Two-phase adaptive cluster sampling with circular field plots

Adaptive cluster sampling (ACS) is extended to the case when the primary sampling units consist of circular field plots. When conducting field work for environmental monitoring, circular field plots are often preferred as they are easily set up by field workers. ACS was developed by tessellating the area frame into square plots. By using a two-phase sampling procedure, a first-phase sample of circular field plots can be established as the primary sampling units, from which ACS can be performed. However, the two-phase approach introduces some additional complexity in estimation. We derive estimators and conservative variance estimators for two-phase ACS using circular field plots. For some populations, ACS may produce a highly variable sample size. To deal with this issue, we provide a way to reduce the maximal possible sample size. By using simulated populations, we compare the efficiencies of two-phase methods with ordinary simple random sampling. The simulations show that the two-phase approach is a competitive alternative to regular ACS, and that adding a restriction to the maximal possible sample size makes ACS a viable alternative for a larger set of populations.