Statistical approaches for spatial sample survey: Persistent misconceptions and new developments

Several misconceptions about the design-based approach for sampling and statistical inference, based on classical sampling theory, seem to be quite persistent. These misconceptions are the result of confusion about basic statistical concepts such as independence, expectation, and bias and variance of estimators or predictors. These concepts have a different meaning in the design-based and model-based approach, because they consider different sources of randomness. Also, a population mean is still often confused with a model mean, and a population variance with a model-variance, leading to invalid formulas for the variance of an estimator of the population mean. In this paper the fundamental differences between these two approaches are illustrated with simulations, so that hopefully more pedometricians get a better understanding of this subject. An overview is presented of how in the design-based approach we can make use of knowledge of the spatial structure of the study variable. In the second part, new developments in both the design-based and model-based approach are described that try to combine the strengths of the two approaches.