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606 – Sample Allocation

Optimal Sampling Fractions for Two-Phase Sampling for Nonresponse in the Real World

at Mathematica Policy Research

Two-phase sampling is a long-standing sampling method. It identifies subpopulations of interest in the first phase of a survey, from which a random subsample is selected in the second phase for further data collection, using the new information to further stratify or to narrow the survey population to a particular subgroup. It is also used to randomly subsample survey nonrespondents for more intensive follow-up. In this context, the phase-one nonrespondents are considered a subpopulation that is identified after data collection efforts have been completed with the initial mode and protocol. The more intensive phase-two data collection protocol is generally more expensive to implement than the first and is expected to have a greater success rate. However, budgetary constraints generally limit how many nonrespondents data collectors can attempt to contact using this more expensive protocol. Hansen et al.'s (1953) work provides optimal values for the fraction of phase-one nonrespondents to be subsampled for phase two (1/k) and for the initial sample size (M) in a two-phase sample with a subsample of proportion 1/k. However, these calculations assume that phase-two methods result in 100 percent response, which is not often the case in real-world scenarios. In this paper, I derive new optimal values for M and k under the more realistic scenario in which not all phase-two attempts result in a response.