  We introduce the notion of "separation of conditions" meaning that a
description of statistical data obtained from experiments, performed under a
set of different conditions, allows for a decomposition such that each partial
description depends on mutually exclusive subsets of these conditions.
Descriptions that allow a separation of conditions are shown to entail the
basic mathematical framework of quantum theory. The Stern-Gerlach and the
Einstein-Podolsky-Rosen-Bohm experiment with three, respectively nine possible
outcomes are used to illustrate how the separation of conditions can be used to
construct their quantum theoretical descriptions. It is shown that the
mathematical structure of separated descriptions implies that, under certain
restrictions, the time evolution of the data can be described by the von
Neumann/Schr\"odinger equation.
