Exact Optimal Sample Allocation for Establishments having More Than Ten Employees in Qatar

Abstract

The primary aim of this study is to select a stratified random sampling with three different techniques which is optimal allocation, proportional allocation and the new method is exact optimal allocation which is a great method with more advantage than other methods. In addition, we use two different stratification method which is: optimal rule of stratification and stratification based on establishment activity. In each two stratification we apply the three methods, and the total sample size is chosen by optimal allocation technique and set for both other techniques, so that we can make a comparison among there variance. The result we get is as following stratification by optimal rule of stratification give smaller variance in all three technique than stratification based on establishment activity. Among the three method we use, the powerful method is exact sampling allocation because it gives smaller variance than the other methods, followed by optimal allocation (Neyman) and the largest variance we get from proportional allocation in both method of stratification. In exact optimal allocation with predetermining variance, we get smaller number of sample size for stratification by establishment activity but with very large variance, otherwise with optimal rule of stratification with predetermining variance we get a large number of sample size with smaller variance.