9.3. Other Sampling Methods
1. Stratified Random Sampling:
 The population is divided into groups of elements called
strata according to some “characteristic” of the data.
 A simple random sample is taken from each stratum.
How to determine the sample size in each stratum?


According to the size of the stratum.
According to the variance of each stratum.
2. Cluster Sampling:
 The population is divided into several separate groups of
elements called clusters.
 A simple random sample of the clusters is taken. All elements
within these sampled or “selected” clusters are in the sample.
Note: one of the primary applications of cluster sampling is area
sampling, where clusters are city blocks or other well-defined areas!!
3. Systematic Sampling:
 Select randomly one of the first
N
elements, where n and N
n
are the sample size and the population size, respectively.
N
 Starting from the first selected element, select every   ’th
n
element after the first element.
Example:
Suppose n  50, N  5000, and y1 , y 2 ,, y5000 are the elements in the population.
Since
N 5000

 100 , by using systematic sampling, we should select randomly
n
50
one from the first 100 elements first. Suppose the third element is selected, i.e.
x1  y3 . Then, select every 100’th element after y 3 , thus
1
x2  y103 , x3  y 203 ,, x50  y 4903.
Example :
Suppose we have a population of 40 elements
148
148
149
149
153
154
155
155
156
156
157
157
158
158
158
158
158
159
159
160
160
160
161
162
162
162
163
163
163
163
164
164
164
164
165
165
165
165
165
166
Suppose the first row of the table of random number is
63271 59986 71744 51102 15141 80714 58683 93108 13554 79945
Please use systematic sampling to obtain
(a) a sample of 5 elements.
(b) the sample mean and sample variance based on (a).
[solution:]
(a) 40/5=8. Thus, we need to divide the original data into 5 subsets and select 1
element from these subsets. The subsets are
Subset
1
148
148
149
149
153
154
155
155
Subset
156
156
157
157
158
158
158
158
Subset
3
158
159
159
160
160
160
161
162
Subset
4
162
162
163
163
163
163
164
164
Subset
5
164
164
165
165
165
165
165
166
2
The first random number between 1 and 8 are 6. Therefore, the sample we select are
154, 158, 160, 163, and 165.
(b) The sample mean is
x
154  158  160  163  165
 160
5
and the sample variance is
s
2
2
2
2
2
2

154  160  158  160  160  160  163  160  165  160

4
 18.5
2
Example :
Suppose we have a population of 27 elements
Stratum
1
1
2
3
4
5
6
7
8
9
Stratum
2
1
3
5
7
9
2
4
6
8
Stratum
3
2
4
6
8
9
1
3
5
7
Suppose the first row of the table of random number is
63271 59986 71744 51102 15141 80714 58683 93108 13554 79945
Please use stratified random sampling to obtain a sample of 5 elements (2 from
stratum 1, 1 from stratum 2, 2 from stratum 3) and find the 60 percentile from the
sample.
Online Exercise:
Exercise 9.3.1
3