Motion during the acquisition of magnetic resonance imaging (MRI) data degrades image quality, hindering our capacity to characterise disease in patient populations. Quality control procedures allow the exclusion of the most affected images from analysis. However, the criterion for exclusion is difficult to determine objectively and exclusion can lead to a suboptimal compromise between image quality and sample size. We provide an alternative, data-driven solution that assigns weights to each image, computed from an index of image quality using restricted maximum likelihood. We illustrate this method through the analysis of quantitative MRI data. The proposed method restores the validity of statistical tests, and performs near optimally in all brain regions, despite local effects of head motion. This method is amenable to the analysis of a broad type of MRI data and can accommodate any measure of image quality.