poststratification

Poststratification is a statistical adjustment technique used in survey sampling to align survey estimates with known characteristics of the target population after data collection. It partitions the population into poststratification cells, or strata, defined by auxiliary variables such as age, sex, region, or education level for which reliable population totals are available. The method aims to reduce bias arising from nonresponse, nonprobability sampling, or unequal selection probabilities by ensuring the sample distribution matches the population distribution within each stratum.

Implementation commonly involves weighting survey responses by poststratification factors. A typical weight is w_i^post = w_i × (N_h / n_h), where w_i is the original design weight for respondent i, h denotes the stratum to which i belongs, N_h is the known population size of stratum h, and n_h is the number of sampled units in that stratum. The poststratified estimate of a population quantity is then the weighted average using these poststratified weights. If a stratum has no sampled units, researchers may borrow strength from related strata or impose smoothing.

Variations include iterative poststratification methods such as raking (iterative proportional fitting), which adjusts weights to match population margins rather than full cell counts. Calibration weighting and general regression calibration extend poststratification by incorporating auxiliary information through models. In recent practice, multilevel regression and poststratification (MRP) combines hierarchical modeling with poststratification to produce model-based population estimates.

Applications span political polling, market research, and public opinion surveys, where timely benchmarks are available. The method relies on accurate and relevant population totals and well-chosen strata. Its limitations include increased estimator variance when weights vary greatly, sensitivity to misspecification of the stratification variables, and potential bias if important population structure is unaccounted for.