Use of Auxiliary Information: Multi-Phase Sampling

Abstract

In the previous chapters we have seen that use of known auxiliary information at the estimation stage as well as at the selection stage leads to improved estimation strategies in survey sampling. When such information is not completely known or lacking and it is relatively cheaper to obtain information on the auxiliary variable(s), one can consider taking a large preliminary sample for estimating population mean(s) of the auxiliary variable(s) to be used at the estimation or selection stage of the ultimate estimation strategies. For example, in the case of single auxiliary variable X, since it is cheaper to obtain information on X, we consider taking a large preliminary sample for estimating population mean. $\bar X$ or distribution of X as the case may be, and only a small sample (some times a subsample) for measuring the study variable Y.