A sampling is carried out in stages

A common
sampling strategy for surveying finite populations is to select the sampled
units in several stages1.
Multistage sampling refers to sampling plans where the sampling is carried out
in stages using smaller and smaller sampling units at each stage2.
In a two-stage sampling design, a sample of primary units is selected and then
a sample of secondary units is selected within each primary unit. The simplest
version of two-stage sampling is to use simple random sampling at each stage an
SRS of primary units, and an SRS of secondary units within each selected
primary unit. The primary units do not need to be the same size and you do not
need to select the same number of secondary units within each primary unit3.

Multistage
samples are used primarily for cost or feasibility (practicality) reasons. In
detail, it becomes an effective tool in collecting primary data from
geographically dispersed population. That is when face-to-face contact are
required to obtain information from the population segment, for example, semi-structured
in-depth interviews.

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Selecting
the sample in stages has practical benefits in the selection process itself. It
permits the sampler to isolate, in successive steps, the geographic locations
where the survey operations – notably, listing households and administering
interviews – will take place. When listing must be carried out because of an
obsolete sampling frame, a stage of selection can be introduced to limit the
size of the area to be listed4.

As noted
from the example made by the United States Census Bureau (2016), to select an
SRS of households in the U.S. would be extremely difficult because no list of
all households exists. However, we could proceed in stages: an SRS of counties in
the U.S., an SRS of locks” within each county, and an SRS of households
within each block. One only need to have a list of households within each block
that was selected.5
With this the multistage or at least the two-stage sampling methodology is afforded
the flexibility to sample more intensely in primary units which are larger or
more variable6.

On the
other hand, the disadvantage of two-stage sampling is that the variance of the
resulting estimators are likely to be larger than for an SRS of the same total
number of secondary units. This may well be more than offset by the cost efficiency
of two-stage sampling. Relatedly, the research finding obtained from the method
will never be 100 percent representative of the population as hinted by the
bloated variance of the estimates. Note that a two-stage sample can never be
better than a cluster sample with the same number of primary units selected
because a census within each primary unit is the best you can do. In addition,
in doing the multistage design, the method allows for high level of
subjectivity to the investigator despite the probability nature of the drawing
information from the segment of the population7.

1
https://www.encyclopediaofmath.org/index.php/Sampling_from_finite_populations

2 Cochran, W. G. (1977).
Sampling Techniques, 3rd ed., John Wiley, New York.

3 https://www.researchgate.net/file.PostFileLoader.html?id=54fe85f1d11b8bf4708b45c2&assetKey=AS%3A273629118435328%401442249673589

4
https://unstats.un.org/unsd/demographic/sources/surveys/Handbook23June05.pdf

5
US Census Bureau, 2016. METHODOLOGY FOR THE UNITED STATES POPULATION ESTIMATES:
VINTAGE 2016 Nation, States, Counties, and Puerto Rico – April 1, 2010 to July
1, 2016.
https://www2.census.gov/programs-surveys/popest/technical-documentation/methodology/2010-2016/2016-natstcopr-meth.pdf

6
Kalton, G. (1983). Quantitative Applications in the Social Sciences:
Introduction to survey sampling Thousand Oaks, CA: SAGE Publications Ltd doi:
10.4135/9781412984683

7
Kalton, G. (1983). Quantitative Applications in the Social Sciences:
Introduction to survey sampling Thousand Oaks, CA: SAGE Publications Ltd doi:
10.4135/9781412984683