6. Double Sampling

Many a time in the survey, additional information is available on another variable, related to the study variable. This variable is known as an auxiliary variable. Generally, the auxiliary variable is highly correlated with the study variable. It is also assumed that the information on the auxiliary variable is not available for all the population units. The auxiliary information is collected with a relatively large sample by using SRSWR or SRSWOR from the population to get the population estimate and information of the study variable, and the auxiliary variable is gathered from the selected units in the first phase or population with a smaller sample size compared to the first phase by using SRSWR or SRSWOR. Such a sampling procedure is called double sampling or two-phase sampling. If a sample is selected in more than two phases, it is called multiphase sampling. For example, the volume of a truck container and the weight of the truck container are correlated, and we want to estimate the volume of the truck container. By using SRSWR or SRSWOR, the large sample of the truck is selected and the weight of the truck container is measured, and from the selected truck container again by employing SRSWR or SRSWOR, the small sample of the truck container is selected and the volume of the truck container is measured. In this sampling scheme, the auxiliary information is utilized to improve the precision of the estimator, and the cost is reduced for the study variable by selecting a small sample.