Comparison of relative efficiencies of sampling plans excluding certain neighboring units: a simulation study

Abstract

Ecological and environmental studies frequently involve work in settings where some physical conditions influence the effectiveness of standard sampling plans. These studies may require expensive and time-consuming sampling processes. These conditions motivate researchers to find sampling plans that provide the highest precision at the lowest cost. Several sampling plans that exclude some types of ‘neighboring’ units are discussed in this article. Sampling of this type is called sampling excluding neighboring units and is a two-dimensional adaptation of balanced sampling excluding contiguous units [Hedayat, A.S., Rao, C.R. and Stufken, J., 1988, Sampling designs excluding contiguous units. Journal of Statistical Planning and Inference, 19, 159–170]. Key features of this article are: (i) the construction of sampling plans designed to yield representative samples by avoiding the simultaneous selection of units that are, in some sense, neighbors; (ii) a simulation study which compares the relative efficiencies of these sampling plans on the basis of different correlations and sample sizes. In this study, we assume that correlations (or correlated errors) between units decrease as a function of the distance between units. The construction of a sampling plan is illustrated using actual data from a 1998 field study, which examined the insect species assemblage in a beech-maple forest.