The diffuse field assumption employed in basic statistical energy analysis (SEA) and in statistical room acoustics is violated for source and receiver positions close to boundaries or discontinuities. A simple approach is proposed to include the correction initially suggested by Waterhouse based on spherical Bessel functions in SEA predictions for rectangular rooms. With this modification the SEA results will be augmented by a position dependence and an additional frequency dependence. The approach is applied and demonstrated also for plate-like structures with different boundary conditions. An analytical solution is shown for the corner position on a simply supported plate and for edge positions on plates with more complex boundary conditions. The validity of the approach is confirmed by means of comparisons with modal analysis and finite element calculations.