Sample Selection and the Choice of Estimator in Two-Way Stratified Populations

Abstract

The paper studies the effect on variance of the method of sample selection and the choice of estimator in a two-way stratified population. Three methods of sampling, simple random and one and two-way stratified, are studied in conjunction with estimators which use no population information, one and two sets of marginal frequencies and cell frequencies. It is shown that whether the information in the population frequencies is used in the sample draw or in the estimator, the sampling variances are approximately the same. Hence efficiency can be associated with the method of sample selection and the estimator by the amount of population information used by each.

Some of the estimators involve post-stratified weighting and hence are subject to biases and inflated variances by the occurrence of small (or zero) sample sizes in the strata; in addition, the comparisons made are unequally affected by small sample sizes, but they are valid for sample sizes large enough to make the ratio estimators become stable.

Data from a real two-way stratified population are used for illustration.