Survey Weights

Survey weights account for the survey design, sampling error, and non-sampling error.

Contents

  1. Survey Weights
    1. Description
    2. Weighted Estimators
    3. Reading Notes

Description

Survey data is collected through a mechanism which can be specified statistically. If it is not specified, bias can be introduced and estimates can be over-confident.

Inverse variance weights are related, but not the same.

Survey weights begin with design weights reflecting probability of selection. Generally this is simply the inverse of the sampling probability: nk/N for all strata k.

All real surveys feature non-sampling error, especially nonresponse. If nonresponse is uncorrelated with key metrics, it is negligible. Otherwise there is potential for nonresponse bias. This bias can be corrected through survey weights in a few ways:

Modeling on insignificant or uncorrelated attributes does not introduce bias, but it does inflate variance.

Calibration can be used to:

The methods here include:

Weighted Estimators

Survey weights w are designed such that a population proportion μ can be calculated using the weighted estimator Σ(wx) / Σw.

In the case that all cases have equal weight, the variance of that estimator is w2σ2.

In any other case, the variance is given by Σ(w2σ2) / (Σw)2. This ratio must then be linearized or simulated to arrive at an approximate variance. Taylor expansion is a common strategy for linearization.

Reading Notes

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Statistics/SurveyWeights (last edited 2026-08-12 20:10:31 by DominicRicottone)