Agriculture Reference
In-Depth Information
interested to test the Mendel's monohybrid
cross ratio (1:2:1) of
F
1
generation under
different experiments using
location against the alternative hypothesis
H
1
: The ratio of different fruit shape in
F
1
generation does not follow 1:2:1 ratio in
each location.
Under the given null hypothesis, the test
statistic is
2
test. Now
the question is whether all these informa-
tion from different experiments testing the
same null hypothesis can be pooled/added
to test for the theoretical ratio.
χ
2
test
for heterogeneity of variances based on
additive property of
χ
X
3
2
ð
Obs
Exp
Þ
2
2
χ
¼
for each place
:
2
χ
variates can be
Exp
i¼
1
used here.
Let us suppose we have
p
experimental
Let the level of significance be
α ¼
0.05.
χ
1
2
; χ
2
2
; χ
3
2
2
setup providing
; ...χ
p
each
2
The
χ
2
value for each place are:
k
χ
2
values
with (
1) d.f. The individual
2
with
2
value
from
p
setup are added to get
χ
s
Place
χ
d.f.
2
value known as
Place A
1.2
2
p
(
k
1) d.f. Then a
χ
Place B
3.276
2
2
is calculated from the pooled sample
of all the
χ
p
Place C
1.666
2
p
experiments with (
k
1) d.f.
2
table value at 5% level of signifi-
cance is 5.991. In all the places, the
2
The
χ
Now the heterogeneity
χ
is calculated
2
value obtained is less than the table value
of
2
2
2
χ
as
χ
h
¼ χ
s
χ
p
with
f
pk
1
ð
Þ
ð
d.f.
Decisions are taken by comparing the cal-
culated value of
k
1
Þg¼p
ð
1
Þ k
ð
1
Þ
2
0
:
05
;
2
, so we can conclude that in all the
places, the null hypothesis cannot be
rejected. That means the experimental
χ
2
with table value of
2
χ
χ
F
1
generation data follow the theoretical ratio
1:2:1.
2. Our next objective is to work out the
at upper level of significance with (
p
1)
(
k
1) degrees of freedom.
Example 9.24.
2
value for pooled data, that is, 130:215:110
:: long:medium:small and to test whether
homogeneity of variances is true for the
whole experiment or not. Thus, the null
hypothesis is that
Three sets of experiments were
conducted at three different places, and the fol-
lowing information are collected to check
whether the data follow Mendel's monohybrid
cross ratio of 1:2:1 or not.
χ
H
0
: Homogeneity of var-
iance exists against the alternative hypo-
thesis that homogeneity of variance does
not exist.
Let the level of significance be
Fruit shape
Long
Places
Medium
Small
Place A
70
120
60
Place B
45
70
30
α ¼
0.05.
Place C
15
25
20
2
p
The calculated value of
for whole data is
3.426, and the sum of all the
χ
2
values
obtained in different places is 6.142.
Thus,
χ
Solution.
Under the given conditions, we are to
test (1) the validity of monohybrid cross ratio
with respect to fruit shape in all the three places
separately and (2) whether we can pool the
2
values from different location to judge the valid-
ity of monohybrid cross ratio for fruit shape for
the given population.
1. The null hypothesis for the first problem is
H
0
: The ratio of different fruit shape in
χ
2
2
2
with
χ
h
¼ χ
s
χ
p
ð
p
1
Þ k
ð
1
Þ
d
:
f
:
¼
6
:
142
3
:
426 with 2
2
¼
4d
:
f
:
¼
2
:
715
:
At 0.05 level of significance, the tabulated
χ
F
1
generation follow 1:2:1 ratio in each
2
value at 4 d.f. is 9.488. So the calculated
