fMRI: Biological Basis and Experiment Design
Lecture 26: Significance
• Review of GLM results
• Baseline trends
• Block designs; Fourier
analysis (correlation)
• Significance and
confidence intervals
Noise in brains
• Spatially correlated
– Big vessels
– Blurring in image
– Neural activity is correlated
• Temporally correlated
– Noise processes have memory
Noise in brains: spatial correlation
• Spatial correlation: use one voxel as "seed" (template) –
calculate correlation with neighbors (whole brain, if you
have time ...)
– Basis of functional connectivity
Seed voxel
Picking a voxel not
significantly modulated
by the stimulus, we still
see correlations locally
Correlation is not seen in white matter; organized
in gray matter
Picking a voxel in white
matter, we still few
correlated voxels either
locally or globally.
Picking a voxel
significantly modulated
by the stimulus, we still
see correlations all over
Noise in brains: temporal correlation
Uncorrelated noise
Time domain
Frequency domain
Smoothed noise
Noise in brains: temporal correlation
• Drift and long trends have biggest effects
Noise in brains: temporal correlations
• (Missing slides, where I took 8 sample gray matter pixels
and 8 sample white matter pixels and looked at the
autorcorrelation function for each pixel)
Noise in brains: temporal correlation
• How to detect?
– Auto correlation with varying lags
– FT: low temporal frequency components indicate temporal
structure
• How to compensate?
– "pre-whiten" data (same effect as low-pass filtering?)
– Reduce degrees of freedom in analysis.
Fourier analysis
• Correlation with basis set: sines and cosines
• Stimulus-related component: amplitude at stimulusrelated frequency (can be z-scored by full spectrum)
• Phase of stimulus-related component has timing
information
Fourier analysis of block design experiment
Time from stim onset:
0s
12s
24s
Fourier analysis of block design experiment
Fourier analysis of block design experiment
Significance
• Which voxels are activated?
Significance: ROI-based analysis
• ICE15.m shows a comparison of 2 methods for assigning
confidence intervals to estimated regression coefficients
– Bootstrapping: repeat simulation many times (1000 times), and look at
the distribution of fits. A 95% confidence interval can be calculated
directly from the standard deviation of this distribution (+/- 1.96*sigma)
– Matlab’s regress.m function, which relies the assumption of normally
distributed independent noise
• The residuals after the fit are used to estimate the distribution of noise
• The standard error of the regression weights is calculated, based on the
standard deviaion of the noise (residuals), and used to assign 95%
confidence intervals.
• When the noise is normal and independent, these two methods
should agree
Multiple comparisons
• How do we correct for the fact that, just by chance, we
could see as many as 500 false positives in our data?
– Bonferonni correction: divide desired significance level (e.g. p <
.05) by number of comparisons (e.g. 10,000 voxels) - display
only voxels significant at p < .000005.
• Too stringent!
– False Discovery Rate: currently implemented in most software
packages
• “FDR controls the expected proportion of false positives among
suprathreshold voxels. A FDR threshold is determined from the
observed p-value distribution, and hence is adaptive to the amount
of signal in your data.” (Tom Nichols’ website)
• See http://www.sph.umich.edu/~nichols/FDR/