Inference for superpopulation parameters using sample surveys

Sample survey inference is historically concerned with finite-population parameters, that is, functions (like means and totals) of the observations for the individuals in the population. In scientific applications, however, interest usually focuses on the "superpopulation" parameters associated with a stochastic mechanism hypothesized to generate the observations in the population rather than the finite-population parameters. Two relevant findings discussed in this paper are that (1) with stratified sampling, it is not sufficient to drop finite-population correction factors from standard design-based valiance formulas to obtain appropriate variance formulas for superpopulation inference, and (2) with cluster sampling, standard design-based variance formulas can dramatically underestimate superpopulation variability, even with a small sampling fraction of the final units. A literature review of inference for superpopulation parameters is given, with emphasis on why these findings have not been previously appreciated. Examples are provided for estimating superpopulation means, linear regression coefficients and logistic regression coefficients using U.S. data from the 1987 National Health Interview Survey, the third National Health and Nutrition Examination Survey and the 1986 National Hospital Discharge Survey.