Journal of Data Science

Abstract: An individual in a finite population is represented by a random variable whose expectation is linearly composed of explanatory variables and a personal effect. This expectation locates her (his) random variable on a scale when s(he) responds to a questionnaire item or physical instrument. This formulation reinterprets design-based sampling, which represents an individual as a constant waiting to be observed. Retaining constant expecta tions , however, along with fixed realizations of random variables, preserves and strengthens design-based theory through the Horvitz-Thompson (1952) theorem. This interpretation reaffirms the usual design-based regression es timates, whose normality is seen to be free of any assumptions about the distribution of the outcome variable. It also formulates response error in a way that renders a superpopulation, postulated by model-based sampling, unnecessary. The value of distribution-free regression is illustrated with an analysis of American presidential approval.