ABSTRACT
One idea, often discussed in the statistical literature, takes the cases for which data are available to be a subset of a larger population of cases and intends a generalization to that population. The conceptual frameworkof statistical variables allows an explicit formulation. Suppose a statistical variable, say X : −→ X , represents the available data. This allows statistical statements about the reference set , basically statements about P[X ], the distribution of X in . The reference set of the data, , is then considered as a subset of a larger population † for which an analogously defined variable, say X † : † −→X , can be assumed. The goal of the generalization is a statement about P[X †], the distribution of X † in the population †, or some quantity derived from that distribution. For example, under certain circumstances it might be reasonable to believe that P[X †] ≈ P[X ]. In any case, the result is a descriptive statement about the distribution of X † in the population for which the generalization is desired; the approach will therefore be called descriptive generalization.
