1
Multistage Sampling
Example
Suppose eligible respondents (age 15+) are
grouped according to their residential addresses
(clusters).
A sampling frame of the addresses is
available.
Simple random sample of addresses is
selected from the frame.
Multistage Sampling
Example (cont)
y
If every eligible respondent in the selected
address is asked to provide individual
information, then we have cluster sampling.
y
However, in most of the cases only one randomly
selected individual from the selected address will
provide individual information.
Then, we have
two stage sampling.
Multistage Sampling
Example (cont)
Suppose 1000 addresses are selected.
Since only
one member from each address is being
interviewed, there are 1000 respondents as well.
Suppose out of these 1000 respondents, 800 are
Chinese.
Is 800/1000 = 0.8 an estimate of the
proportion of Chinese in the target population?
Ans: No, but why?
Multistage Sampling
Two-stage Cluster Sampling
A two-stage cluster sampling is obtained by first
selecting a simple random sample of cluster
(primary sampling unit, psu) and then selecting a
simple random sample of element (secondary
sampling units, ssu) from each sampled cluster.
Multistage Sampling
Two-stage cluster sampling
Notations:
For the population:
M
:
Number of cluster (psu) in the population
N
:
Number of elements (ssu) in the
i
th cluster
i
N
:
Number of elements in the population
:
Average cluster size of the population
Y
ij
:
Measurement of the
j
th element in the
i
th cluster
T
i
:
The
i
th cluster total
:
The
i
th cluster mean
N
i
Y
Multistage Sampling
Two-stage Cluster Sampling
Notations
T
:
Population total
:
Population mean
:
Average per cluster
Y
Y
c

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