Modified Two-Stage Cluster Sampling Estimators for Finite Population Total

Abstract

This work proposes modified versions of the conventional estimators for finite population total under two stage cluster sampling scheme by combining the efficiency gain in Probability Proportional to Size and stratification using both Equal and Unequal probability of selection methods. The population is first stratified into strata and independent samples of equal size is selected from each stratum using probability Proportional to size (PPS) without
replacement in the first stage. In the second stage, hm and him units are selected for equal and unequal probability methods respectively using Simple Random Sampling without replacement (SRSWOR). The variances of the suggested estimators are expressed mathematically.The empirical comparison of the variances, standard errors and the coefficient of variations were used in obtaining the most efficient estimator. It was established that, the proposed estimators were better than the conventional ones. The one that uses unequal probability of selection method performs better amongst the proposed ones and therefore recommended.