A General Algorithm for Univariate Stratification

Summary 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 [bh−1, bh) . The stratum boundaries {bh} 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).