Double sampling for stratification

Double sampling is a common alternative to simple random sampling when there are expected to be gains from using stratified sampling, but the units cannot be assigned to strata prior to sampling. It is assumed throughout that the survey objective is estimation of the finite population mean. We compare simple random sampling and three allocation methods for double sampling: (a) proportional, (b) Rao’s (Rao 1973a, b) and (c) optimal. There is also an investigation of the effect on sample size selection of misspecification of an important design parameter.