Multistage Sampling

Multistage sampling refers to SURVEY designs in which the POPULATION units are hierarchically arranged and the sample is selected in stages corresponding to the levels of the hierarchy. At each stage, only units within the higher level units selected at the previous stage are considered. (It should not be confused with multiphase sampling.)

The simplest type of multistage sampling is two-stage sampling. At the first stage, a sample of higher level units is selected. At the second stage, a sample of lower level units within the higher level units selected at the first stage is selected. For example, the first-stage units may be schools and the second-stage units pupils, or the first-stage units may be businesses and the second-stage units employees. In surveys of households or individuals covering a large geographical territory (e.g., national surveys), it is common for first-stage sampling units to be small geographical areas, with a modest number of addresses or households—perhaps 10 or 20—selected at the second stage within each selected first-stage unit.

Multistage designs result in samples that are “clustered” within a limited set of higher level units. If the design is to include all units at the latter stage—for example, all pupils in each selected school—then the sample is referred to as a CLUSTER SAMPLE because it consists of entire clusters. Otherwise, if the units are subsampled at the latter stage, the sample is said to be a clustered sample.

The main motivation for multistage sampling is usually cost reduction. In the case of field interview surveys, each cluster in the sample can form a workload for one interviewer. Thus, each interviewer has a number of interviews to carry out in the same location, reducing travel time relative to a single-stage (unclustered) sample. In consequence, the unit cost of an interview is reduced so a larger sample size can be achieved for a fixed budget. Often (not only for field interview surveys), there is a fixed cost associated with each first-stage unit included in the sample. For example, in a survey of school pupils, it may be necessary to liaise with each school. The cost of this liaison, which may include visits to the school, may be independent of the number of pupils to be sampled within the school. Again, then, the unit cost of data collection can be reduced by clustering the sample of pupils within a restricted number of schools.

However, sample clustering also has a disadvantage. Because units within higher stage units (e.g., pupils within schools, households within small areas) tend to be more homogeneous than units in the population as a whole, clustering tends to reduce the precision of survey estimates. In other words, clustering tends to have the opposite effect to proportionate sample stratification (see STRATIFIED SAMPLE). Whereas stratification ensures that all strata are represented in the sample, clustering causes only some clusters to be represented in the sample. The resultant reduction in precision can be measured by the DESIGN EFFECT due to clustering. In general, the reduction in precision will be greater the larger the mean sample size per cluster and the more homogeneous the clustering units. For example, a sample of 10 pupils from each of 100 classes will result in less precision than a sample of 10 pupils from each of 100 schools if pupils within classes are more homogeneous than pupils within schools.

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