US Geological Survey


Date of this Version



Environmetrics 2012; 23: 306–316; DOI: 10.1002/env.2144


A main benefit from taking a systematic sample is the ease of implementation when field sampling. However, it is not uncommon for a researcher to sample only one primary sampling unit (PSU) but to assume that the secondary sampling units (SSUs) were selected by simple random sampling to obtain a variance estimate. To obtain an unbiased estimator of variance for conventional or adaptive systematic sampling, it is necessary to sample >1 PSUs, and this can marginally increase cost and complicate implementation. We show that it is possible to obtain an unbiased estimate of variance if the researcher takes only a single PSU and one or more SSUs. Although this is no longer a true systematic sample, such a design retains much of the simplicity of sampling a single PSU and allows for a valid variance estimate.

This paper introduces three new sampling strategies stemming from systematic adaptive cluster sampling and the Raj estimator. The new sampling designs will be referred to as partial systematic adaptive cluster sampling. The sampling strategies are investigated in a simulation study that utilizes distance traveled as a measure of cost when comparing sampling strategies. When only a single PSU can be sampled because of cost or logistics concerns, we recommend also sampling one or more SSUs to obtain an unbiased estimate of variance.