Arndt,, S., Cizadlo,, T., Andreasen,, N., Heckel,, D., Gold,, S., & O`Leary,, D. (1996). Tests for comparing images based on randomization and permutation methods. Journal of Cerebral Blood Flow and Metabolism, 16(6), 1271–1279. https://doi.org/10.1097/00004647-199611000-00023

Basu,, D. (1980). Randomization analysis of experimental data: The fisher randomization test. Journal of the American Statistical Association, 75(371), 575–582. https://doi.org/10.2307/2287648

Benjamini,, Y., & Yu,, B. (2013). The shuffle estimator for explainable variance in fMRI experiments. The Annals of Applied Statistics, 7(4), 2007–2033. https://doi.org/10.1214/13-AOAS681

Blair,, R. C., Higgins,, J. J., Karniski,, W., & Kromrey,, J. D. (1994). A study of multivariate permutation tests which may replace Hotelling`s T2 test in prescribed circumstances. Multivariate Behavioral Research, 29(2), 141–163. https://doi.org/10.1207/s15327906mbr2902 2

Blair,, R. C., & Karniski,, W. (1994). Distribution‐free statistical analyses of surface and volumetric maps. In R. W. Thatcher,, M. Hallett,, E. R. John,, & M. Huerta, (Eds.), Functional neuroimaging: Technical foundations. San Diego, CA: Academic Press.

Brunner,, E., & Munzel,, U. (2000). The nonparametric Behrens‐fisher problem: Asymptotic theory and a small‐sample approximation. Biometrical Journal, 42(1), 17–25. https://doi.org/10.1002/(SICI)1521-4036(200001)42:1h17::AID-BIMJ17i3.0.CO;2-U

Bullmore,, E., Brammer,, M., Williams,, S. C. R., Rabe‐Hesketh,, S., Janot,, N., David,, A., … Sham,, R. H. P. (1996). Statistical methods of estimation and inference for functional MR image analysis. Magnetic Resonance in Medicine, 35(2), 261–277. https://doi.org/10.1002/mrm.1910350219

Bullmore,, E., Long,, C., Suckling,, J., Fadili,, J., Calvert,, G., Zelaya,, F., … Brammer,, M. (2000). Colored noise and computational inference in neurophysiological (fMRI) time series analysis: Resampling methods in time and wavelet domains. Human Brain Mapping, 12(2), 61–78. https://doi.org/10.1002/1097-0193(200102)12:2h61::AID-HBM1004i3.0.CO;2-W

Bullmore,, E., Suckling,, J., Overmeyer,, S., Rabe‐Hesketh,, S., Taylor,, E., & Brammer,, M. J. (1999). Global, voxel, and cluster tests, by theory and permutation, for a difference between two groups of structural MR images of the brain. IEEE Transactions on Medical Imaging, 18(1), 32–42. https://doi.org/10.1109/42.750253

Chung,, E., & Romano,, J. P. (2013). Exact and asymptotically robust permutation tests. The Annals of Statistics, 41(2), 484–507. https://doi.org/10.1214/13-AOS1090

Chung,, E., & Romano,, J. P. (2016). Asymptotically valid and exact permutation tests based on two‐sample *U*‐statistics. Journal of Statistical Planning and Inference, 168, 97–105. https://doi.org/10.1016/j.jspi.2015.07.004

De Mazière,, P. A., & Van Hulle,, M. M. (2007). fMRI bold signal analysis using a novel nonparametric statistical method. Journal of Magnetic Resonance, 185(1), 138–151. https://doi.org/10.1016/j.jmr.2006.12.001

DiCiccio,, C. J., & Romano,, J. P. (2017). Robust permutation tests for correlation and regression coefficients. Journal of the American Statistical Association, 112(519), 1211–1220. https://doi.org/10.1080/01621459.2016.1202117

Ding,, P. (2016). On the conditional distribution of the multivariate *t* distribution. The American Statistician, 70(3), 293–295. https://doi.org/10.1080/00031305.2016.1164756

Draper,, N. R., & Stoneman,, D. M. (1966). Testing for the inclusion of variables in linear regression by a randomisation technique. Technometrics, 8(4), 695–699. https://doi.org/10.2307/1266641

Edgington,, E. S. (1964). Randomization tests. The Journal of Psychology, 57(2), 445–449. https://doi.org/10.1080/00223980.1964.9916711

Edgington,, E. S. (1969). Approximate randomization tests. The Journal of Psychology, 72(2), 143–149. https://doi.org/10.1080/00223980.1969.10543491

Edgington,, E. S., & Onghena,, P. (2007). Randomization tests (Fourth ed.). Boca Raton, FL: Chapman and Hall/CRC.

