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survey weights are used when data are collected according to a probability sampling design with unequal probabilities of selection and/or response

Survey weights are used when data are collected according to a probability sampling design with unequal probabilities of selection and/or response.

In survey sampling, the inferential goal is to generalize from the sample to the finite population. The original motivation for survey weights comes from Horvitz-Thompson estimator of the population total: $$t[y] = \sum_{i \in \mbox{units in sample}} \frac{y_i}{\pi_i}$$ where $\pi_i$ is the probability of selection. In this expression, $1/\pi_i$ can be interpreted as a weight attached to unit $i$, $w_i=\pi_i^{-1}$.

In practice, survey weights also include corrections for nonresponse, lack of population coverage, and other corrections for imbalance between the sample and the population.

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