Reducing Variance with Sample Allocation Based on Expected Response Rates in Stratified Sample Designs

This paper demonstrates that the sample allocation that takes the expected response rates (ERRs) into account has certain advantages over other approaches in terms of reducing the variances of the estimates. The performance of the ERR allocation is assessed within the framework of stratified sampling by comparing the resulting variances with those obtained using the classical procedure of proportional-to-stratum size (PS) allocation and then applying poststratification. The main theoretical tool is asymptotic calculations using the delta-method, which are complemented with extensive finite sample evaluations using various combinations of specific population parameters. The main finding was that within a stratified sample design, ERR allocation leads to lower variances than PS allocation, not only when the response rates are correctly specified but also under a wide range of conditions where the response rates can only be approximately specified in advance.