Eklund,, A., Andersson,, M., Josephson,, C., Johannesson,, M., & Knutsson,, H. (2012). Does parametric fMRI analysis with SPM yield valid results?—An empirical study of 1484 rest datasets. NeuroImage, 61(3), 565–578. https://doi.org/10.1016/j.neuroimage.2012.03.093

Eklund,, A., Nichols,, T. E., & Knutsson,, H. (2016). Cluster failure: Why fMRI inferences for spatial extent have inated false‐positive rates. Proceedings of the National Academy of Sciences of the United States of America, 113(28), 7900–7905. https://doi.org/10.1073/pnas.1602413113

Etévenon,, P., Bertaut,, A., Mitermite,, F., Eustache,, F., Lepaisant,, J., Lechevalier,, B., & Zarifian,, E. (1989). Inter‐ and intra‐individual probability maps in EEG cartography by use of nonparametric fisher tests. Brain Topography, 2(1), 81–89. https://doi.org/10.1007/BF01128846

Etévenon,, P., Peron‐Magnan,, P., Guillou,, S., Toussaint,, M., Gueguen,, B., Boulenger,, J., … Loo,, H. (1988). Caffeine and EEG mapping: Effects of a visuo‐spatial task in healthy volunteers [cafeine et cartographie EEG: Effets d`une tache visuospatiale chez des volontaires sains. strategie d`analyse des donnees electropharmacologiques]. Neurophysiologie Clinique/Clinical Neurophysiology, 18(4), 355–367. https://doi.org/10.1016/S0987-7053(88)80092-3

Etévenon,, P., Tortrat,, D., & Benkelfat,, C. (1985). Electroencephalographic cartography. Neuropsychobiology, 13(3), 141–146. https://doi.org/10.1159/000118177

Etévenon,, P., Tortrat,, D., Guillou,, S., & Wendling,, B. (1985). EEG cartography during visuo‐spatial task: Averaged maps and group statistics [cartographie EEG au cours d`une tache visuo‐spatiale: Cartes moyennes et statistiques de groupes]. Re‐vue d`Electroencephalographie et de/Neurophysiologie Clinique, 15(2), 139–147. https://doi.org/10.1016/S0370-4475(85)80018-6

Fisher,, R. A. (1925). Statistical methods for research workers. Edinburgh, England: Oliver and Boyd.

Fisher,, R. A. (1935). The design of experiments. Edinburgh, England: Oliver and Boyd.

Fisher,, R. A. (1936). “The coefficient of racial likeness” and the future of craniometry. The Journal of the Royal Anthropological Institute of Great Britain and Ireland, 66, 57–63. https://doi.org/10.2307/2844116

Fisher,, R. A. (1960). The design of experiments (Seventh ed.). Edinburgh, England: Oliver and Boyd.

Flandin,, G., & Friston,, K. J. (2017). Analysis of family‐wise error rates in statistical parametric mapping using random field theory. Human Brain Mapping. https://doi.org/10.1002/hbm.23839

Freedman,, D., & Lane,, D. (1983). A nonstochastic interpretation of reported significance levels. Journal of Business and Economic Statistics, 1(4), 292–298. https://doi.org/10.2307/1391660

Fritsch,, V., Mota,, B. D., Loth,, E., Varoquaux,, G., Banaschewski,, T., Barker,, G. J., … Thirion,, B. (2015). Robust regression for large‐scale neuroimaging studies. NeuroImage, 111, 431–441. https://doi.org/10.1016/j.neuroimage.2015.02.048

Ganjgahi,, H., Winkler,, A. M., Glahn,, D. C., Blangero,, J., Kochunov,, P., & Nichols,, T. E. (2015). Fast and powerful heritability inference for family‐based neuroimaging studies. NeuroImage, 115, 256–268. https://doi.org/10.1016/j.neuroimage.2015.03.005

Ge,, T., Feng,, J., Hibar,, D. P., Thompson,, P. M., & Nichols,, T. E. (2012). Increasing power for voxel‐wise genome‐wide association studies: The random field theory, least square kernel machines and fast permutation procedures. NeuroImage, 63(2), 858–873. https://doi.org/10.1016/j.neuroimage.2012.07.012

Good,, P. I. (2005). Permutation, parametric, and bootstrap tests of hypotheses. New York, NY: Springer‐Verlag. https://doi.org/10.1007/b138696

Hayasaka,, S., & Nichols,, T. E. (2004). Combining voxel intensity and cluster extent with permutation test framework. NeuroImage, 23(1), 54–63. https://doi.org/10.1016/j.neuroimage.2004.04.035

Hesterberg,, T. C. (2015). What teachers should know about the bootstrap: Resampling in the undergraduate statistics curriculum. The American Statistician, 69(4), 371–386. https://doi.org/10.1080/00031305.2015.1089789

Hoeffding,, W. (1952). The large‐sample power of tests based on permutations of observations. The Annals of Mathematical Statistics, 23(2), 169–192. https://doi.org/10.1214/aoms/1177729436

Holm,, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6(2), 65–70.

