Sample allocation balancing overall representativeness and stratum precision

Abstract

Purpose: In large-scale surveys, it is often necessary to distribute a preset sample size among a number of strata. Researchers must make a decision between prioritizing overall representativeness or precision of stratum estimates. Hence, I evaluated different sample allocation strategies based on stratum size.

Methods: The strategies evaluated herein included allocation proportional to stratum population; equal sample for all strata; and proportional to the natural logarithm, cubic root, and square root of the stratum population. This study considered the fact that, from a preset sample size, the dispersion index of stratum sampling fractions is correlated with the population estimator error and the dispersion index of stratum-specific sampling errors would measure the inequality in precision distribution. Identification of a balanced and efficient strategy was based on comparing those both dispersion indices.

Results: Balance and efficiency of the strategies changed depending on overall sample size. As the sample to be distributed increased, the most efficient allocation strategies were equal sample for each stratum; proportional to the logarithm, to the cubic root, to square root; and that proportional to the stratum population, respectively.

Conclusions: Depending on sample size, each of the strategies evaluated could be considered in optimizing the sample to keep both overall representativeness and stratum-specific precision.

Keywords: Precision; Representativeness; Sample allocation; Sample size; Stratified sampling.