This article proposes a new measure called Apparent Fibre Density (AFD) for the analysis of high angular resolution diffusion-weighted images using higher-order information provided by Fibre Orientation Distributions (FODs) computed using spherical deconvolution. AFD has the potential to provide specific information regarding differences between populations by identifying not only the location, but also the orientations along which differences exist. In this work, analytical and numerical Monte-Carlo simulations are used to support the use of the FOD amplitude as a quantitative measure (i.e. AFD) for population and longitudinal analysis. To perform robust voxel-based analysis of AFD, we present and evaluate a novel method to modulate the FOD to account for changes in fibre bundle cross-sectional area that occur during spatial normalisation. We then describe a novel approach for statistical analysis of AFD that uses cluster-based inference of differences extended throughout space and orientation. Finally, we demonstrate the capability of the proposed method by performing voxel-based AFD comparisons between of a group of Motor Neurone Disease patients and healthy control subjects. A significant decrease in AFD was detected along voxels and orientations corresponding to both the corticospinal tract and corpus callosal fibres that connect the primary motor cortices. In addition to corroborating previous findings in MND, this study demonstrates the clear advantage of using this type of analysis by identifying differences along single fibre bundles in regions containing multiple fibre populations.