An alternative solution is to use a part of the budget for collecting information on auxiliary variable to
collect a large preliminary sample in which i x alone is measured. The purpose of this sampling is to
furnish a good estimate of X . This method is appropriate when the information about i x is on file
cards that have not been tabulated. After collecting a large preliminary sample of size n' units from
the population, select a smaller sample of size n from it and collect the information on y . These two
estimates are then used to obtain an estimator of population mean Y. This procedure of selecting a
large sample for collecting information on auxiliary variable x and then selecting a sub-sample from
it for collecting the information on the study variable y is called double sampling or two phase
sampling. It is useful when it is considerably cheaper and quicker to collect data on x than y and
there is high correlation between x and y.
In