Abstract
AbstractSeveral 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.Highlights Ignorance of fundamental differences between design‐based and model‐based approaches still cause errors in statistical inference. Basic statistical concepts such as independence, variance and bias of an estimator have a different meaning in the two approaches. In estimating and testing it is important to distinguish population parameters from model parameters. Hybrid methods that combine the strengths of the two approaches are reviewed.
Highlights
In 1990, de Gruijter and ter Braak (1990) published their ground-breaking paper about the fundamental difference between the design-based approach for spatial sampling and inference, based on classical sampling theory, and the model-based approach, based on geostatistical theory
There is ongoing confusion about the design-based approach for spatial sample surveys, which has led to new publications with wrong formulas for the variance of an estimated population mean and the required sample size
The confusion is caused by ignorance of the fundamental difference between the design-based and modelbased approaches due to the different sources of randomness that are accounted for in the two approaches
Summary
In 1990, de Gruijter and ter Braak (1990) published their ground-breaking paper about the fundamental difference between the design-based approach for spatial sampling and inference, based on classical sampling theory, and the model-based approach, based on geostatistical theory. According to de Gruijter, Brus, Bierkens, and Knotters (2006) the choice between the design-based and model-based approach is the most important decision to be taken in designing sampling schemes. Since quite a few publications appeared in which the old misconceptions popped up again Among these are papers of widely acknowledged spatial statisticians, so that there is a serious risk that the more applied pedometricians get confused again. A second reason for writing this paper is that there are several new developments in spatial sample survey, in both the design-based and model-based approach, trying to combine the strengths of the two approaches, which seem to be unnoticed by many pedometricians until now. The aim of this paper, is to unravel once more the misconceptions about the design-based approach and to draw the attention of pedometricians to new developments in this area
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