  Nonlinear systems are often subject to random influences. Sometimes the noise
enters the system through physical boundaries and this leads to stochastic
dynamic boundary conditions. A dynamic, as opposed to static, boundary
condition involves the time derivative as well as spatial derivatives for the
system state variables on the boundary. Although stochastic \emph{static}
(Neumann or Dirichet type) boundary conditions have been applied for stochastic
partial differential equations, not much is known about the dynamical impact of
stochastic \emph{dynamic} boundary conditions. The purpose of this paper is to
study possible impacts of stochastic dynamic boundary conditions on the long
term dynamics of the Cahn-Hilliard equation arising in the materials science.
We show that the dimension estimation of the random attractor increases as the
coefficient for the dynamic term in the stochastic dynamic boundary condition
decreases. However, the dimension of the random attractor is not affected by
the corresponding stochastic static boundary condition.
