ABSTRACT
The fundamental theory and practical procedures for estimation and inference for complex sample survey data have been under development for almost a century. The foundations are present in the work on randomization and the "representative method" and what is generally agreed to be the breakthrough paper by Neyman on the theory of design-based inference from probability sample designs. This chapter talks about finite populations and a superpopulation model, two theoretical concepts that have only subtle implications for how the survey data are actually analyzed but are important concepts for interpretation and reporting of the survey findings. Confidence intervals (CIs) are a primary tool for presenting survey estimates and the corresponding degree of uncertainty due to population sampling. The chapter discusses the CI as the organizing framework for discussion of the three main components of design-based inference: weighted sample estimates of population statistics.
