We give a brief overview of common sampling designs used in a survey setting, and introduce the principal inferential paradigms under which data from complex surveys may be analyzed. In particular, we distinguish between design-based, model-based and model-assisted approaches. Simple examples highlight the key differences between the approaches. We discuss the interplay between inferential approaches and targets of inference and the important issue of variance estimation.
"Introduction to the Design and Analysis of Complex Survey Data." Statist. Sci. 32 (2) 165 - 175, May 2017. https://doi.org/10.1214/17-STS614