Holmes,, A. P., Blair,, R. C., Watson,, J. D. G., & Ford,, I. (1996). Nonparametric analysis of statistic images from functional mapping experiments. Journal of Cerebral Blood Flow and Metabolism, 16(1), 7–22. https://doi.org/10.1097/00004647-199601000-00002

Janssen,, A. (1997). Studentized permutation tests for non‐i.i.d. hypotheses and the generalized Behrens‐fisher problem. Statistics %26 Probability Letters, 36(1), 9–21. https://doi.org/10.1016/S0167-7152(97)00043-6

Johnson,, N. J. (1978). Modified *t* tests and confidence intervals for asymmetrical populations. Journal of the American Statistical Association, 73(363), 536–544. https://doi.org/10.2307/2286597

Karniski,, W., Blair,, R. C., & Snider,, A. D. (1994). An exact statistical method for comparing topographic maps, with any number of subjects and electrodes. Brain Topography, 6(3), 203–210. https://doi.org/10.1007/BF01187710

Kempthorne,, O. (1955). The randomization theory of experimental inference. Journal of the American Statistical Association, 50(271), 946–967. https://doi.org/10.2307/2281178

Kessler,, D., Angstadt,, M., & Sripada,, C. S. (2017). Reevaluating “cluster failure” in fMRI using nonparametric control of the false discovery rate. Proceedings of the National Academy of Sciences of the United States of America, 114(17), E3372–E3373. https://doi.org/10.1073/pnas.1614502114

Lehmann,, E. L., & Stein,, C. (1949). On the theory of some non‐parametric hypotheses. The Annals of Mathematical Statistics, 20(1), 28–45. https://doi.org/10.2307/2236802

Locascio,, J. J., Jennings,, P. J., Moore,, C. I., & Corkin,, S. (1997). Time series analysis in the time domain and resampling methods for studies of functional magnetic resonance brain imaging. Human Brain Mapping, 5(3), 168–193. https://doi.org/10.1002/(SICI)1097-0193(1997)5:3h168::AID-HBM3i3.0.CO;2-1

Mann,, H. B., & Whitney,, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics, 18(1), 50–60. https://doi.org/10.1214/aoms/1177730491

Medina,, J., Kimberg,, D. Y., Chatterjee,, A., & Coslett,, H. B. (2010). Inappropriate usage of the Brunner–Munzel test in recent voxel‐based lesion‐symptom mapping studies. Neuropsychologia, 48(1), 341–343. https://doi.org/10.1016/j.neuropsychologia.2009.09.016

Meriaux,, S., Roche,, A., Thirion,, B., & Dehaene‐Lambertz,, G. (2006, April). Robust statistics for nonparametric group analysis in fMRI. In *3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro* (pp. 936–939). doi: https://doi.org/10.1109/ISBI.2006.1625073

Neuhaus,, G. (1993). Conditional rank tests for the two‐sample problem under random censorship. The Annals of Statistics, 21(4), 1760–1779. https://doi.org/10.1214/aos/1176349396

Nichols,, T. E. (2012). Multiple testing corrections, nonparametric methods, and random field theory. NeuroImage, 62(2), 811–815. https://doi.org/10.1016/j.neuroimage.2012.04.014

Nichols,, T. E., & Hayasaka,, S. (2003). Controlling the familywise error rate in functional neuroimaging: A comparative review. Statistical Methods in Medical Research, 12(5), 419–446. https://doi.org/10.1191/0962280203sm341ra

Nichols,, T. E., Holmes,, A. P.. (1996). *SnPM—Statistical nonparametric mapping—A toolbox for SPM*. Retrieved from http://warwick.ac.uk/snpm

Nichols,, T. E., & Holmes,, A. P. (2002). Nonparametric permutation tests for functional neuroimaging: A primer with examples. Human Brain Mapping, 15(1), 1–25. https://doi.org/10.1002/hbm.1058

Pantazis,, D., Nichols,, T. E., Baillet,, S., & Leahy,, R. M. (2003, July). Spatiotemporal localization of significant activation in MEG using permutation tests. In C. Taylor, & J. A. Noble, (Eds.), Information processing in medical imaging (pp. 512–523). Berlin, Heidelberg: Springer Berlin Heidelberg.

