New Estimation Method in Two-Stage Cluster Sampling Using Finite Population.

Abstract

This research investigates the use of a two-stage cluster sampling design in estimating the population total. We focus on a special design where certain number of visits is being considered for estimating the population size and a weighted factor of N_i⁄〖n_i〗^2 is introduced. In particular, attempt was made at deriving a new method for a three-stage sampling design. In this study, we compared the newly proposed estimator with some of the existing estimators in a two-stage sampling design. Eight (8) data sets were used to justify this paper. The first four (4) data sets were obtained from Horvitz and Thompson (1952), Raj (1972), Cochran (1977) and Okafor (2002) respectively while the second four (4) data sets represent the number of diabetic patients in Niger state, Nigeria for the years 2005, 2006, 2007 and 2008 respectively. The computation was done with software developed in Microsoft Visual C++ programming language. The population totals were obtained for illustrated data and life data. We obtained the biases of the estimated population totals for illustrated and life data respectively. For all the populations considered, the biases of our proposed estimator are the least among all estimators compared. The variance of the newly proposed method is less than the variances of those of the existing methods. All the estimated population totals are also found to fall within the computed confidence intervals for α = 5%. The coefficients of variations obtained for the estimated population totals using both illustrated and life data show that our newly proposed estimator has the least coefficient of variation. Therefore, our newly proposed estimator (Y ̂_2NPE) is recommended when considering a two-stage cluster sampling design.