Evidence for the presence of undulations or temperature variations, or both, at the core-mantle boundary comes from the remarkably high correlation between the pattern of long-wavelength gravitational anomalies and the corresponding pattern of anomalies in the geomagnetic potential when the latter is rotated in longitude. Since gravitational anomalies originate at or above the core surface and the magnetic anomalies originate within the core, the correlation, if statistically significant, must be a manifestation of processes occurring at the core-mantle interface and has important implications for the structure and dynamics of the Earth's deep interior. Indeed, the discovery of the correlation stemmed from considerations of interactions between motions in the core and mantle and can be regarded as evidence in favour of deep mantle convection. The large value for the correlation coefficient is now accepted but, notwithstanding our published statistical tests to the contrary, opinions are often expressed in the literature that any low-order convergent field might be expected to show a high correlation with gravity when rotated to the optimum position. Here we reiterate that this is not so, and illustrate our argument with a number of randomly generated field models that have correlation coefficients from 0.2 to 0.8.