Two-stage complete allocation sampling

Abstract

An adaptive sample involves modifying the sampling design on the basis of information obtained during the survey while remaining in the probability sampling framework. Complete allocation sampling is an efficient and easily implemented 2-phase adaptive sampling design that targets field effort to rare species and is logistically feasible. The population is partitioned into strata that contain (secondary) units, and a simple random sample of secondary units is selected from each of the strata. If an individual is observed in any selected unit, all the units in its stratum will then be sampled in the second phase. However, the condition of observing at least 1 individual in a unit to survey all units in its stratum might be too restrictive for some populations and too expensive. We extend the design 2 ways. First, we introduce a 2-stage sampling scheme with primary units taking over the role of strata and taking a random sample of primary units. A simple random sample of the secondary units in each selected primary unit is then carried out and if any more than a certain number of rare units (and not just any) are found, the whole primary unit is sampled. This more general criterion for selection is the second extension. If we choose all the primary units, then we are back to complete allocation sampling with strata. We derive an unbiased estimator for the total and its variance estimator for this new 2-stage design. Using a real-life population of buttercups, we show that this 2-stage design observes more buttercups and its estimator can be considerably more precise compared to its conventional sampling design counterpart.