and Salsburg have no obvious interpretation, so they cannot be used as the basis for an attributable e⁄ect. It turns out, however, that Conover and SalsburgGLYPH<146>s ranks are almost the same as ranks proposed by Stephenson (1981); see also related work by Deshpande and Kochar (1980) and Stephenson and Gosh (1985). Using StephensonGLYPH<146>s ranks, a conGLYPH<133>dence interval for attributable e⁄ects becomes available (Rosenbaum 2007b), thereby permitting inference about the magnitude of the e⁄ect in the presence of interference. Although the main goal is to illustrate these three ideas in the context of an fMRI experiment, along the way a technical issue arises. The experiment is not a perfectly balanced design, and for unbalanced designs the attributable e⁄ect has a more natural interpretation if it is not formulated in terms of a linear rank statistic, but rather in terms of a linear placement statistic in the sense of Orban and Wolfe (1982), which is a form of nonlinear rank statistic. Because perfect balance is di¢ cult to achieve in cognitive neuroscience experiments, we develop the formalities in terms of the placement statistics that are most likely to be useful in practice. 1.3 A randomized experiment in the cognitive neuroscience of motor inhibition In the experiment by Duann, Ide, Luo and Li (2009), each of 58 experimental subjects was observed in four experimental sessions that were each about ten minutes in length. At random times during a session, a trial began, with a median of 97 trials per session. With probability 3 $_{4}$, the trial was a GLYPH<147>go trial:GLYPH<148>a dot was presented on a screen, and after a interval of time of random length, the dot became a circle signifying that the subject was to quickly press a button. With probability 1 $_{4}$, the trial was a GLYPH<147>stop trial:GLYPH<148>the trial began as a go trial, but brieGLYPH<135>y after the circle appeared it was replaced by an X signifying GLYPH<147>do not press the button.GLYPH<148> In a stop trial, the subject is instructed to do something, and then the instruction is cancelled. Here, an experimental unit is a trial, with stop trials called 6