Below is a draft piece of text that can be used for describing, in the “Methods” section of a manuscript, the statistics used in the sLORETA/eLORETA package. Note that references are included below.
NOTE: what follows is applicable only if the option:
“Perform randomization SnPM, and compute bullet proof, corrected critical thresholds and p-values”
under the sub-program “Statistics”, of the “sLORETA/eLORETA” package was used, and the thresholds obtained by this procedure used for declaring significant locations.
The sLORETA/eLORETA software package was used to perform the statistical analyses. The methodology used is non-parametric. It is based on estimating, via randomization, the empirical probability distribution for the max-statistic (e.g. the maximum of a t or an F statistic), under the null hypothesis. This methodology corrects for multiple testing (i.e., for the collection of tests performed for all electrodes and/or voxels, and for all time samples and/or discrete frequencies – CHOOSE YOUR CASE, red or blue or both). Due to the non-parametric nature of the method, its validity need not rely on any assumption of Gaussianity.
The interested reader is referred to  for a complete overview of the methodology, where details about the properties (e.g. pertaining to its non-parametric nature, and pertaining to how it properly corrects for multiple testing) can be found.
: TE Nichols and AP Holmes. Nonparametric Permutation Tests for Functional Neuroimaging: A Primer with Examples. Human Brain Mapping, 15:1-25, 2002.