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.

中文翻译：

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空间抽样调查的统计方法：持续存在的误解和新发展

关于基于经典抽样理论的基于设计的抽样和统计推断方法的一些误解似乎相当持久。这些误解是对基本统计概念（例如估计量或预测量的独立性、期望以及偏差和方差）混淆的结果。这些概念在基于设计和基于模型的方法中具有不同的含义，因为它们考虑了不同的随机源。此外，总体均值仍然经常与模型均值以及总体方差与模型方差相混淆，从而导致总体均值估计量方差的公式无效。在本文中，通过模拟说明了这两种方法之间的根本区别，希望更多的计步师能够更好地理解这个主题。概述了如何在基于设计的方法中利用研究变量的空间结构知识。在第二部分中，描述了基于设计和基于模型的方法的新发展，它们试图结合这两种方法的优势。