  Averaging is an important method to extract effective macroscopic dynamics
from complex systems with slow modes and fast modes. This article derives an
averaged equation for a class of stochastic partial differential equations
without any Lipschitz assumption on the slow modes. The rate of convergence in
probability is obtained as a byproduct. Importantly, the deviation between the
original equation and the averaged equation is also studied. A martingale
approach proves that the deviation is described by a Gaussian process. This
gives an approximation to errors of $\mathcal{O}(\e)$ instead of
$\mathcal{O}(\sqrt{\e})$ attained in previous averaging.
