Complex Sample Surveys

Stratification

One aspect of a complex sampling design may involve stratification, defined as a partition of the population into mutually exclusive and collectively exhaustive subsets called “strata.” One primary reason for using stratification is usually associated with the recognition that members of the same stratum are likely to be more similar to each other than members of different strata. Other reasons for using stratification include the desire to have every part of the population represented, or the desire to reduce sampling variance by using a larger sampling fraction in strata when the unit variance is larger than in more homogeneous strata, or it may reflect a strategy based on differential data collection costs from stratum to stratum. Stratification could also be used if stratum-specific domain estimates are desired. As previously alluded to, the sampling fractions used within the different strata may or may not be the same across all the strata. Strata may be explicit, and the number of units to be selected from each strata may be determined beforehand. Or stratification may be [Page 114]implicit, when systematic sampling is used and the units are arranged with all the units in each stratum appearing together when the population is ordered. In the case where strata are explicit, algorithms such as Neyman allocations for single estimands or the Chromy allocation algorithm for multiple estimands may be used to decide how many units to select from each stratum. A minimum of 2 units per stratum is usually recommended, as this facilitates variance estimation.

Cluster Designs

While stratification attempts to partition the population into sets that are as similar to each other as possible, clustering tries to partition the population into sets that are as heterogeneous as possible, but where data collection is less expensive by selecting a number of clusters that contain population units. One example is in a survey of students in which a given number of schools are selected, and then students are sampled within each of those chosen schools or clusters. In this case, the schools are called the “primary sampling units” (PSUs), while the students within the schools are referred to as the “secondary sampling units” (SSUs). It is possible to take either a sample or census of the secondary sampling units contained within each of the selected clusters. This would be the case when sampling additional units is extremely inexpensive, such as sampling entire classrooms from selected schools. More common, however, is to select clusters as a first sampling stage and then to select a subset of units within the clusters as a second stage. Sometimes there are more than two stages within a design, such as when school districts are selected first, then schools within the districts, and then intact classrooms within the schools.

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