The dramatic effect of preferential sampling of spatial data on variance estimates

Classic probability-based designs are widely used for spatial sampling in environmental research. When sampling over large regions researchers may wish to preferentially sample some sites due to ease of access. If such non-standard probability designs are implemented, Horvitz-Thompson analysis provides unbiased estimates for spatial means and variances provided first and second order inclusion probabilities can be evaluated. However, even with minor departures from standard designs the effect of preferential sampling on the sampling variance can be dramatic. We find significant increases in sampling variance as sampling becomes more and more preferential. We conclude that some non-standard designs can result in significantly weaker sampling performance and recommend they be examined by simulation prior to implementation.