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Variance refers to the degree of variability (dispersion) among a collection of observations. Although estimation of the size of the variance in a distribution of numbers often is a complex process, it is an extremely important endeavor for survey researchers, as it helps make valid inferences of population parameters.

Standard variance estimation formulas for simple random sampling, stratified sampling, and cluster sampling can be found in essentially any survey sampling textbook, such as those by William G. Cochran or Leslie Kish. However, most large survey samples use combinations of unequal probabilities, stratification, and clustering. Often, survey weights are used in estimation that account for unequal probabilities, nonresponse, and post-stratification. These are usually ratio estimates with the numerator being the weighted average and the denominator being the ...

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