On the Validity of Inferences from Non-random Sample

SUMMARY Random sampling schemes satisfy the conditions for ignoring the selection mechanism in a model-based approach to inference in an observational study, such as a sample survey. In many studies non-random sampling is employed. Conditions for ignoring non-random selection mechanisms are examined. Particular attention is paid to post- statification and to quota sampling. Randomization, whether in the application of treatments to experimental material or in the selection of units to be observed in a sample survey, is one of the most important contributions of statistics to science. The arguments for randomization are twofold. The first, and most important for science, is that randomization eliminates personal choice and hence eliminates the possibility of subjective selection bias. The second is that the randomization distribution provides a basis for statistical inference. The question for scientists is whether such statistical inferences are relevant for scientific inference. In most of applied science any uncertainty in nature is represented by a stochastic model of the phenomenon under study. The problems of statistical inference are then the problems of testing the fit of alternative models and of making inferences about the parameters of a given model. Even when randomization is employed the randomization distribution plays no direct role in this type of statistical inference. However, the selection of the units to be studied can affect