of power. In the non-null cases, GLYPH<23> > 1 , the test with the highest power is in bold . No one test is uniformly best in the situations considered in Tables 5 and 6, but the t-test and the Mann-Whitney-Wilcoxon test are never much better than k = 5 and are often much worse. The statistic with k = 10 performs well only in Table 6 where successful trials occur only 10% of the time. The permutational t -statistic performs well only when both F ( GLYPH<1> ) and the autoregressive errors are Normal, and it performs poorly when the F ( GLYPH<1> ) is the t -distribution with 2 df. When F ( GLYPH<1> ) is Normal and there are no autoregressive errors, the permutational t -statistic typically had less power than k = 5 . Tables 5 and 6 exhibit many patterns. It is not surprising that the addition of Gaussian autoregressive errors reduces power: the power in the top half of Tables 5 and 6 is typically quite a bit higher than the corresponding power in the lower half of the tables. Both types of interference, A and B, reduce power when compared with no interference, but in Tables 5 and 6 interference A and B had similar e⁄ects on power. Interference patterns C and D reduce the number of responses that di⁄er from control, so they reduce power relative to case A, but the suggestion of Conover and Salsburg, namely k = 5 , exhibits decent relative performance in most if not all cases. 5.3 Comparison with SPM A common approach to the analysis of fMRI data is the statistical parametric map (SPM) approach of Friston et al. (1995). Using responses convolved with a hemodynamic response function (HRF) as in Figure 2, the SPM approach entails testing a hypothesis of the equality of two regression coe¢ cients in a generalized least squares analysis. We simulated this analysis with and without interference, with and without autoregressive errors, and with mixtures of successful and unsuccessful trials. The SPM approach uses a parametric 32