Home Statistical Dictionary Survey Weighting
Survey Weighting
The general practice of assigning each survey respondent a numerical weight, reflecting their inverse selection probability and often further adjustments for nonresponse and known population totals, so that weighted sample statistics validly estimate population quantities.
In Plain English
Survey weighting is the umbrella term for the whole process of figuring out how much each individual respondent's answer should 'count' when you compute a summary statistic from the survey. It usually starts with a base design weight, the inverse of that person's probability of being selected in the first place, and then layers on further adjustments, a nonresponse adjustment to compensate for the fact that not everyone who was sampled actually responded, and often a calibration step like post-stratification or raking to make the weighted sample line up with known population totals. The end result, the final weight attached to each respondent's row in the dataset, is what turns a raw, unweighted sample average into a defensible estimate of the population value.
Definition
Survey weighting assigns each sampled and responding unit a final analysis weight , typically constructed as the product of successive adjustment factors: the base design weight (the inverse of the unit's known selection probability), a nonresponse adjustment factor (compensating for units sampled but not observed, often computed within nonresponse-adjustment cells or via response-propensity modeling), and a calibration adjustment (post-stratification, raking, or another calibration estimator) that forces weighted sample totals to match known population benchmarks. Correctly constructed weights are essential for valid design-based or model-assisted inference from complex survey data, unweighted sample statistics generally do not equal the correct point estimates whenever selection probabilities, response propensities, or calibration adjustments differ across units, and virtually all analysis of complex survey data, from simple weighted means to full regression models, requires incorporating these weights (and the design information behind them, for correct variance estimation) rather than treating the data as an ordinary simple random sample.
Formula
Notation
Properties
- Ignoring survey weights when analyzing complex survey data (treating a weighted probability sample as if it were an ordinary unweighted dataset) generally produces biased point estimates whenever selection probabilities or response rates differ across subgroups, this is one of the most common and consequential analytical mistakes made with public-use survey microdata files.
- Weights alone are not sufficient for correct statistical inference, valid standard errors and confidence intervals from weighted survey data also require accounting for the underlying sample design (stratification, clustering) via specialized methods like Taylor series linearization or replicate weights, software that only applies weights to point estimates while computing standard errors as if the data were an SRS will understate uncertainty.
- Extremely large or small final weights, often arising from very low selection probabilities combined with substantial nonresponse and calibration adjustments compounding together, can make an estimator's variance disproportionately sensitive to a small number of highly weighted respondents, which is why weight trimming (capping extreme weights) is a standard, if debated, practical technique in applied survey weighting.
At a Glance