A new approach to analyzing macromolecular single-crystal X-ray diffraction intensity statistics is presented. Instead of considering reflections in resolution shells, differences between local pairs of reflection intensities are taken and normalized separately. When the two reflections to be compared (having intensities I(1) and I(2), respectively) are chosen appropriately, the behavior of the parameter L = (I(1) - I(2))/(I(1) + I(2)) is insensitive to phenomena that tend to confound traditional intensity statistics, such as anisotropic diffraction and pseudo-centering. The distributions and expected values for L take simple forms when the intensity data are from ordinary crystals or from perfectly twinned specimens. The robustness of the approach is demonstrated with examples using real proteins whose diffraction data appear aberrant by other methods of intensity analysis. The new statistic is better suited than other available methods for diagnosing perfect hemihedral twinning.