ABSTRACT
Sometimes you would like to use stratification or ratio estimation to increase the precision of your estimator but do not have the population information needed to form strata or ratio estimates. Two-phase sampling is useful when the variable of interest is relatively expensive to measure, but a related variable can be measured fairly easily. A first-phase sample is drawn to measure the related variable, and then the variable of interest is measured on a subsample (the second-phase sample) of the first-phase sample. Two-phase sampling can give more accurate estimators without increasing costs. It is often used when there is nonresponse; in that setting, a subsample of the nonrespondents serves as the second-phase sample.
