Functional MRI is aimed at localizing cortical activity to understand the role of specific cortical regions, providing insight into the neurophysiological underpinnings of brain function. Scientists developing fMRI methodology seek to improve detection of subtle activations and to spatially localize these activations more precisely. Except for applications in the clinical environment, such as functional mapping in patients prior to neurosurgical intervention, most basic neuroscience studies involve group level random-effects analyses. Prior to grouping data, the data from each individual are typically smoothed. A wide range of motivations for smoothing have been given including to match the spatial scale of hemodynamic responses, to normalize the error distribution (by the Central Limit Theorem) to improve the validity of inferences based on parametric tests, and, in the context of inter-subject averaging smoothing has been shown necessary to project the data down to a scale where homologies in functional anatomy are expressed across subjects. This work demonstrates that, for single-subject studies, if smoothing is to be employed, the data should be acquired at lower resolutions to maximize SNR. The benefits of a low-resolution acquisition are limited by partial volume effects and by the weak impact of resolution-dependent noise on the overall group level statistics. Given that inter-subject noise dominates across a range of tasks, improvements in within-subject noise, through changes in acquisition strategy or even moving to higher field strength, may do little to improve group statistics. Such improvements however may greatly impact single-subject studies such as those used in neurosurgical planning.