A General Algorithm for Univariate Stratification

This paper presents a general algorithm for constructing strata in a population using  X , a univariate stratification variable known for all the units in the population. Stratum  h  consists of all the units with an  X  value in the interval   b _{h −1},  b_h )   . The stratum boundaries   { b_h }   are obtained by minimizing the anticipated sample size for estimating the population total of a survey variable  Y  with a given level of precision. The stratification criterion allows the presence of a take-none and of a take-all stratum. The sample is allocated to the strata using a general rule that features proportional allocation, Neyman allocation, and power allocation as special cases. The optimization can take into account a stratum-specific anticipated non-response and a model for the relationship between the stratification variable  X  and the survey variable  Y . A loglinear model with stratum-specific mortality for  Y  given  X  is presented in detail. Two numerical algorithms for determining the optimal stratum boundaries, attributable to Sethi and Kozak, are compared in a numerical study. Several examples illustrate the stratified designs that can be constructed with the proposed methodology. All the calculations presented in this paper were carried out with stratification , an R package that will be available on CRAN (Comprehensive R Archive Network).