Some Studies in Two Stage Successive Sampling

Abstract

It is well known that in sample surveys auxiliary information can be used to improve upon the estimates. In the case of successive sampling the same variate is kept under observation on different occasions. The observations on the earlier occasions are used as ancillary information to improve the estimate of the population character under study at the subsequent occasions. In this investigation an attempt has been made to obtain the minimum variance linear unbiased estimates of 1. the population mean on the most recent occasion 2. the change in the population mean from one occasion to another ; and 3. An overall estimate of the population mean over all occasions, for a dynamic population using a two stage design.

The study is confined to two cases viz. (a) Partially replacing primary stage units (psu’s) and keeping second stage units (sau’s) fixed; and (b) Keeping psu’s fixed and partially replacing sau’s, for a fixed sample size ‘n’ and under the retention pattern in which ‘np’ units retained over all occasions and ‘nq’ units are selected afresh at each occasion (p + q = 1)

The entire investigation has been made under a general correlation pattern. The results obtained by some of the other research workers in the field follow particular cases of this investigation. A comparison of the efficiency of the two sampling patterns has been discussed. A suitable example is also given to illustrate the application of the estimates obtained.