Abstract
Sample designs are developed and estimators are chosen to efficiently fulfill specified analysis plans. Efficiency is generally defined to encompass three primary areas—accurate estimates (bias) with high levels of precision (small standard errors) calculated from data collected with procedures that make economical use of the study funds without exceeding the specified budget (cost). Sections 3.1 and 3.2 and Chap. 15 detail the gains achieved in precision if auxiliary information that is highly associated with the analysis variables can be used. This includes, for example, auxiliary variables used (i) in sampling as a stratification variable or to construct the measure of size for a probability proportional to size (pps) design or (ii) in estimation with a regression (or ratio) estimator. However, what if the only available sampling frame does not have useful auxiliary information? Without the auxiliary information, how might the statistician address concerns that the inflated sample size required for the specified level of precision will exceed the study budget?
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Sampling rates are typically set to limit the variation in the base weights and to limit the burden placed on the participating schools as measured by the student sample size.
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The cancer treatment centers under this design are treated as the first-stage strata for point and variance estimation because all and not a sample of centers are included in the study. As an aside, mathematical modelers would label this “cancer treatment variable” a fixed effect. If a subset of centers were randomly chosen, then these first-stage clusters (PSUs) usually would be modeled with random effects.
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Also, see the panel discussion on the appropriate uses of an fpc at http://web.cos.gmu.edu/∼wss/wss070328paper.pdf.
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Valliant, R., Dever, J.A., Kreuter, F. (2013). Multiphase Designs. In: Practical Tools for Designing and Weighting Survey Samples. Statistics for Social and Behavioral Sciences, vol 51. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6449-5_17
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