Home Statistical Dictionary Multistage Sampling
Multistage Sampling
A sampling design that selects the sample through two or more successive stages of random selection, typically sampling larger units first (like regions), then progressively smaller units nested within them (like households, then individuals).
In Plain English
Multistage sampling is how most large national surveys are actually fielded: rather than trying to build one master list of every single person in the country, you sample in stages, first pick a random set of regions or districts, then within each chosen region pick a random set of neighborhoods, then within each chosen neighborhood pick a random set of households, then within each household pick a person to interview. Each stage only requires a sampling frame for units nested within the previous stage's selections, which is dramatically more practical than needing a complete list of every individual in the population up front.
Definition
Multistage sampling selects the final sample through a hierarchy of sampling stages: at the first stage, primary sampling units (PSUs, such as regions or districts) are selected from the full population, typically with probability proportional to size; at each subsequent stage, secondary sampling units nested within the previously selected units are sampled, down to the final stage, which selects the ultimate units to be observed. Multistage sampling is the practical generalization of two-stage cluster sampling to more than two levels, and its overall design effect compounds across stages, the intraclass correlation and cluster sizes at each level each contribute to the total loss of precision relative to an equivalent SRS, which is the trade-off made in exchange for not needing a complete population-wide sampling frame.
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Notation
Properties
- Multistage sampling is the standard design for large national household surveys and censuses of establishments precisely because it eliminates the need for a single, complete, population-wide sampling frame; only a frame of units nested within already-selected units at the previous stage is ever required.
- Selecting PSUs with probability proportional to size (PPS) at the first stage, so that larger regions or clusters are more likely to be chosen, and then applying a compensating unequal-probability adjustment (like the Horvitz-Thompson estimator) at analysis time, is standard practice to keep later-stage sample sizes roughly balanced across PSUs.
- Because design effects compound across every stage of clustering, the survey weights, replicate weights, and variance-estimation methods (like Taylor series linearization or jackknife/BRR replication) used to analyze multistage survey data must explicitly account for the full nested design, treating the data as if it came from SRS will understate standard errors, sometimes severely.
At a Glance