A common sampling strategy for surveying finite populations is toselect the sampled units in several stages1.
Multistage samplingrefers to sampling plans where the sampling is carried out in stages usingsmaller and smaller sampling units at each stage2. In a two-stage samplingdesign, a sample of primary units is selected and then a sample of secondaryunits is selected within each primary unit. The simplest version of two-stagesampling is to use simple random sampling at each stage an SRS of primaryunits, and an SRS of secondary units within each selected primary unit. Theprimary units do not need to be the same size and you do not need to select thesame number of secondary units within each primary unit3.
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Multistage samples are used primarily for cost or feasibility(practicality) reasons. In detail, it becomes an effective tool in collecting primarydata from geographically dispersed population. That is when face-to-facecontact are required to obtain information from the population segment, forexample, semi-structured in-depth interviews.Selecting the sample in stages has practical benefits in theselection process itself. It permits the sampler to isolate, in successivesteps, the geographic locations where the survey operations – notably, listinghouseholds and administering interviews – will take place.
When listing must becarried out because of an obsolete sampling frame, a stage of selection can be introducedto 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 difficultbecause 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, andan SRS of households within each block. One only need to have a list ofhouseholds within each block that was selected.5 With this the multistageor at least the two-stage sampling methodology is afforded the flexibility tosample more intensely in primary units which are larger or more variable6.
On the other hand, the disadvantage of two-stage sampling is thatthe variance of the resulting estimators are likely to be larger than for anSRS of the same total number of secondary units. This may well be more than offsetby the cost efficiency of two-stage sampling. Relatedly, the research findingobtained from the method will never be 100 percent representative of thepopulation as hinted by the bloated variance of the estimates. Note that atwo-stage sample can never be better than a cluster sample with the same numberof primary units selected because a census within each primary unit is the bestyou can do. In addition, in doing the multistage design, the method allows forhigh level of subjectivity to the investigator despite the probability natureof the drawing information from the segment of the population7. 1https://www.
encyclopediaofmath.org/index.php/Sampling_from_finite_populations2 Cochran, W. G. (1977). SamplingTechniques, 3rd ed., John Wiley, New York.
3 https://www.researchgate.net/file.PostFileLoader.html?id=54fe85f1d11b8bf4708b45c2&assetKey=AS%3A273629118435328%4014422496735894https://unstats.un.org/unsd/demographic/sources/surveys/Handbook23June05.pdf5 US Census Bureau, 2016.
METHODOLOGY FORTHE 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.
pdf6 Kalton, G. (1983). QuantitativeApplications in the Social Sciences: Introduction to survey sampling ThousandOaks, CA: SAGE Publications Ltd doi: 10.4135/97814129846837Kalton, G. (1983).
Quantitative Applications in the Social Sciences:Introduction to survey sampling Thousand Oaks, CA: SAGE Publications Ltd doi:10.4135/9781412984683