Head movement during functional magnetic resonance imaging (fMRI) degrades data quality. The effects of small movements can be ameliorated during data postprocessing, but data associated with severe movement is frequently discarded. In discarding these data, it is often assumed that head-movement is a source of random error, and that data can be discarded from subjects with severe movement without biasing the sample. We tested this assumption by examining whether head movement was related to task difficulty and cognitive status among persons with multiple sclerosis (MS). Thirty-four persons with MS were scanned while performing a working memory task with three levels of difficulty (the N-back task). Maximum movement (angle, shift) was estimated for each difficulty level. Cognitive status was assessed by combining performance on a working memory and processing speed task. An interaction was found between task difficulty and cognitive status (high vs. low cognitive ability): there was a linear increase in movement as task difficulty increased that was larger among subjects with lower cognitive ability. Analyses of the signal-to-noise ratio (SNR) confirmed that increases in movement degraded data quality. Similar, though far smaller, effects were found in a cohort of healthy control (HC) subjects. Therefore, discarding data with severe movement artifact may bias MS samples such that only those with less-severe cognitive impairment are included in the analyses. However, even if such data are not discarded outright, subjects who move more (MS and HC) will contribute less to the group-level results because of degraded SNR. Hum Brain Mapp 35:1–13, 2014. © 2012 Wiley Periodicals, Inc.