Simple Latin Square Sampling + 1: A Spatial Design Using Quadrats

Good sample coverage is often an essential component to observational studies of biological species or communities. Whether the goals of the survey center on pattern recognition and prediction or parameter estimation, designs which ensure the sample is spread over the region of interest may provide more information than schemes that do not. This additional information could be qualitative in nature; for example, the investigator gleans a deeper understanding of the biological system. Alternatively, good coverage could translate to better precision in estimating parameters associated with the system. We present a new class of spatial sampling designs, simple latin square sampling + 1. Our approach is quadrat-based in that the study region is partitioned into nonoverlapping quadrats or sampling units from which a sample or subset of units is selected. The design falls into the classical sampling framework in that the sample selection probabilities are independent of the underlying variable(s) of interest. We illustrate that estimators generated by the design are generally more efficient than those from simple random samples and certain systematic designs when spatial autocorrelation among units is suspected or known to exist. Further, our design can provide better sample coverage than either of the latter designs.