Summary. A different approach to statistical inference is outlined based not on a probabilistic model of the data-generating process but on the randomization used in study design. The implications of this are developed in simple cases, first for sampling and then for the design of experiments.

General remarks

The discussion throughout the book so far rests centrally on the notion of a probability model for the data under analysis. Such a model represents, often in considerably idealized form, the data-generating process. The parameters of interest are intended to capture important and interpretable features of that generating process, separated from the accidental features of the particular data. That is, the probability model is a model of physically generated variability, of course using the word ‘physical’ in some broad sense. This whole approach may be called model-based.

In some contexts of sampling existing populations and of experimental design there is a different approach in which the probability calculations are based on the randomization used by the investigator in the planning phases of the investigation. We call this a design-based formulation.

Fortunately there is a close similarity between the methods of analysis emerging from the two approaches. The more important differences between them concern interpretation of the conclusions. Despite the close similarities it seems not to be possible to merge a theory of the purely design-based approach seamlessly into the theory developed earlier in the book.