Nonparametric permutation tests for functional neuroimaging: A primer with examples

Thomas E. Nichols, Andrew P. Holmes
2001 Human Brain Mapping  
Requiring only minimal assumptions for validity, nonparametric permutation testing provides a flexible and intuitive methodology for the statistical analysis of data from functional neuroimaging experiments, at some computational expense. Introduced into the functional neuroimaging literature by : J Cereb Blood Flow Metab 16:7-22), the permutation approach readily accounts for the multiple comparisons problem implicit in the standard voxel-by-voxel hypothesis testing framework. When the
more » ... ate assumptions hold, the nonparametric permutation approach gives results similar to those obtained from a comparable Statistical Parametric Mapping approach using a general linear model with multiple comparisons corrections derived from random field theory. For analyses with low degrees of freedom, such as single subject PET/SPECT experiments or multi-subject PET/SPECT or fMRI designs assessed for population effects, the nonparametric approach employing a locally pooled (smoothed) variance estimate can outperform the comparable Statistical Parametric Mapping approach. Thus, these nonparametric techniques can be used to verify the validity of less computationally expensive parametric approaches. Although the theory and relative advantages of permutation approaches have been discussed by various authors, there has been no accessible explication of the method, and no freely distributed software implementing it. Consequently, there have been few practical applications of the technique. This article, and the accompanying MATLAB software, attempts to address these issues. The standard nonparametric randomization and permutation testing ideas are developed at an accessible level, using practical examples from functional neuroimaging, and the extensions for multiple comparisons described. Three worked examples from PET and fMRI are presented, with discussion, and comparisons with standard parametric approaches made where appropriate. Practical considerations are given throughout, and relevant statistical concepts are expounded in appendices. Hum. Brain Mapping 15:1-25, 2001. ᭜ Permutation Tests for Functional Neuroimaging ᭜ ᭜ 17 ᭜ ᭜ Nichols and Holmes ᭜ ᭜ 18 ᭜ ᭜ Permutation Tests for Functional Neuroimaging ᭜ ᭜ 19 ᭜ * The minimum corrected P-value and number of significant voxels give an overall measure of sensitivity; corrected thresholds can only be compared within statistic type. For this data, the Bonferroni and random field results are very similar, and the nonparametric methods are more powerful. The nonparametric t method detects 10 times as many voxels as the parametric method, and the nonparametric pseudo-t detects 60 times as many. ᭜ Nichols and Holmes ᭜ ᭜ 20 ᭜ ᭜ Permutation Tests for Functional Neuroimaging ᭜ ᭜ 21 ᭜
doi:10.1002/hbm.1058 pmid:11747097 fatcat:fytq6xmepje45cznb3h4yakize