Pantazis,, D., Nichols,, T. E., Baillet,, S., & Leahy,, R. M. (2005). A comparison of random field theory and permutation methods for the statistical analysis of MEG data. NeuroImage, 25(2), 383–394. https://doi.org/10.1016/j.neuroimage.2004.09.040

Pearson,, E. S. (1937). Some aspects of the problem of randomization. Biometrika, 29(1/2), 53–64. https://doi.org/10.2307/2332406

Pernet,, C. R., Latinus,, M., Nichols,, T. E., & Rousselet,, G. A. (2015). Cluster‐based computational methods for mass univariate analyses of event‐related brain potentials/fields: A simulation study. Journal of Neuroscience Methods, 250, 85–93. https://doi.org/10.1016/j.jneumeth.2014.08.003

Pesarin,, F. (2001). Multivariate permutation tests: With applications in biostatistics. New York, NY: Wiley.

Petsche,, H., Linder,, K., Rappelsberger,, P., & Gruber,, G. (1988). The EEG: An adequate method to concretize brain processes elicited by music. Music Perception, 6(2), 133–159. https://doi.org/10.2307/40285422

Pitman,, E. J. G. (1937a). Significance tests which may be applied to samples from any populations. Supplement to the Journal of the Royal Statistical Society, 4(1), 119–130. https://doi.org/10.2307/2984124

Pitman,, E. J. G. (1937b). Significance tests which may be applied to samples from any populations. II. The correlation coefficient test. Supplement to the Journal of the Royal Statistical Society, 4(2), 225–232. https://doi.org/10.2307/2983647

Poline,, J.‐B., & Mazoyer,, B. M. (1993). Analysis of individual positron emission tomography activation maps by detection of high signal‐to‐noise‐ratio pixel clusters. Journal of Cerebral Blood Flow and Metabolism, 13(3), 425–437. https://doi.org/10.1038/jcbfm.1993.57

Politis,, D. (2016). T and *χ*2: Revisiting the classical tests for the 21st century classroom. IMS Bulletin, 45(4), 10–11.

Rappelsberger,, P., & Petsche,, H. (1988). Probability mapping: Power and coherence analyses of cognitive processes. Brain Topography, 1(1), 46–54. https://doi.org/10.1007/BF01129339

Raz,, J., Zheng,, H., Ombao,, H., & Turetsky,, B. (2003). Statistical tests for fMRI based on experimental randomization. NeuroImage, 19(2 Pt 1), 226–232. https://doi.org/10.1016/S1053-8119(03)00115-0

Roland,, P. E., Levin,, B., Kawashima,, R., & Akerman,, S. (1993). Three‐dimensional analysis of clustered voxels in 15o‐butanol brain activation images. Human Brain Mapping, 1(1), 3–19. https://doi.org/10.1002/hbm.460010103

Romano,, J. P. (1990). On the behavior of randomization tests without a group invariance assumption. Journal of the American Statistical Association, 85(411), 686–692. https://doi.org/10.1080/01621459.1990.10474928

Romano,, J. P., & Wolf,, M. (2005). Exact and approximate stepdown methods for multiple hypothesis testing. Journal of the American Statistical Association, 100(469), 94–108. https://doi.org/10.1198/016214504000000539

Romano,, J. P., & Wolf,, M. (2007). Control of generalized error rates in multiple testing. The Annals of Statistics, 35(4), 1378–1408. https://doi.org/10.1214/009053606000001622

Romano,, J. P., & Wolf,, M. (2016). Efficient computation of adjusted *p*‐values for resamplingbased stepdown multiple testing. Statistics %26 Probability Letters, 113, 38–40. https://doi.org/10.1016/j.spl.2016.02.012

Rorden,, C., Bonilha,, L., & Nichols,, T. E. (2007). Rank‐order versus mean based statistics for neuroimaging. NeuroImage, 35(4), 1531–1537. https://doi.org/10.1016/j.neuroimage.2006.12.043

Rorden,, C., Fridriksson,, J., & Karnath,, H.‐O. (2009). An evaluation of traditional and novel tools for lesion behavior mapping. NeuroImage, 44(4), 1355–1362. https://doi.org/10.1016/j.neuroimage.2008.09.031

