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Nonparametric permutation tests for functional neuroimaging: A primer with examples
Open accessAbstract
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 Holmes et al. ([ 1996 ]: 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 appropriate 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 f MRI 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 f MRI 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. © 2001 Wiley‐Liss, Inc.
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“Statistical significance of decoding performance was assessed via permutation test, randomly permuting the sample labels and repeating the decoding analysis 1,000 times, corrected for multiple comparisons using a cluster-based correction (cluster mass inference with cluster forming threshold at P < 0.05)105,106.”
From Adversarial testing of global neuronal workspace and integrated information theories of consciousness (2025) · cites this paper as [105]
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“The permutation p-value in Equation ( 10) is super-uniform under H 0 (i.e., P H0 (p ≤ α) ≤ α for all α ∈ [0, 1]), a standard consequence of randomization inference (Nichols & Holmes, 2002;Phipson & Smyth, 2010;Good, 2005)”
From Revisiting the Platonic Representation Hypothesis: An Aristotelian View (2026) · cites this paper as Nichols & Holmes, 2002
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“While resampling-based “maxT” procedures (Westfall & Young, 1993;Nichols & Holmes, 2002) can calibrate such aggregates, this has not yet been applied in representational similarity studies.”
From Revisiting the Platonic Representation Hypothesis: An Aristotelian View (2026) · cites this paper as Nichols & Holmes, 2002
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“To find the true type I error rate, we performed Monte Carlo simulations that permute the sign of the whole-brain maps from individual subjects58.”
From Anchoring the neural compass: coding of local spatial reference frames in human medial parietal lobe (2014) · cites this paper as [58]
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Metadata
- Authors
- Nichols, T. E., & Holmes, A. P.
- Affiliations
- University of Michigan (US)
- UCL Queen Square Institute of Neurology (GB)
- ORCID
- Nichols, Thomas E.
- Venue
- Human Brain Mapping
- Publisher
- Wiley
- Published
- 2001-10-15
- Volume
- 15
- Issue
- 1
- Pages
- 1-25
- ISSN
- 1065-9471 (ISSN-L)
- 1097-0193
- PMC
- PMC6871862
- OpenAlex
- W2138790588
- Cited by
- 6,256
- References
- 56
- Citations by year
- 2026: 223 · 2025: 264 · 2024: 255 · 2023: 275 · 2022: 321 · 2021: 350 · 2020: 392 · 2019: 368 · 2018: 381 · 2017: 368 · 2016: 343 · 2015: 385 · 2014: 365 · 2013: 356 · 2012: 314
- FWCI
- 16.77
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Human Brain Mapping (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Deep Blue (University of Michigan) (submittedVersion)
- Funders
- Wellcome Trust
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced MRI Techniques and Applications
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Medical Imaging Techniques and Applications
- Keywords
- permutation tests, functional neuroimaging, multiple testing correction, statistical parametric mapping, random field theory, PET, functional MRI, population effects, MATLAB software
- MeSH terms
- Brain, Brain Mapping, Data Interpretation, Statistical, Humans, Image Processing, Computer-Assisted, Magnetic Resonance Imaging, Signal Processing, Computer-Assisted, Tomography, Emission-Computed, Statistical Distributions
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