Ordered Cluster Sampling

Abstract

In survey practice, choice of clusters of elements as the sampling units is unavailable. This choice is dictated on account of low cost and operational convenience. The current theory of cluster sampling presumes that the frame of district clusters is available before sampling. For instance, the list of households as clusters of individuals, list of rows of trees in forests would be available before hand for adopting cluster sampling. Such cases do not present any difficulty in the development of theory of cluster sampling. However, in many large scale surveys, the clusters of households or clusters of villages are to be chosen as sampling units. There may be many ways of forming these clusters and element of the population is likely to enter in more than one cluster. Such cluster can be termed as over –lapping cluster. For instance, in many of the sample surveys conducted by institute of Agricultural Research statistics, the given list of villages around each of which he is asked to select a sample of villages within a specified distance to form clusters at field level. In such cases also the cluster become over-lapping and the usual procedures of estimating mean or total according to conventional method are not appropriate and lead to considerable bias in the estimate which itself cannot be estimated. Some work in this direction has been attempted by Goel (1973), but methods of estimation have not been suggested to build up an unbiased estimate of the total in such situation. In this dissertation a sampling procedure is slightly modified to build up an unbiased estimate and also to obtain the estimate of the variance of the estimate. This procedure is termed as Ordered Cluster Sampling. The procedure consists in selecting a main village and forming a cluster one by one without replacement. The main advantage of this method is that the distance between villages need not be known for all villages in the population, but only to know the distances between those villages which are selected at every draw. The procedure has been illustrated by taking an example for estimating castle population in velvadam firm in Vijayawada Taluk, Krishna Delta Area in Andhra Pradesh. The estimation procedure is given in Chapter-II and as also the estimation of the variance on the similar lines with Das Raj’ estimator with varying probabilities without replacement.