Two-Phase Sampling

Publisher Summary Two-phase sampling is typically used when it is very expensive to collect data on the variables of interest, but it is relatively inexpensive to collect data on variables that are correlated with the variables of interest. For example, in forest surveys, it is very difficult and expensive to travel to remote areas to make on-ground determinations. However, aerial photographs are relatively inexpensive and determinations on forest type are strongly correlated with ground determinations. Two-phase sampling was called “double sampling” by Neyman. The problem was posed to him at the U.S. Department of Agriculture. A survey was to be conducted to estimate the total of a characteristic y . The determinations were very costly, but another variable x was known to be correlated with y and was cheap to observe. Two-phase samplings reduce the variance of the estimated total by using the correlation between x and y in constructing a total estimator. However, two-phase samplings are not always superior to one-phase designs. Given a fixed cost, selecting a first-phase sample reduces the number of observations on the response variable y . The two-phase framework can be applied in missing data problems, sampling at multiple occasions, and situations without a good frame.