Rorden,, C., Karnath,, H.‐O., & Bonilha,, L. (2007). Improving lesion‐symptom mapping. Journal of Cognitive Neuroscience, 19(7), 1081–1088. https://doi.org/10.1162/jocn.2007.19.7.1081

Salimi‐Khorshidi,, G., Smith,, S. M., & Nichols,, T. E. (2011). Adjusting the effect of nonstationarity in cluster‐based and TFCE inference. NeuroImage, 54(3), 2006–2019. https://doi.org/10.1016/j.neuroimage.2010.09.088

Scheffé,, H. (1943). Statistical inference in the non‐parametric case. The Annals of Mathematical Statistics, 14(4), 305–332. https://doi.org/10.1214/aoms/1177731355

Silver,, M., Montana,, G., Nichols,, T. E., & Alzheimer`s Disease Neuroimaging Initiative. (2011). False positives in neuroimaging genetics using voxel‐based morphometry data. NeuroImage, 54(2), 992–1000. https://doi.org/10.1016/j.neuroimage.2010.08.049

Smith,, S. M., & Nichols,, T. E. (2009). Threshold‐free cluster enhancement: Addressing problems of smoothing, threshold dependence and localisation in cluster inference. NeuroImage, 44(1), 83–98. https://doi.org/10.1016/j.neuroimage.2008.03.061

Student. (1908). The probable error of a mean. Biometrika, 6(1), 1–25. https://doi.org/10.2307/2331554

Thau,, K., Rappelsberger,, P., Lovrek,, A., Petsche,, H., Simhandl,, C., & Topitz,, A. (1988). Effect of lithium on the EEG of healthy males and females. Neuropsychobiology, 20(3), 158–163. https://doi.org/10.1159/000118491

Welch,, B. L. (1938). The significance of the difference between two means when the population variances are unequal. Biometrika, 39(3/4), 350–362. https://doi.org/10.2307/2332010

Welch,, B. L. (1947). The generalization of “Student`s” problem when several different population variances are involved. Biometrika, 34(1–2), 28–35. https://doi.org/10.1093/biomet/34.1-2.28

Westfall,, P. H., & Young,, S. S. (1993). Resampling‐based multiple testing. New York, NY: Wiley.

White,, H. (1980). A heteroscedasticity‐consistent covariance matrix and a direct test for heteroscedasticity. Econometrica, 48(4), 817–838. https://doi.org/10.2307/1912934

Wilcoxon,, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80–83. https://doi.org/10.2307/3001968

Winkler,, A. M., Ridgway,, G. R., Douaud,, G., Nichols,, T. E., & Smith,, S. M. (2016). Faster permutation inference in brain imaging. NeuroImage, 141, 502–516. https://doi.org/10.1016/j.neuroimage.2016.05.068

Winkler,, A. M., Ridgway,, G. R., Webster,, M. A., Smith,, S. M., & Nichols,, T. E. (2014). Permutation inference for the general linear model. NeuroImage, 92, 381–397. https://doi.org/10.1016/j.neuroimage.2014.01.060

Winkler,, A. M., Webster,, M. A., Brooks,, J. C., Tracey,, I., Smith,, S. M., & Nichols,, T. E. (2016). Non‐parametric combination and related permutation tests for neuroimaging. Human Brain Mapping, 37(4), 1486–1511. https://doi.org/10.1002/hbm.23115

Winkler,, A. M., Webster,, M. A., Vidaurre,, D., Nichols,, T. E., & Smith,, S. M. (2015). Multi‐level block permutation. NeuroImage, 123, 253–268. https://doi.org/10.1016/j.neuroimage.2015.05.092

Xu,, Y., Sudre,, G. P., Wang,, W., Weber,, D. J., & Kassa,, R. E. (2011). Characterizing global statistical significance of spatiotemporal hot spots in magnetoencephalography/electroencephalography source space via excursion algorithms. Statistics in Medicine, 30(23), 2854–2866. https://doi.org/10.1002/sim.4309

Yang,, X., Beason‐Held,, L., Resnick,, S. M., & Landman,, B. A. (2011). Biological parametric mapping with robust and non‐parametric statistics. NeuroImage, 57(2), 423–430. https://doi.org/10.1016/j.neuroimage.2011.04.046

Zhang,, H., Nichols,, T. E., & Johnson,, T. D. (2009). Cluster mass inference via random field theory. NeuroImage, 44(1), 51–61. https://doi.org/10.1016/j.neuroimage.2008.08.017