Hi Mario,
If your artificial data includes temporal autocorrelation, that equation won't hold because it assumes that each time point is independent of the others, which isn't the case in FMRI unless your TR is rather long.  See any of the papers on "temporal autocorrelation fMRI" in PubMed for an introduction to the issue (e.g., Purdon 1998, Woolrich 2001, and many others).

cheers,
-MH

-- 
Michael Harms, Ph.D.
-----------------------------------------------------------
Conte Center for the Neuroscience of Mental Disorders
Washington University School of Medicine
Department of Psychiatry, Box 8134
660 South Euclid Ave. Tel: 314-747-6173
St. Louis, MO  63110 Email: [log in to unmask]

From: Mario Zeller <[log in to unmask]>
Reply-To: FSL - FMRIB's Software Library <[log in to unmask]>
Date: Thursday, December 6, 2012 10:33 AM
To: FSL - FMRIB's Software Library <[log in to unmask]>
Subject: [FSL] Relation of CNR to detected activation strength

Dear FSL list members,

this is my first post in this group, so please forgive me, if I do anything wrong.

I was wondering if anyone has ever investigated how a change in SNR or CNR at fixed TE (e.g. by applying a filter) changes the activation strength observable by statistical analysis of the data.

Parrish (Neuroreport. 2001 12(16):3461-4) suggests the relation

SNR = 2 * t / \Delta S * sqrt(N)

where t is the t value, \Delta S the contrast and N the number of volumes.

However, if I simulate a change in SNR/CNR on artificial data, I get a non-linear increase of detected activation when performing a fixed effects analysis in FEAT.

Do you have any hints or do you know papers covering that topic?

Thank you and have a nice day,
Mario Zeller