  This paper addresses the problem of how much information we can extract
without disturbing a statistical experiment, which is a family of partially
known normal states on a von Neumann algebra. We define the classical part of a
statistical experiment as the restriction of the equivalent minimal sufficient
statistical experiment to the center of the outcome space, which, in the case
of density operators on a Hilbert space, corresponds to the classical
probability distributions appearing in the maximal decomposition by Koashi and
Imoto [Phys.~Rev.~A $\textbf{66}$, 022318 (2002)]. We show that we can access
by a Schwarz or completely positive channel at most the classical part of a
statistical experiment if we do not disturb the states. We apply this result to
the broadcasting problem of a statistical experiment. We also show that the
classical part of the direct product of statistical experiments is the direct
product of the classical parts of the statistical experiments. The proof of the
latter result is based on the theorem that the direct product of minimal
sufficient statistical experiments is also minimal sufficient.
