Stratification by Size Revisited

Stratification is one of the most widely used techniques in finite population sampling. Strata are disjoint subdivisions of a population, the union of which exhaust the universe, each of which contains a portion of the sample. Two of its essential statistical purposes are to: (1) allow for efficient estimation, especially in the case of stratification by size, and (2) deal statistically with subpopulations or domains by controlling their sample allocations. Stratification by size is typically considered as serving purpose (1) by creating strata in an efficient way and optimally allocating the sample to the strata. Using model-based analysis, we show that, in the situation where stratification by size is generally used, optimal allocation of a weighted balanced sample achieves exactly the same variance as unstratified, best linear unbiased (BLU) prediction coupled with weighted balanced sampling. In other words, stratification by size has no advantage over the optimal, unstratified procedure. This and other theoretical findings are illustrated with simulations using real populations.