Statistical analysis of multichannel scalp field data

König, Thomas; Melie-Garcia, Lester (2009). Statistical analysis of multichannel scalp field data. In: Michel, Christoph M; König, Thomas; Brandeis, Daniel; Gianotti, Lorena R R; Wackermann, Jiří (eds.) Electrical Neuroimaging (pp. 169-190). Cambridge: Cambridge University Press 10.1017/CBO9780511596889.009

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High density spatial and temporal sampling of EEG data enhances the quality of results of electrophysiological experiments. Because EEG sources typically produce widespread electric fields (see Chapter 3) and operate at frequencies well below the sampling rate, increasing the number of electrodes and time samples will not necessarily increase the number of observed processes, but mainly increase the accuracy of the representation of these processes. This is namely the case when inverse solutions are computed.

As a consequence, increasing the sampling in space and time increases the redundancy of the data (in space, because electrodes are correlated due to volume conduction, and time, because neighboring time points are correlated), while the degrees of freedom of the data change only little. This has to be taken into account when statistical inferences are to be made from the data. However, in many ERP studies, the intrinsic correlation structure of the data has been disregarded. Often, some electrodes or groups of electrodes are a priori selected as the analysis entity and considered as repeated (within subject) measures that are analyzed using standard univariate statistics. The increased spatial resolution obtained with more electrodes is thus poorly represented by the resulting statistics. In addition, the assumptions made (e.g. in terms of what constitutes a repeated measure) are not supported by what we know about the properties of EEG data.

From the point of view of physics (see Chapter 3), the natural “atomic” analysis entity of EEG and ERP data is the scalp electric field

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