Strata Boundary Determination

This paper provides a method of strata boundary determination that generalizes the method of Dalenius and Hodges. The method holds for general populations. It makes no restrictive assumptions about the population distribution or about the ignorability of the finite population correction. 1. INTRODUCTION This paper describes a strategy for strata boundary determination that generalizes the classical approach of Dalenius and Hodges. Given a fixed sample size and a fixed number of strata, the Dalenius-Hodges method provides a quick means of determining strata boundaries that approximately minimizes coefficients of variation (cv). Applying their method requires assuming that the finite population correction (fpc) can be ignored, that the underlying population distribution is continuous, and that the probability density of the variable of interest is constant within strata. The minimization basically depends on one variable, strata boundary break points. The method of this paper allows determining strata boundaries for general populations. For a given sample size, approximate minimization depends on five discrete variables: number of strata, sample allocations within strata, population variance within strata, population size within strata, and strata boundary break points. If sample design considerations require that certain stratification variables, say number of strata and sample allocations within strata, be restricted, minimization can still be performed. The methods of this paper depend on standard ideas in sampling theory (e.g. Cochran 1977). The outline of the paper is as follows. In the second section, we present notation and definitions. We also describe the stratification methods of Dalenius and Hodges (1959) and of Ekman (1959). The third section contains a description of the empirical data base and the stratification method. In the fourth section, we prove the main theoretical result and present some empirical examples. The fifth section gives discussion of the relationship of the results with some of the generalizations of the Dalenius-Hodges method. In particular, the relationship with the method of Ekman is noted. The final section contains a summary.