Equal-precision allocations and other constraints in stratified random sampling

Abstract

Selecting the number of observations from each stratum is a primary decision in stratified random sampling design. Typically, allocation schemes aim to minimize or bound the variance associated with estimating some overall population parameter, subject to a limitation on sampling resources. This paper examines the impact of further constraints on allocations for stratified sampling; it was motivated by an application requiring all stratum means to be estimated with equal precision. Simple procedures for analyzing trade-offs between equal-precision allocations and those optimizing total cost or precision of overall population estimates are presented. The effect of equal-precision allocation is illustrated within the context of an anthropological study of eight strata defined by villages. In this example, the equal-precision allocation greatly improves the precision of estimating the stratum-specific means over the customary proportional allocation, with only mild degradation in the precision used to estimate the population mean.

Keywords:

• Optimal sampling allocation
• Stratum means
• Sampling costs

Acknowledgements

The authors would like to thank Dr S. Crane for posing such a simple question that led to interesting discussions.