A study of variance estimation methods for systematic spatial sampling

•Three estimators for variance in systematic spatial samples were compared.•A correction factor based on the autocorrelation often underestimated the variance.•A local stratified estimator and a model-based prediction both gave good estimates.

An undesirable property of systematic spatial sampling is that there is no known method allowing unbiased estimation of the uncertainty of statistical estimates from these surveys. A number of alternative variance estimation methods have been tested and reported by various authors. Studies comparing these estimators are inconclusive, partly because the studies compare different sets of estimators. In this paper, three estimators recommended in recent studies are compared using a single test dataset with known properties.The first estimator compared in this study (ST4) is based on post-stratification of the data. The second estimator (V08) is using a predetermined correction factor calculated from the spatial autocorrelation. The third estimator (MB) is a model based prediction calculated using values from the semivariogram. MB and ST4 were both found to be fairly accurate, while V08 consistently underestimated the variance in this study. V08 relies on the assumption that the autocorrelation structure in the dataset can be described using a particular exponential function. The most likely explanation of the weak result for V08 is that this assumption is violated by the empirical data used in the experiment. A better correction factor can be calculated, but the safe approach is to use MB or ST4.