Surface plasmon polaritons (SPPs) and diffraction effects such as Rayleigh anomalies (RAs) play key roles in the transmission of light through periodic subwavelength hole arrays in metal films. Using a combination of theory and experiment we show how refractive index (RI) sensitive transmission features arise from hole arrays in thin gold films. We show that large transmission amplitude changes occur over a narrow range of RI values due to coupling between RAs and SPPs on opposite sides of the metal film. Furthermore, we show how to predict, on the basis of a relatively simple analysis, the periodicity and other system parameters that should be used to achieve this "RA-SPP" effect for any desired RI range.