Random sampling and randomized experimentation are inextricably linked. Beginning with their common origins in the work of Fisher and Neyman from the 1920s and the 1930s, one can trace the development of parallel concepts and structures in the two areas (see Fienberg and Tanur [Bull. Int. Stat. Inst. 51 (1985) Art. ID 10.1; Int. Stat. Rev. 55 (1987) 75–96]). One of the more important lessons to be learned from the parallel concepts and structures is that they can profitably be linked and intertwined, with sampling embedded in experiments and formal experimental structures embedded in sampling designs.
In this paper, we trace some of parallels between sampling theory and theory of experimental design. We then explore some of the ways that experimental and sampling structures have been combined in statistical practice and the principles that underlie their combination; we also make some suggestions toward the improvement of practice.
"The interlocking world of surveys and experiments." Ann. Appl. Stat. 12 (2) 1157 - 1179, June 2018. https://doi.org/10.1214/18-AOAS1184