Approximately Optimal Stratification

The cum method of Dalenius and Hodges for approximately optimal construction of strata is utilized to approximate the variance of the stratified estimate, for estimation of the population mean of a random variable Y by the technique of stratified random sampling. The approximation provides a basis for choosing optimally, for fixed cost, the number of strata to be constructed and the total sample size to be used. It also facilitates other purposes, such as the comparison of optimal stratified with optimal simple random sampling. The study is carried out for the situations of stratification on the estimation variable and of stratification on a covariable closely associated with the estimation variable.