How to Weight a Survey: Base Weights, Nonresponse, and Raking, Step by Step

Last updated October 30, 2026·4 min read

A sample never quite matches its population. Some groups answer more readily, some were sampled at higher rates on purpose, and chance alone tilts the rest. Weighting rebalances the sample so each respondent stands for the right number of people like them. Done in the right order, with diagnostics read at each step, it removes a known class of bias at a known cost in precision. Done in the wrong order, or without the diagnostics, it manufactures confidence the data never earned.

Step one: base weights

The base weight is the inverse of the selection probability. A respondent drawn with probability one in fifty carries a base weight of fifty: in the sample, that person represents fifty people. Stratified designs state the probabilities by construction, one sampling fraction per stratum. Where the frame gives stratum counts instead, base weights come from the ratio of population to sample within each stratum. Everything later multiplies from here, so an error in the base weights propagates through the whole run, and the step deserves its arithmetic checked twice.

Step two: nonresponse adjustment

Not everyone selected responds, and response is rarely random. The adjustment inflates the weights of respondents in groups that responded at low rates, so respondents stand in for similar nonrespondents. Two standard constructions:

• Weighting classes: group cases by variables known for respondents and nonrespondents alike, and scale each class by the inverse of its response rate.
• Propensity quintiles: model response with logistic regression on frame variables, sort respondents into fifths by predicted response probability, and adjust within each fifth.

The honesty note for this step: adjustment corrects for the variables in the classes or the model. A group that differs on something unmeasured stays different, and the methods section should say which variables carried the adjustment.

Step three: calibration to known margins

Calibration forces the weighted sample to match population totals known from outside the survey: census counts by age, sex, region, education. Three forms:

• Post-stratification calibrates to one variable, or to a full cross of variables where the joint population distribution is known.
• Raking, or iterative proportional fitting, calibrates to several margins in rotation when only the separate distributions are known, which is the common case. Each margin is matched in turn until all match within tolerance.
• GREG calibration adjusts weights by a regression model, useful when continuous benchmarks join the categorical ones.

Calibration is the step that visibly moves estimates, and it should. The worked figures from the weighting calculator page: a sample of forty with twenty-two men and eighteen women, calibrated to a population that is 48 percent men and 52 percent women, gives weights of 21.818 and 28.889, and moves a mean from 54.5 unweighted to 55.2 weighted, because the higher-scoring group was the underrepresented one. Small move, clear reason. When calibration moves an estimate a long way, the explanation has to be found before the estimate is reported, and the diagnostics in step five are where it will be found.

Step four: trimming, then re-raking

A few respondents sometimes carry weights many times the average, and each one then steers estimates like a small crowd. Trimming caps weights at a stated bound, commonly a multiple of the mean or a percentile, and redistributes the excess. Two disciplines make trimming defensible: the bound is chosen on variance grounds and reported with the count of trimmed weights, and the trimmed weights are re-raked afterward, because trimming breaks the margin matches that calibration just achieved.

Step five: read the diagnostics before anything is reported

• Margin check: weighted counts against calibration targets, line by line. A margin that misses is a failed run, not a footnote.
• Design effect and effective sample size: the Kish design effect prices the weighting. An effect of 1.5 turns 900 completes into an effective 600, and every interval in the report should be built on the effective reality, not the nominal count.
• Weight distribution: the spread, the maximum against the mean, and the trimmed count. A healthy run has no single respondent standing for an implausible crowd.
• Weighted against unweighted estimates on key variables: the deltas, each with its explanation from the sample composition.

Step six: write the methods paragraph as you go

A weighting run documented afterward invites reconstruction errors. The steps above, with their variables, targets, tolerances, and bounds, are the methods paragraph. Analysis Studio generates that paragraph from the run itself, which is the reliable way to keep the document and the arithmetic in agreement.

Run the workflow

Module 11 of Analysis Studio executes these steps in order, with the diagnostics on the same screen:

Module 11: Survey Weighting and RakingOpen in Analysis Studio →

Sources and method notes

Procedures follow standard survey practice: inverse-probability base weights, response-propensity adjustment, raking at tight convergence tolerance, and the Kish design effect for precision accounting. Worked figures are shared with the weighting calculator page and re-verified at build.