is rejected.
For large
n
1
and
10) or any one of
them is greater than 20, the distribution of
n
1
and
n
2
(say,
>
r
is
asymptotically normal with
Sample
Plant 1
Plant 2
Plant 3
Plant 4
Plant 5
Plant 6
Plant 7
Plant 8
Plant 9
Sample 1
140
135
85
90
75
110
112
95
100
Sample 2
80
125
95
100
112
90
105
108
Solution.
Null hypothesis is
H
0
: Samples have
come from identical distribution against
alternative hypothesis that they have come from
different populations.
We arrange the observations as follows:
the
Nut/plant
75
80
85
90
90
95
95
100
100
Sample
1
2
1
1
2
1
2
1
2
Nut/plant
105
108
110
112
112
125
135
140
Sample
2
2
1
1
2
2
1
1
counted from the above table is
11 and the table value of
The value of
r
the same or different sample sizes are from
identical distributions against the alternative
hypotheses that they have different location
parameters (medians).
Let us draw two random independent samples
of sizes
corresponding to 9 and
8 is 5. Thus, we cannot reject the null hypothesis
of equality of distributions. Hence, we conclude
that the two samples have been drawn from the
same population.
3.
r
n
2
from two populations. Make
an ordered combined sample of size
n
1
and
Two-Sample Median Test
The test parallel to equality of two means test
in parametric procedure is the two-sample
median tests in nonparametric method. The
objective of this test is to test that the two
independent samples drawn at random having
n
1
+
and get the median (
θ
n
2
¼ N
) of the com-
bined sample. Next, we count the number of
observations below and above the estimated
median value
θ
for all the two samples, which
can be presented as follows (Table
9.6
):
