Stratification of Skewed Populations: A Comparison of Optimisation‐based versus Approximate Methods

Survey statisticians use either approximate or optimisation‐based methods to stratify finite populations. Examples of the former are the cumrootf (Dalenius & Hodges, 1957 ) and geometric (Gunning & Horgan, 2004 ) methods, while examples of the latter are Sethi ( 1963 ) and Kozak ( 2004 ) algorithms. The approximate procedures result in inflexible stratum boundaries; this lack of flexibility results in non‐optimal boundaries. On the other hand, optimisation‐based methods provide stratum boundaries that can simultaneously account for (i) a chosen allocation scheme, (ii) overall sample size or required reliability of the estimator of a studied parameter and (iii) presence or absence of a take‐all stratum. Given these additional conditions, optimisation‐based methods will result in optimal boundaries. The only disadvantage of these methods is their complexity. However, in the second decade of 21st century, this complexity does not actually pose a problem. We illustrate how these two groups of methods differ by comparing their efficiency for two artificial populations and a real population. Our final point is that statistical offices should prefer optimisation‐based over approximate stratification methods; such a decision will help them either save much public money or, if funds are already allocated to a survey, result in more precise estimates of national statistics.