Precise and accurate quantification of whole-brain atrophy based on magnetic resonance imaging (MRI) data is an important goal in understanding the natural progression of neurodegenerative disorders such as Alzheimer's disease and multiple sclerosis. We found that inconsistent MRI positioning of subjects is common in typically acquired clinical trial data - particularly along the magnet's long (i.e., Z) axis. We also found that, if not corrected for, the gradient distortion effects associated with such Z-shifts can significantly decrease the accuracy and precision of MRI-derived measures of whole-brain atrophy - negative effects that increase in magnitude with (i) increases in the Z-distance between the brains to be compared and (ii) increases in the Z-distance from magnet isocenter of the center of the pair of brains to be compared. These gradient distortion effects can be reduced by accurate subject positioning, and they can also be corrected post hoc with the use of appropriately-generated gradient-distortion correction fields. We used a novel DUPLO-based phantom to develop a spherical-harmonics-based gradient distortion field that was used to (i) correct for observed Z-shift-associated gradient distortion effects on SIENA-generated measures of brain atrophy and (ii) simulate the gradient distortion effects that might be expected with a greater range of Z-shifts than those that we were able to acquire. Our results suggest that consistent alignment to magnet isocenter and/or correcting for the observed effects of gradient distortion should lead to more accurate and precise estimates of brain-related changes and, as a result, to increased statistical power in studies aimed at understanding the natural progression and the effective treatment of neurodegenerative disorders.