Agriculture Reference
In-Depth Information
N
1
P
n
2
Table 6.5
Selection of sample using cumulative total
i¼
1
Y
i
Y
2
1
where
S
¼
ð
Þ
is the population
method
Farm
area
(cents)
(
X
i
)
f ¼
N
¼
mean square and
sampling fraction
:
The factor
N
N
¼ð
is a correction
factor for the finite size of the population and
is called the finite population correction factor.
It is noted that
1
f Þ
Farm
no.
Cumulative
total
Numbers
associated
PPSWR
1
20
20
1-20
2
15
35
21-35
V
WOR
ðyÞ¼
Nn
N
1
σ
2
n
¼
n
1
N
1
1
3
10
45
36-45
2
n
!
σ
2
n
σ
VðyÞ;
which is equal to
when
N !1:
4
30
75
46-75
5
60
135
76-135
√
6
100
235
136-235
6.2.1.2 Varying Probability Sampling
(Probability Proportional to Size
Sampling)
In many practical situations, the units vary in size
and the variable under study is directly related to
the size of the unit. In this case, probabilities may
be assigned to all the units proportional to their
sizes and be employed probability proportional
to size sampling technique. Let there be “
7
40
275
236-275
8
25
300
276-300
9
35
335
301-335
10
45
380
336-380
11
50
430
381-430
12
55
485
431-485
13
20
505
486-505
14
10
515
506-515
15
70
585
516-585
√
N
” units
16
75
660
586-660
in a population having sizes
X
N
,
the total of the sizes of all the units in the popu-
lation being
P
i¼
1
X
i
¼ X
X
1
,
X
2
,
X
3
,
...
,
17
90
750
661-750
√
18
65
815
751-815
. In this method, the
19
40
855
816-855
√
i
X
i
=X
probability of selecting
. The
selection of sample according to probability pro-
portional to size sampling with replacement can
be made in two different ways: (a)
th unit is
20
45
900
856-900
Example 6.2.
Suppose there are 20 farms.
We are to select 5 farms with probability propor-
tional to size with replacement.
cumulative
total method
and (b)
Lahiri's method
.
Solution. With size being the area of farms by
cumulative total method, we have Table
6.5
prepared:
Select five random numbers from 1 to 900
from the random number table. Random numbers
selected from the random number table at the 1st
row and 9th column and moving vertically down-
ward are 843, 122, 735, 82, and 559. The units
associated with these numbers are 19th, 5th,
17th, 5th, and 15th, respectively. Thus, according
to PPS, with replacement the sample contains
farms with serial numbers 5, 5, 15, 17, and 19.
Cumulative Total Method
Let the size of the
i
th unit in the population be
X
i
(
), and suppose that these
are integers. Then the procedure is given in the
following steps:
1. Assign 1 to
i ¼
1, 2, 3,
...
,
N
X
1
numbers to the first unit,
X
1
+1
to (
X
1
+
X
2
) numbers to the second unit,
X
1
X
2
+1 to
X
1
+
X
2
+
X
3
numbers to the third unit,
and so on.
2. Select a random number from 1 to
from the
random number table using the method for
selection of sample according to simple ran-
dom sampling technique.
3. The unit in whose range the random number
falls is taken in the sample.
4. Steps in (2) and (3) are repeated “
X
Lahiri's Method
According to Lahiri's (1951) method of PPS
selection, we do not require accumulation of the
sizes at all. It consists in selecting a number at
random from 1 to
n
” times to
get a sample of size “
” with probability pro-
portional to size with replacement.
n
and noting down the unit with
the corresponding serial number provisionally.
N
