Allocating Sampling Effort among Strata
After deciding to use stratify random sampling, we need to decide how to divide sampling effort among different strata; that process is called allocation. When deciding where to expend effort, the question becomes how best to allocate sampling effort among strata so that the sampling process will be the most efficient balance of effort, cost, and precision. Should we allocate the same sampling effort to
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each stratum? If strata are of different sizes, as is usually the case, should we allocate more effort to larger stratum? There are many strategies for allocating sampling effort, and the more information available about the population of interest, the more efficient the allocation strategy can be. Information on the variability of samples within each stratum, the relative cost of obtaining a sample from each stratum, and the number of sample units in each stratum can all help to increase sampling efficiency. Some of the most common allocations strategies are uniform, proportional to size, variation, and cost, and optimal, which simultaneously considers size, variation, and cost or whichever combination of those is available. All strategies function by create a simple proportional multiplier by which a fixed number of samples can be allocated among strata. Uniform Allocation The simplest allocation strategy is to select the same number of samples from each stratum, which is an ideal approach if there is no information available about variability of units within strata, the cost of sampling is similar for all strata, and strata are of similar size. Allocation Proportional to Size or Variation The number of sample units to select from each stratum can be made proportional to the number of sample units (or size) within each stratum. Variation in a stratum often increases with a the size of a stratum, so in some cases this approach can be considered as a rough approach for allocating more effort to strata that are likely to be more variable strata. To allocation proportional to stratum size: