Agriculture Reference
In-Depth Information
Solution.
Under the given situation, we are to
test
H
0
: ρ
1
:
2
;
3
;...;p
¼
0 against
H
1
: ρ
1
:
2
;
3
;...;p
>
0.
Given that
(a) The
test
statistic
for
H
0
: ρ
13
:
245
¼
0
t ¼
r
13
:
245
p
1
r
np
p
against
H
0
: ρ
13
:
245
6¼
0is
¼
2
13
:
245
n ¼
20 and
p ¼
6, so the appropri-
0
:
609
p
1
0
:
609
2
35
¼
:
¼
4
543with (40
5
) 35 d.f.
ate test statistic would be
p
From the table, we have
t
0.005,35
¼
2.725.
2
1
98
2
R
=
ðp
1
Þ
=
1
0
:
98
2
0
:
ð
6
1
Þ
725, so the null
hypothesis of zero partial correlation coeffi-
cient between yield and weight of primary
figure is rejected.
(b) The test
Since the calculated
jj>
2
:
:
23
...p
F ¼
ðn pÞ
¼
1
R
2
1
=
ð
Þ ð
20
6
Þ
=
:
23
...p
¼
67
:
2 with
ð
6
1
;
20
6
Þ
d
:
f
:
Cal
F>F
0
:
05
;
5
;
14
; H
0
is rejected
:
statistic under
H
0
: ρ
1
:
2345
¼
0
against
H
0
: ρ
1
:
2345
>
0 is given by
15.
Test for Significance of Population Partial
Correlation Coefficient
With the above variable consideration of
multiple correlations, let
2
1
:
2345
R
=
ðp
1
Þ
F ¼
ð
1
R
2
1
:
2345
Þ ðn pÞ
=
ρ
21
:
34
...p
be the par-
tial correlation coefficient of
2
x
1
and
x
2
after
ð
0
:
85
Þ
=
4
0
:
181
¼
¼
00793
¼
22
:
8247
:
eliminating the effect of
x
3
; x
4
; ...x
p
, and the
corresponding sample partial correlation
coefficient from a random sample of size
ð
1
0
:
85
2
Þ
=
35
0
:
n
The calculated value of
F
is greater than the
is given by
r
12
:
34
...p
.
The test statistic for
table value of
F
0.01;4,35
, so the test is signifi-
cant and the null hypothesis of zero multiple
correlation coefficient is rejected. That
means the population multiple correlation
coefficient differs significantly from zero.
H
0
: ρ
12
:
34
...p
¼
0is
t ¼
r
12
:
34
...p
p
1
n p
p
with
ðn pÞ
d
:
f
:
r
2
12
:
34
...p
Decision on rejection/acceptance of null
hypothesis is taken on the basis of compari-
son of the calculated value of
9.4
Large Sample Test
t
with that of
table value of
t
at (
n p
) d.f. for
α
level of
Large sample tests are based on the followings
facets:
1. Any sample having sample size more than 30
is treated as large.
2. If a random sample of size
significance.
Example 9.15.
During yield component analysis
in ginger, the partial correlation coefficient of
yield (
is drawn from
an arbitrary population with mean
n
X
1
) with the weight of primary finger
μ
and vari-
(
X
3
) was found to be 0.609, eliminating the
effects of no. of tillers (
2
and any statistic be
ance
σ
t
with mean
E
(
t
)
X
2
), no. of secondary
and variance
is asymptotically
normally distributed with mean
V
(
t
), then
t
finger (
X
5
). Again the multiple
correlation coefficient of yield (
X
4
), and finger (
E
t
(
) and vari-
X
1
) on all other
four components was found to be 0.85 from a
sample of 40 plants drawn at random. Test for
significant difference for both partial correlation
coefficient and multiple correlation coefficients
from zero.
ance
V
(
t
)as
n
gets larger and larger, that is,
t
~
N
(
E
(
t
),
V
(
t
)) as
n !1
. The standard
normal variate is
τ ¼
t EðtÞ
p
VðtÞ
Nð
0
;
1
Þ:
Solution.
Given that
n ¼
40, number of vari-
ables (
p
)
¼
5,
r
13
:
245
¼
0
:
609
;
and
R
1
:
2345
¼
Let us now discuss some of the important and
mostly used tests under this large sample test.
0
:
85. Let us take
α ¼
0
:
01.
