Agriculture Reference
In-Depth Information
Besides the above, some complex and mixed
sampling techniques like (a) two-stage or three-
stage sampling with stratification, (b) double
sampling for stratification, and (c) sampling on
successive occasions are useful in studies related
to socioeconomic, agronomic, and animal hus-
bandry aspects.
with the help of random numbers. A unit is
selected, noted, and returned to the population
before drawing the second unit, and the process
is repeated “
n
” times to get a simple random
sample of “
” units. This procedure of selecting
a sample is known as “simple random sampling
with replacement (SRSWR).” On the other hand,
if the above procedure is continued till “
n
n
”
dis-
tinct
units are selected ignoring all repetitions, a
“simple random sampling without replacement
(SRSWOR)” is obtained.
How to use random number from a random
number table for drawing a random sample from
a finite population is illustrated in the following
example.
6.2.1 Probability Sampling
6.2.1.1 Simple Random Sampling
Simple random sampling is the most widely
used, simplest method of drawing sample from
a population such that each and every unit in the
population has an equal probability of being
included in the sample. Simple random sampling
is of two different types: (a)
Example 6.1.
Let 48 different lots of bulbs,
each containing 100 bulbs, be studied for defec-
tive bulbs, and the following figures give the
number of defective bulbs in each lot. We are
to draw two random samples of 10 lots: (1) with
replacement and (2) without replacement.
simple random sam-
pling with replacement
(
SRSWR
) and (b)
simple
random sampling without replacement
SRSWOR
(
).
units, we select one
unit by giving equal probability 1/
N
to all units
From a population of
N
Lot no.
1
2
3
4
5
6
7
8
9
10
11
12
No. of defective bulbs/lot
2
12
10
8
9
11
3
8
10
12
7
9
Lot no.
13
14
15
16
17
18
19
20
21
22
23
24
No. of defective bulbs/lot
4
5
7
12
14
8
10
0
5
6
10
12
Lot no.
25
26
27
28
29
30
31
32
33
34
35
36
No. of defective bulbs/lot
14
15
2
5
15
17
8
9
12
13
14
5
Lot no.
37
38
39
40
41
42
43
44
45
46
47
48
No. of defective bulbs/lot
6
7
8
12
11
9
12
15
18
16
9
10
The sampling units, that is, lots, are already
serially numbered from 1 to 48. Now
downward. The numbers selected from the ran-
dom number table
6.7
are given in Table
6.3
:
The random samples of size 10 with replace-
ment and without replacement consist of the unit
numbers 12, 4, 36, 36, 32, 18, 11, 45, 15, and 32
and 12, 4, 36, 32, 18, 11, 45, 15, 27, and 33,
respectively. While selecting the random numbers
according to the SRSWR, we have kept some
random numbers, namely, 36 and 32, more than
once because these units after selection were
returned to the population. But no repetition of
random number is found in SRSWOR method.
Demerit of the direct approach is that a large
number of random numbers are rejected simply
because these are more than the population size.
N ¼
48 is a
two-digit number.
Method 1 (Direct Approach)
Since
48 is a two-digit number, we shall use
a two-digit random number table, consider ran-
dom numbers from 01 to 48, and reject numbers
greater than 48 and 00. One can start from any
point (number) in the random number table, which
is arranged in rows and columns. We can move in
any random way we like; it can be vertically
downward or upward, to the right or to the left.
Let us start at random from a number in the
1st row and 12th column and move vertically
N ¼
