Some Aspects of Successive Sampling in Multistage Designs

Abstract

Application of successive sampling with a two-stage sampling design to some of the problems where the survey is repeated at regular intervals has been indicated. Partial replacement of units is advantageous in field operation. Estimate of the population mean and its variance has been obtained (a) for two occasions and (b) for h occasions, the sampling scheme being that a fixed proportion of the pau’s taken on the preceding occasion has been replaced on the current occasion, the ssu’s within each selected psu’s being completely retained. Also an estimate for the change between any two consecutive occasions and its variance has been obtained under a different sampling pattern, viz. that the same psu’s are taken on both occasions, but a fraction p of the ssu’s within each selected psu is retained on the second occasion, and a fraction q selected afresh. A comparative study of the two sampling patterns has also been made. Data collected from the scheme conducted in Punjab (1956-57) to study the milk-yield or bovines there has been taken and a cost function for the scheme has been obtained. Optimum size of the sample to be taken in the second season to estimate the milk-yield of cows has been obtained. It has been observed that the size of the sample is not affected if some tehsils are replaced on the second season. Optimum values for n and m to be taken on the second occasion to estimate the mean and the change have been tabulated for a set of values of the correlations row one and row 2.