Agriculture Reference
In-Depth Information
Example 9.23.
An experiment with the same
protocol was practiced in three consecutive
seasons for a particular variety of wheat. The
following table gives the error mean squares
along with degrees of freedom for three seasons.
Test whether pooling of data from the three
experiments can be done or not.
Solution.
The error mean squares are the
estimates of the variances. So the null hypothesis
for the present problem is
H
0
: Variances of the
three experiments conducted in three seasons
are homogeneous in nature, against the alter-
native hypothesis
H
1
: Variances of the three
experiments conducted in three seasons are not
homogeneous in nature.
The test statistic is
Season
d.f.
Error mean square
Season 1
15
380
Season 2
12
320
Season 3
12
412
P
k
2
s
i
P
2
s
i
log
s
3
log
s
1
ðn
i
1
Þ
1
ðn
i
1
Þ
2
2
i¼
i¼
2
2
4
8
<
:
9
=
;
2
4
8
<
:
9
=
;
χ
¼
¼
at 2 d
:
f
:
k
1
X
k
X
3
1
1
ðn
i
1
1
1
ðn
i
1
1
þ
Þ
1
þ
Þ
3
ðk
1
Þ
1
P
k
i¼
1
ðn
i
1
Þ
3
ð
3
1
Þ
1
3
i¼
1
ðn
i
P
i¼
1
i¼
1
1
Þ
Let the level of significance
α ¼
0
:
05
:
2
i
2
(
n
i
1)
s
(
n
i
1) log
e
s
1
n
i
1
2
i
n
i
1
s
s
2
i
15
380
5,700
0.3440
0.0667
12
320
3,840
1.7870
0.0833
12
412
4,944
1.2454
0.0833
Total
14,484
0.1976
0.2333
X
3
1
14484
39
¼
2
2
Now
s
¼
1
ðn
i
1
Þðs
i
Þ
¼
371
:
385
:
P
3
i¼
1
ðn
i
1
Þ
i¼
0
:
1976
0
:
1976
2
¼
χ
2
¼
0346
¼
0
:
1910 with 2 d
:
f
:
1
6
1
39
1
þ
0
:
2333
1
:
(testing materials) in one experiment.
For example, when we test hundreds of
germplasms to test a particular null
hypothesis, then it becomes almost impos-
sible to accommodate all these materials
in one experiment even in one experimen-
tal station. So we are forced to lay down
the experiment in different plots, some-
times in different experimental stations
having different environmental conditions
and sometimes being tested over dif-
ferent seasons. For example, we may be
From the table, we have
χ
0
:
05
;
2
¼
5
:
99.
2
The calculated value of
χ
(0.1910) is less
χ
2
than the table value of
0
:
05
;
2
, hence we cannot
reject the null hypothesis. That means the
variances are homogeneous in nature. So we
can pool the information of three experiments.
(c)
2
χ
Test for Heterogeneity
When a null hypothesis is to be tested
for a large amount of test materials
(treatments), it becomes sometimes diffi-
cult to accommodate all the treatments
