False discoveries in the results to a desired value

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false discoveries in the results to a desired value (Ben- jamini and Hochberg, 1995; Benjamini and Yekutieli, 2001). For the purposes of this contrast the propor- tion of false discoveries was set at FDR = 0 . 05 . A second additional contrast controlled for the fami- lywise error rate in the results. The selected method controls the FWER through the use of Gaussian Ran- dom Field Theory (Friston et al. , 1996; Worsley et al. , 1996, 2004). Using this strategy the spatial smooth- ness of the results is estimated and the probability of a false positive in a random field of similar Gaussians is calculated. For the purposes of this contrast the proba- bility of a familywise error was set at FWER = 0 . 05 . Both of the additional contrasts controlling for multiple comparisons indicated that no significant voxels were present in the dataset. This was true even at the relaxed thresholds of FDR = 0 . 25 and FWER = 0 . 25 . 4 DISCUSSION Either we have stumbled onto a rather amazing dis- covery in terms of post-mortem ichthyological cogni- tion, or there is something a bit off with regard to our uncorrected statistical approach. Could we con- clude from this data that the salmon is engaging in the perspective-taking task? Certainly not. By control- ling for the cognitive ability of the subject we have thoroughly eliminated that possibility. What we can conclude is that random noise in the EPI timeseries may yield spurious results if multiple testing is not con- trolled for. In a functional image volume of 130 , 000 voxels the probability of a false discovery is almost cer- tain. Even in the restricted set of 60 , 000 voxels that represent the human brain false positives will continue to be present. This issue has faced the neuroimaging field for some time, but the implementation of statisti- cal correction remains optional when publishing results of neuroimaging analyses. What, then, is the best solution to the multiple com- parisons problem in functional imaging? The Bonfer- roni correction (Bonferroni, 1936) is perhaps the most well-known formula for the control of false positives. The Bonferroni correction is quite flexible as it does not require the data to be independent for it to be effective. However, there is some consensus that Bon- ferroni may be too conservative for most fMRI data 3
Bennett et al. Fig. 1. Sagittal and axial images of significant brain voxels in the task > rest contrast. The parameters for this comparison were t (131) > 3 . 15 , p (uncorrected) < 0 . 001 , 3 voxel extent threshold. Two clusters were observed in the salmon central nervous system. One cluster was observed in the medial brain cavity and another was observed in the upper spinal column. sets (Logan et al. , 2008). This is because the value of one voxel is not an independent estimate of local signal. Instead, it is highly correlated with the values of sur- rounding voxels due to the intrinsic spatial correlation of the BOLD signal and to Gaussian smoothing applied during preprocessing. This causes the corrected Bonfer- roni threshold to be unnecessarily high, leading to Type II error and the elimination of valid results. More adap-

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