Psychology is focused on variation between cases (interindividual variation). Results thus obtained are considered to be generalizable to the understanding and explanation of variation within single cases (intraindividual variation). It is indicated, however, that the direct consequences of the classical ergodic theorems for psychology and psychometrics invalidate this conjectured generalizability: only under very strict conditions--which are hardly obtained in real psychological processes--can a generalization be made from a structure of interindividual variation to the analogous structure of intraindividual variation. Illustrations of the lack of this generalizability are given in the contexts of psychometrics, developmental psychology, and personality theory. (Contains 3 footnotes.)