Home Statistical Dictionary Post-Stratification

Post-Stratification

A weighting adjustment applied after data collection that reweights the achieved sample so that its distribution across a set of categories (such as age and sex) matches known population totals for those same categories.

Sampling Theory & Survey MethodsIntermediateFree

In Plain English

Post-stratification is stratified sampling's after-the-fact cousin: instead of controlling the sample's composition by design before data collection (true stratification), you let the sample fall where it falls, and then, once the data are in, adjust the weights so that the sample's breakdown by category, age group, sex, region, whatever variables you have reliable population totals for, matches the real population's breakdown exactly. If your achieved sample happened to undersample young adults relative to the true population, post-stratification gives each young-adult respondent a bit more weight to compensate, correcting for both random sampling variation and some forms of nonresponse or coverage gaps, as long as they're correlated with the categories used.

Definition

Post-stratification adjusts the survey weight of each respondent so that the weighted sample distribution across a set of post-strata (categories, typically cross-classifications of demographic variables like age × sex × region) exactly matches known population totals for those categories, computed as $w_{i}^{PS} = d_{i} \times \frac{N _{h}}{N ^ _{h}}$ for a respondent in post-stratum $h$ , where $d_{i}$ is the original design weight, $N_{h}$ is the known population total in stratum $h$ , and $\hat{N}_{h}$ is the weighted sample estimate of that total before adjustment. Unlike design-time stratification, post-stratification can be applied using any categorical variable measured for both the sample and available as a known population total, regardless of whether it was used in the original sampling design, and it corrects for random sampling fluctuations in the achieved sample's composition as well as, to the extent that nonresponse or coverage gaps are correlated with the post-stratification variables, some portion of nonresponse bias and coverage error; post-stratification is a special case of the broader calibration estimation framework, corresponding to calibrating exactly against a full categorical cross-classification.

Formula

w_{i}^{PS} = d_{i} \times \frac{N _{h}}{N ^ _{h}}

Notation

d_{i}

—Original design weight of respondent i

N_{h}

—Known population total in post-stratum h

\hat{N}_{h}

—Weighted sample estimate of the total in post-stratum h, before adjustment

Properties

Post-stratification only corrects for nonresponse or coverage bias to the extent that the bias is correlated with the post-stratification variables used, if nonrespondents differ from respondents in ways unrelated to the categories being adjusted for (an unmeasured attitude or behavior, say), post-stratification cannot detect or fix that discrepancy.
Post-stratification cells with very few sample observations produce unstable, highly variable weights, a well-known practical pitfall, which is why practitioners typically collapse overly sparse cells (combining adjacent age groups, for example) or switch to raking when the full cross-classification of variables would produce too many thin cells to weight reliably.
Post-stratification is distinct from stratified sampling despite the similar name and shared goal of controlling subgroup representation, stratified sampling controls sample allocation at the design stage before data collection, post-stratification is a purely after-the-fact weighting adjustment that requires no advance knowledge of respondents' categories, only their values after the survey is complete.

At a Glance

Appliedafter data collection, using any measured categorical variable with known population totals

Corrects forsampling fluctuation, and some nonresponse/coverage bias correlated with the variable

Requirespost-strata cells with enough sample observations to avoid unstable weights

Special case ofcalibration estimation, matching a full categorical cross-classification exactly

Last updated September 8, 2026← Back to the Dictionary