Spatial normalization of diffusion tensor images plays a key role in voxel-based analysis of white matter (WM) group differences. Currently, it has been achieved using low-dimensional registration methods in the large majority of clinical studies. This paper aims to motivate the use of high-dimensional normalization approaches by generating evidence of their impact on the findings of such studies. Using an ongoing amyotrophic lateral sclerosis (ALS) study, we evaluated three normalization methods representing the current range of available approaches: low-dimensional normalization using the fractional anisotropy (FA), high-dimensional normalization using the FA, and high-dimensional normalization using full tensor information. Each method was assessed in terms of its ability to detect significant differences between ALS patients and controls. Our findings suggest that inadequate normalization with low-dimensional approaches can result in insufficient removal of shape differences which in turn can confound FA differences in a complex manner, and that utilizing high-dimensional normalization can both significantly minimize the confounding effect of shape differences to FA differences and provide a more complete description of WM differences in terms of both size and tissue architecture differences. We also found that high-dimensional approaches, by leveraging full tensor features instead of tensor-derived indices, can further improve the alignment of WM tracts.