Summary
Statistical methods for testing differences between neural images (e.g., PET, MRI or EEG maps) are problematic because they require (1) an untenable assumption of data sphericity and (2) a high subject to electrode ratio. We propose and demonstrate an exact and distribution-free method of significance testing which avoids the sphericity assumption and may be computed for any combination of electrode and subject numbers. While this procedure is rigorously rooted in permutation test theory, it is intuitively comprehensible. The sensitivity of the permutation test to graded changes in dipole location for systematically varying levels of signal/noise ratio, intersubject variability and number of subjects was demonstrated through a simulation of 70 different conditions, generating 5,000 different data sets for each condition. Data sets were simulated from a homogenous single-shell dipole model. For noise levels commonly encountered in evoked potential studies and for situations where the number of subjects was less than the number of electrodes, the permutation test was very sensitive to a change in dipole location of less than 0.75 cm. This method is especially sensitive to localized changes that would be “washed-out‘ by more traditional methods of analysis. It is superior to all previous methods of statistical analysis for comparing topographical maps, because the test is exact, there is no assumption of a multivariate normal distribution or of the correlation structure of the data requiring correction, the test can be tailored to the specific experimental hypotheses rather than allowing the statistical tests to limit the experimental design, and there is no limitation on the number of electrodes that can be simultaneously analyzed.
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Blair, R.C. and Karniski, W. Distribution-free statistical analyses of surface and volumetric maps. In: R.W. Thatcher, M. Hallett, E.R. John and M. Huerta (Eds.), Functional Neuroimaging: Technical Foundations, Academic Press, San Diego, California, in press, 1994.
Blair, R.C. and Karniski, W. An alternative method for significance testing of waveform difference potentials, Psychophysiology, 1993, 30: 518–524.
Cohen, M.J. Analysis of variance with repeated measures on autonomic responses. Psychophysiology, 1987, 24: 475–476.
Donchin, E. A multivariate approach to the analysis of averaged evoked potentials. IEEE Trans. Biomed. Engng., 1966, BME-13: 131–139.
Donchin, E. and Heffley, E.F. Multivariate analysis of event-related potential data: A tutorial review. In: D. Otto (Ed.), Multidisciplinary Perspectives in Event-Related Brain Potential Research. Washington, DC: US Government Printing Office, 1978: 555–572.
Duffy, F.H., Bartels, P.H. and Burchfiel, J.L. Significance probability mapping: An aid in the topographic analysis of brain electrical activity. Electroenceph. clin. Neurophysiol., 1981, 51: 455–462.
Duffy, F.H., Bartels, P.H. and Neff, R. A response to Oken and Chiappa. Annals of Neurology, 1986, 19: 494–496.
Duffy, F.H., Jones, K., Bartels, P., Albert, M., McAnulty, G.B. and Als, H. Quantified neurophysiology with mapping: statistical inference, exploratory and confirmatory data analysis. Brain Topography, 1990, 3: 3–12.
Edgington, E.S. Randomization tests (2nd ed.). New York, Marcel Dekker, 1987.
Etevenon, P. Applications and perspectives of EEG cartography. In: F.H. Duffy (Ed.), Topographic Mapping of Brain Electrical Activity, Stoneham, Butterworth Publishers, 1986: 113–142.
Etevenon, P., Bertaut, A., Mitermite, F., Eustache, F., Lepaisant, J., Lechevalier, B. and Zarifian, E. Inter- and intra-individual probability maps in EEG cartography by use of nonparametric Fisher tests. Brain Topography, 1989, 2: 81–89.
Faux, S.F. and McCarley R.W. Analysis of scalp voltage asymmetries using Hotelling's T methodology. Brain Topography, 1990, 2: 237–245.
Fischer, R.A. The design of experiments, Edinburgh: Oliver and Boyd Ltd., 1935.
Harner, R.N. Clinical application of computed EEG topography. In: F.H. Duffy (Ed.), Topographic Mapping of Brain Electrical Activity, Boston, Butterworth Publishers, 1986: 347–356.
Harner, R.N. and Riggio, S. Application of singular value decomposition to topographic analysis of flash-evoked potentials. Brain Topography, 1989: 91–98.
Harner, R.N. Singular value decomposition: a general linear model for analysis of multivariate structure in the electroencephalogram. Brain Topography, 1990, 3: 43–47.
Holm, S. A simple sequentially rejective multiple test procedure. Scand. J. Stat., 1979, 6: 665–670.
Kavanagh, R.N., Darcey, T.M., Lehmann, D. and Fender, D.H. Evaluation of methods for three-dimensional localization of electrical sources in the human brain. IEEE Trans. Biomed. Eng., 1978, 25: 421–429.
Keselman, H.J. and Keselman, J.C. Comparing repeated measures means in factorial designs. Psychophysiology, 1988, 25: 612–618.
Lehmann, D. Principles of spatial analysis, In: A.S. Gevins and A. Remond (Eds.), Methods of Analysis of Brain Electrical and Magnetic Signals. EEG Handbook (revised series, Vol. I) Elsevier Science Publishers, Amsterdam, 1987: 309–354.
Maus, A. and Endresen, J. Misuse of computer-generated results. Med. Biol. Eng. Comput., 1979, 17: 126–129.
Oken, B.S. and Chiappa, K.H. Statistical issues concerning computerized analysis of brainwave topography. Annals of Neurology, 1986, 19: 493–494.
Rappelsberger, P. and Petsche, H. Probability mapping: power and coherence analysis of cognitive processes, Brain Topography, 1988, 1: 46–54.
Samson-Dollfus, D., Guieu, J.D., Gotman, J. and Etevenon, P. Statistics and topography in quantitative EEG. Amsterdam: Elsevier, 1988.
Silberstein, R.B. and Cadusch, P.J. Measurement processes and spatial principal components analysis. Brain Topography, 1992, 4: 267–276.
Vasey, M.W. and Thayer, J.F. The continuing problem of false positives in repeated measures ANOVA in psychophysiology: A multivariate solution. Psychophysiology, 1987, 24: 479–486.
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This research was funded in part by the University of South Florida's Research and Creative Scholarship program.
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Karniski, W., Blair, R.C. & Snider, A.D. An exact statistical method for comparing topographic maps, with any number of subjects and electrodes. Brain Topogr 6, 203–210 (1994). https://doi.org/10.1007/BF01187710
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DOI: https://doi.org/10.1007/BF01187710