arXiv:1110.6560v2 [stat.ME] 10 Jan 2017 Inference with interference between units in an fMRI experiment of motor inhibition Xi Luo, Dylan S. Small, Chiang-shan R. Li, Paul R. Rosenbaum 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. $^{1}$Address for correspondence: Xi Luo is assistant professor in the Department of Biostatistics at Brown University. Dylan S. Small is associate professor and Paul R. Rosenbaum is professor in the Department of Statistics, The Wharton School, University of Pennsylvania, 473 Jon M. Huntsman Hall, 3730 Walnut Street, Philadelphia, PA 19104-6340 US. Chiang-Shan R. Li is associate professor of psychiatry and neurobiology, Department of Psychiatry, Yale University, CMHC S103, 34 Park Street, New Haven, CT 06519 US. This work was supported by grants from the Measurement, Methodology and Statistics Program of the U.S. National Science Foundation. Imaging data were collected under the support of NIH grants R01DA023248, K02DA026990 and R21AA018004. 11 August 2011 E-mail: xluo@stat.brown.edu . 1