ABSTRACT
This chapter explains the fundamental differences between design-based and the model-based approach for sampling and statistical inference. In the design-based approach, the random process is the random selection of sampling units, whereas in the model-based approach randomness is introduced via the statistical model of the spatial variation. The spatial variation model used in the model-based approach contains two terms, one for the mean (deterministic part) and one for the error with a specified probability distribution. In the design-based approach, only one population is considered, the one sampled, but the statistical inference is based on all samples that can be generated by a probability sampling. Bias and variance are commonly used statistics to quantify the quality of an estimator. Bias quantifies the systematic error, variance the random error of the estimator. The model-assisted approach is a hybrid approach in between the design-based and the model-based approach.
