507 – Business, Time Series, and Spatial Analysis Methods
New Stratification and Allocation Procedures for Stratified Simple Random Sampling Without Replacement, with Application to Business Surveys
Naomi Baum
Israel Central Bureau of Statistics
The number of strata, the strata boundaries, the total sample size and the allocated number of sample units to each stratum, all affect the magnitude of the standard error of estimators of totals. The total sample size is usually given, since it is determined by the available budget. This paper considers stratified, simple random sampling without replacement (SRSWOR), when there are lower bounds to the sampling probabilities and to the number of allocated units per stratum, but the number of strata may vary. We propose to create as many strata as possible. A new procedure for an appropriate sampling design satisfying the bounds conditions is proposed. By this procedure, the sampling frame is divided into three sub-frames of large, medium and small size units. Next, the medium size sub-frame is stratified using the equal-strata-total stratification method and the small size sub-frame is stratified using the equal-size method, in both cases into as many strata as possible. The large units are all sampled. An allocation which under a commonly used assumption coincides with Neyman's allocation is applied for the medium size sub-frame. Proportional allocation is used for the small size sub-frame, as to meet the lower bound of the sampling probabilities. The procedure is easily programmed. A simulation study shows considerable reduction of the standard errors of estimators of totals.