model and is not a randomization inference, so there is no reason to expect that it will have the correct level when there is no treatment e⁄ect but the parametric model is false. Indeed, in nominal 0.05 level tests in our simulation, true null hypotheses of no e⁄ect were rejected more often than 5% of the time, in some cases with probabilities as high as 30%. In light of this, a power comparison is not appropriate. It is not a fault of the SPM method that it does not control the type one error rate when the null hypothesis of no e⁄ect is true but the model itself is false; that type of error control is not expected from standard parametric inference. Presumably, a careful user of the SPM approach would check for model failures using residuals and diagnostics, and alter the parametric model in appropriate ways. Nonetheless, it is convenient that the randomization inferences in §3 do control the type one error rate at 5% in the presence of autocorrelation, interference between units, unsuccessful trials and error distributions (such as the t -distribution with 2 degrees of freedom) that lack a GLYPH<133>nite variance. 5.4 Alternative designs and power The simulation has compared the power of di⁄erent statistics in given situations with interference. Another potential source of increased power entails alternative experimental designs which alter the degree of interference by altering the time interval between trials. In the absence of interference, we generally expect more power with more trials, so naively we might expect increased power from ever more trials ever more rapidly paced. However, in cross-over designs, it is also commonly said that interference should be reduced by allowing time for a wash-out period between trials. In particular, it is possible that few trials with more time between them would yield less interference and fMRI activity that is more sharply distinct following treatment or control. If one were using a statistic that is valid only in the absence of interference, then the power in these two situation could not be 33