Impact of Stratum Composition Changes on the Accuracy of the Estimates in a Sample Survey

Abstract

The study is devoted to measuring the impact of the element changes on the bias and variance of the estimator of the total in a sample business survey. Stratified simple random sampling is usually used in business surveys. Enterprises may join, split or change the stratum between sample selection and data collection. Assuming a model for enterprises joining and a model for the enterprises changing the stratum with some probability, expressions for the adjusted estimators of the total and the adjusted estimators of their variances are proposed. The influence of the enterprise changes on the variances of the estimators of the total is measured by the relative differences, i.e., by comparing them with the estimators, if there were no changes. The analytic results are illustrated with a simulation study using modified enterprise data. The simulation results demonstrate a large impact of the enterprise changes on the accuracy of the estimates, even in the case of the low probability of changes. The simulation results justify the need for adjustment of the enterprise changes between the sample selection and data collection, in order to improve the accuracy of results and the adjustment method available.

Keywords

• simple random stratified sample
• joining units
• inclusion probabilities
• splitting units
• relative variance change of the estimator for the total
• statistical simulation