An important consideration when designing hybrid algorithms is how the coupling of two different types of solvers impacts the accuracy of the individual methods. For the most part, the development and testing of hybrids or Algorithm Refinement schemes have focused on the mean behavior of system states. In a fluid hybrid this may be for example the average density or temperature. Yet simulations of many systems may require the computation of the higher moments (e.g., variances) of these quantities, which capture spontaneous fluctuations. This is important for modeling phenomena where the microscopic fluctuations drive a macroscopic phenomenon. For example, fluctuations initiate onset of instabilities and the nucleation of phase transitions out of a metastable state. This article discusses the effects, both positive and negative, of statistical fluctuations on hybrid computational methods, focusing on schemes that combine a particle algorithm with a partial differential equation solver.