Some Contribution of two-stage Sampling

Abstract

In two-stage sampling design, the primary sampling units are genrally of unequal size. For the choice of number of s.s.u’s to be drawn from different p.s.u’s the most common method is to be take them either equal or in proportion to their sizes. The drawback in taking s.s.u’s equal in number from each s.u. is that the size and the variability of s.s.u’s in different p.s.u.’s which are important for efficient estimation are ignored. The method of taking the number of s.s.u.’s proportionate to the total number of s.s.u.’s in the p.s.u.’s is also not desirable because it renders the ultimate sampling size a random variable which poses serious problems from field operation and point of view.

In this dissertation, the problem of allocation and selection of sample of fixed size in two stage sampling has been attempted.

In Chapter II, two procedures of allocation of s.s.u.’s to the selected p.s.u.’s have been suggested. The efficiencies of these procedures as compared to constant allocation procedures have been studied theoretically as well as empirically. It has been observed that of these, optimum allocation procedure is superior to the other two, followed by proportional allocation procedure. Further, the gain in efficiency is also substantial.

In Chapter III, a new sampling scheme of selection of sample of fixed number of s.s.u.’s has been suggested. Under this sampling scheme, three estimators namely Horvitz-Thompson estimator, Font-identification estimator and estimator based on sample mean are considered.

The relative efficiencies of these estimators together with the usual estimators under different allocation procedures have been investigated empirically on two small populations and it has been observed that the performance of the Horvits-Thompson estimator is the best of all estimates for these two populations.