# Inference with interference between units in an fMRI experiment of motor inhibition 

Xi Luo, Dylan S. Small, Chiang-shan R. Li, Paul R. Rosenbaum 1 

University of Pennsylvania, Philadelphia 

Abstract. An experimental unit is an opportunity to randomly apply or withhold a treatment. There is interference between units if the application of the treatment to one unit may also a⁄ect other units. In cognitive neuroscience, a common form of experiment presents a sequence of stimuli or requests for cognitive activity at random to each experimental subject and measures biological aspects of brain activity that follow these requests. Each subject is then many experimental units, and interference between units within an experimental subject is likely, in part because the stimuli follow one another quickly and in part because human subjects learn or become experienced or primed or bored as the experiment proceeds. We use a recent fMRI experiment concerned with the inhibition of motor activity to illustrate and further develop recently proposed methodology for inference in the presence of interference. A simulation evaluates the power of competing procedures. 

Keywords: Attributable e⁄ects; interference between units; placements; randomized experi- ment. 

