In this study, comparison has been made for different sampling designs, using the HIES data of North West Frontier Province (NWFP) for 2001-02 and 1998-99 collected from the Federal Bureau of Statistics, Statistical Division, Government of Pakistan, Islamabad. The performance of the estimators has also been considered using bootstrap and Jacknife.
A two-stage stratified random sample design is adopted by HIES. In the first stage, enumeration blocks and villages are treated as the first stage Primary Sampling Units (PSU). The sample PSU’s are selected with probability proportional to size. Secondary Sampling Units (SSU) i.e., households are selected by systematic sampling with a random start.
They have used a single study variable. We have compared the HIES technique with some other designs, which are: Stratified Simple Random Sampling. Stratified Systematic Sampling. Stratified Ranked Set Sampling. Stratified Two Phase Sampling. Ratio and Regression methods were applied with two study variables, which are: Income (y) and Household sizes (x). Jacknife and Bootstrap are used for variance replication.
Simple Random Sampling with sample size (462 to 561) gave moderate variances both by Jacknife and Bootstrap. By applying Systematic Sampling, we received moderate variance with sample size (467). In Jacknife with Systematic Sampling, we obtained variance of regression estimator greater than that of ratio estimator for a sample size (467 to 631). At a sample size (952) variance of ratio estimator gets greater than that of regression estimator. The most efficient design comes out to be Ranked set sampling compared with other designs. The Ranked set sampling with jackknife and bootstrap, gives minimum variance even with the smallest sample size (467). Two Phase sampling gave poor performance.
Multi-stage sampling applied by HIES gave large variances especially if used with a single study variable.