Agriculture Reference
In-Depth Information
(continued)
Original Scores
Ordered score
Rank
Group
Score
Group
Score
Unified rank
Group A
Group B
Group C
Group D
Group E
E
51
E
46
29
29
E
46
E
51
30
30
E
37
D
52
31
31
R
j
80.5
85.5
97
132
101
n
j
7
6
5
7
6
925.75
1218.375
1881.8
2489.143
1700.167
R
2
j
n
j
X
k
R
2
j
n
j
12
nðn þ
1
Þ
H ¼
3
ðn þ
1
Þ
j¼
1
12
¼
½
925
:
75
þ
1218
:
375
þ
1881
:
8
þ
2489
:
143
þ
1700
:
167
3
ð
31
þ
1
Þ
31
ð
31
þ
1
Þ
12
¼
32
8215
½
:
235
3
ð
32
Þ¼
99
:
378
96
¼
3
:
378
:
31
As all the groups have five or more
observations, so
means one should go for
testing
H
0
:
P
2
with
(
a
)
¼ P
(
d
) against
the alternative
H
1
:
P
H
is distributed as
χ
2
at 5%
level of significance and 4 d.f. is 9.488 which is
greater than the calculated value, so we cannot
reject the null hypothesis of equality of means of
five farmers groups.
7.
(
a
)
6¼ P
(
b
), and the appropriate test statistic
(5
1
¼
)4 d.f. The table value of
χ
2
2
is
χ
1
¼ a d
ð
j
j
1
Þ
=
ða þ dÞ
.
Example 9.37.
Eight hundred farmers were asked
about the effectiveness of SRI (system rice inten-
sification); then these farmers were demonstrated
the practice. The following table gives the
responses before and after the demonstration.
Examine whether the demonstration has got any
impact on farmers' attitude towards SRI or not.
The McNemar Test
Just like to that of paired
-test, McNemar test
is applicable for related samples, particularly
concerned with nominal data. Initially when
the subjects are categorized into two groups,
treatment is applied and again the responses
are recorded and subjects are grouped. This
test is used to record whether there has been
any significant change in grouping due to
treatment or not.
t
After demonstration
Before demonstration
Disliked
Liked
Liked
125
225
Disliked
75
375
After treatment
Solution.
Under the given condition, we are to
test
Before treatment
Disliked
Liked
H
0
:
P
(like, dislike)
¼ P
(dislike, like) against
H
1
:
P
(like, dislike)
6¼ P
(dislike,
like). The
Liked
a
b
2
2
appropriate test statistic is
χ
1
¼ a d
ð
j
j
1
Þ
=
c
d
Disliked
ða þ dÞ
; here
a ¼
125,
d ¼
375, so the
Where
a
,
b
,
c
, and
d
are the respective cell
frequencies. Clearly
is the change in
response due to treatment whereas
a
+
d
2
2
ð
a d
j
Þ
ð
j
Þ
j
1
j
125
375
1
2
χ
1
¼
¼
c
does not indicate any change. Thus, under
normal situation one can expect equal proba-
bility of changes in either direction;
b
+
ða þ dÞ
ð
125
þ
375
Þ
2
ðÞ
249
¼
Þ
¼
124
:
002
:
ð
500
that
