Stratification of Skewed Populations: A review

Abstract

When Dalenius provided a set of equations for the determination of stratum boundaries of a single auxiliary variable, that minimise the variance of the Horvitz-Thompson estimator of the mean or total under Neyman allocation for a fixed sample size, he pointed out that, though mathematically correct, those equations are troublesome to solve. Since then there has been a proliferation of approximations of an iterative nature, or otherwise cumbersome, tendered for this problem; many of these approximations assume a uniform distribution within strata, and, in the case of skewed populations, that all strata have the same relative variation. What seems to have been missed is that the combination of these two assumptions offers a much simpler and equally effective method of subdivision for skewed populations; take the stratum boundaries in geometric progression.