There has been much recent interest in using magnetic resonance diffusion imaging to provide information about anatomical connectivity in the brain, by measuring the anisotropic diffusion of water in white matter tracts. One of the measures most commonly derived from diffusion data is fractional anisotropy (FA), which quantifies how strongly directional the local tract structure is. Many imaging studies are starting to use FA images in voxelwise statistical analyses, in order to localise brain changes related to development, degeneration and disease. However, optimal analysis is compromised by the use of standard registration algorithms; there has not to date been a satisfactory solution to the question of how to align FA images from multiple subjects in a way that allows for valid conclusions to be drawn from the subsequent voxelwise analysis. Furthermore, the arbitrariness of the choice of spatial smoothing extent has not yet been resolved. In this paper, we present a new method that aims to solve these issues via (a) carefully tuned non-linear registration, followed by (b) projection onto an alignment-invariant tract representation (the "mean FA skeleton"). We refer to this new approach as Tract-Based Spatial Statistics (TBSS). TBSS aims to improve the sensitivity, objectivity and interpretability of analysis of multi-subject diffusion imaging studies. We describe TBSS in detail and present example TBSS results from several diffusion imaging studies.