fMRI response. Salsburg (1986), Conover and Salsburg (1988) and Rosenbaum (2007b) consider rank tests that are particularly e⁄ective when only a subset of experimental units respond to treatment. These rank tests score the ranks in such a way that little weight is given to lower ranks. In the current paper, a similar approach is taken in studies with interference between units. 

When a region of the brain is stimulated to activity, the change in blood oxygenation measured by fMRI is not immediate. There is a brief delay, perhaps a dip, for about 2 sec- onds, followed by a sharp rise, a sharp fall to slightly below baseline, followed by a gradual return to baseline; see Lindquist (2008, Figure 3). This curve is known as the hemodynamic response function (HRF). We use the form developed by Friston et al. (1998), speciGLYPH<133>cally a weighted di⁄erence of two gamma densities, GLYPH<13> ( x ; !; # ) = # $^{!}$x $^{!}$GLYPH<0> $^{1}$exp ( GLYPH<0> #x ) = GLYPH<0> ( ! ) , both with parameter # = 1 = 16 , and with shape parameters !$_{1}$ = 6 and !$_{2}$ = 16 , speciGLYPH<133>cally the function hrf ( x ) = GLYPH<13> (16 x ; 6 ; 1 = 16) GLYPH<0> GLYPH<13> (16 x ; 16 ; 1 = 16) = 6 where x is in seconds. Although we do not report these results, we tried a second form for the HRF with a similar shape but built from inverse logit functions (Lindquist and Wager 2007), obtaining qualitatively similar results in a table parallel to Table 2. 

Recall that the measurements in Figure 1 occur at two second intervals. Evaluating the hemodynamic response function, hrf ( x ) , at two-second intervals, we computed 17 weights for 17 two-second intervals that follow each trial, that is, for the 2 GLYPH<2> 17 = 34 seconds that follow a trial. These weights sum to one. The GLYPH<133>rst weight is zero, the third and fourth weights are the largest (.375 and .385), and beginning at the eighth the weights turn slightly negative (weight eight is GLYPH<0> 0 : 031 ) gradually returning to zero (weight 17 is GLYPH<0> 0 : 0001 ). At the end of a session, if fewer than 17 two-second intervals remained, we used the remaining intervals and renormalized the weights so that they again summed to one. For a region such as STN in Figure 1, after each trial, we computed the sum of the HRF 

