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Dear Stavros, I will direct you to a couple of references; let me know this doesn't take care of your questions. As always, the place to start is the SPM book <http://www.fil.ion.ucl.ac.uk/spm/doc/books/hbf2/>: Chapters 14 & 15 go over Random Field Theory, the approach used to compute p-values for cluster size and voxel/peak intensity; Chapter 16 covers the nonparametric/permutation approach to the same. For more details see papers referenced in those chapters. As for "standard deviation of the values within the cluster" I'm afraid there are no standard results for that; if you pick a random voxel in a T statistic image, it should have stdev of 1 and mean equal to it's non-centrality parameter (approximately). But the values within the cluster are selected and thus will have some different distribution that depends on the cluster forming threshold and the smoothness of the image. About voxel resolution of the images (acquired or normalized) and FWHM of the applied smoothing, that is under your control. Consult your local MR physicist for the actual resolution of the images acquired (usually a sinc-shaped point spread function that is just a tiny bit larger than your voxels). Note that for Random Field Theory, the key parameter is not the applied smoothness but the intrinsic smoothness, estimated by the residuals (see Kiebel et al. 1999 for details). -Tom Kiebel, S., Poline, J.-B., Friston, K. J., Holmes, A. P., & Worsley, K. J. (1999). Robust smoothness estimation in statistical parametric maps using standardized residuals from the general linear model. *NeuroImage*, *10*, 756–766. On Thu, Sep 14, 2017 at 2:35 PM, Stavros Skouras <[log in to unmask]> wrote: > Dear SPM/SnPM experts, > > Could someone please share the mathematical formula for finding the > corrected p-value of a cluster (after correction for multiple comparisons > through Monte Carlo simulations), given some or all of the following > variables? > > - the cluster z-score (max or mean) > - the cluster-size (voxels or volume) > - the standard deviation of the values within the cluster > - the size of the brain mask used for multiple comparisons correction > (voxels or volume) > - the cluster-forming threshold (p-value or z-score) > - the significance level α (p-value or z-score) > - the voxel resolution of the images (acquired or normalized) > - the FWHM of the smoothing applied > > Many thanks in advance, > Stavros > > -- > You received this message because you are subscribed to the Google Groups > "Statistical Nonparametric Mapping" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [log in to unmask] > To post to this group, send email to [log in to unmask] > Visit this group at https://groups.google.com/group/snpm-support. > To view this discussion on the web, visit https://groups.google.com/d/ > msgid/snpm-support/CA%2Bmu31qL3HPofFUOn0D8KNv4MQ9xv7 > nJT9X-6-3Cu%3DyE3Dd8cA%40mail.gmail.com > <https://groups.google.com/d/msgid/snpm-support/CA%2Bmu31qL3HPofFUOn0D8KNv4MQ9xv7nJT9X-6-3Cu%3DyE3Dd8cA%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > For more options, visit https://groups.google.com/d/optout. > -- __________________________________________________________ Thomas Nichols, PhD Professor of Neuroimaging Statistics Oxford Big Data Institute Li Ka Shing Centre for Health Information and Discovery Nuffield Department of Population Health University of Oxford Email: [log in to unmask] Web: http://nisox.org