Abstract Voxelwise analysis of white matter properties typically relies on scalar measurements derived, for example, from a tensor model fit to diffusion MRI data. These are spatially matched across subjects prior to statistical modelling. In this paper, we show why and how this can be improved through the use of directionally dependent measurements. In the case where different orientations relate to different fibre populations (e.g., in the presence of crossing fibres), distinguishing and matching those populations of fibres across subjects are important prior to any statistical modelling. It allows one to compare measurements that are related to the same fibres across subjects. We show how this framework applies to the parameters of a crossing fibre model and discuss its implications for voxelwise analysis of the white matter.