1. fMRI data analysis – t-tests and correlations.

2. Hypotheses vs. Data Hypothesis-driven Data-driven
Examples: t-tests, correlations, general linear model (GLM)
a priori model of activation is suggested
comparison between data and model is made
most commonly used approach
Data-driven
Independent Component Analysis (ICA)
no prior hypotheses are necessary – operates somewhat like factor analysis
multivariate techniques determine the patterns in the data that account for the most variance across all voxels
can be used to validate a model (see if the math comes up with the components you would’ve predicted)
can be inspected to see if there are things happening in your data that you didn’t predict
need a way to organize the many possible components
new and upcoming

3. Why do we need statistics?
MR Signal intensities are arbitrary
-vary from magnet to magnet, coil to coil, within a coil (especially surface coil), day to day, even run to run
-may also vary from area to area (some areas may be more metabolically active)
We must always have a comparison condition within the same run (baseline or control contrasts)
We need to know whether the “eyeball tests of significance” are real.
Because we do so many comparisons, we need a way to compensate (e.g., Bonferroni, clusters, etc.).

4. Example Experiment Simple vs complex finger tapping sequences protocol
experiment in patient SP – with large porencephalic syst
Purpose: Can we identify regions responding to simple and complex motor tasks in remaining left hemisphere cortex
3 conditions – simple alternating tapping (tap index and middle fingers alternately for 20 seconds), complex tapping (tap fingers in sequences indicated on screen) and rest
protocol
images 1 21 41 % s i g n a l c h e 2 3 -1
head coil
19 quasi-axial slices
volume time = 4 sec
3 x 3 x 6 voxels
sequential tapping
alternating tapping

5. Statistical Analyses: T-test
simple, sometimes seems more reliable than fancy stuff
compare the means and standard deviations between two conditions
shift activation to compensate for hemodynamic lag (HDL) – assume a 4- 6 sec lag so with a 4 sec TR this would be a one or two volume shift (can’t do a one a half volume shift)
given that only means are tested the shift for the HDL is not an accurate model of the function
each voxel considered an ‘n’ – so Bonferroni correction is made for the number of voxels compared
images 1 21 41 % s i g n a l c h e 2 3 -1
simple shift of
function to
accommodate HRF
Kolmogorov-Smirnov
non-parametric version of t-test – instead of comparing means of two populations,
the cumulative distributions are compared
sensitive to differences in variance as well as means – so could detect a difference between
two populations with the same means but different SDs (t-test can’t do this)
more conservative than t-tests

6. T-test: Stats e h c l a n g i s % images
To look for Complex vs. Simple tapping activation, for a given voxel:
Measure average MR signal and SD for each volume in which complex tapping was performed (2 epochs x 5 volumes/epoch = 10 volumes)
images 1 21 41 % s i g n a l c h e 2 3 -1
Measure average MR signal and SD for each volume in which simple tapping was performed (10 volumes)
complex
simple
To look for Simple > Complex tapping activation, look at the negative tail of the comparison
S>C
C>S MR
Signal
Determine if mean difference is statistically significant:
Calculate t-value.
Use t to look up p value for that number of degrees of freedom (df = 10 x 2 = 20).
e.g., For ~20 df
t >1.98  p <.05 (1/20 chance)
t > 3.39  p < .001 (1/1000 chance)
complex
simple
Notice a problem yet?… With a probability of .001 and 49,152 voxels, 49152*.001 = 49 voxels could be significant purely by chance
Repeat this process 49,152 more times (64x64x12), once for each voxel in the volume obtained.

7. T-test: Maps
For each voxel in the brain, we can now color code a map based on the computed t and p values:
We can do this for the positive tail (Complex > Simple tapping)
Orange = low significance
Yellow = high significance
Schmutz or ESP voxels?
And we can also do this for the negative tail (Simple > Complex tapping)
Blue = low significance
Green = high significance

8. T-test: Surfing
We can surf the significant voxels to see what their time courses look like s g l c h a n e 1 21
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images 6 4 2 -1 1 3 5 % s i g n a l c h e
images
Creating event related averages.
sync activation to same starting point
average across epochs (determine variance)
compare activation in a given area

9. Correcting for linear trends
We can surf the significant voxels to see what their time courses look like
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images
Linear trend
- could be due to magnet (e.g., warming up) or subject (e.g., head slowly settling)
Bad paradigm design – linear confound
Problematic for two reasons
If it is correlated with our paradigm, it could give us false positives or false rejections
It adds extra variability to our statistical computations and makes it less likely to reach significance

10. Linear Trend Removal
After LTR, significance levels increase considerably.

11. Linear Trend Removal
Because our statistics are now more reliable, we can bump up the threshold and get rid of some of the schmutz.
We can also superimpose the stat map on top of the anatomical image to compare it to landmarks.

12. Hemodynamic Response Function
% signal change
= (point – baseline)/baseline
usually 0.5-3%
initial dip
-more focal and potentially a better measure
-somewhat elusive so far, not everyone can find it
time to rise
signal begins to rise soon after stimulus begins
time to peak
signal peaks 4-6 sec after stimulus begins
post stimulus undershoot
signal suppressed after stimulation ends

13. Correlations: Incorporating the HRF
We can model the expected curve of the data by convolving our predictor with the hemodynamic response function.
basic model
standard box-car function
convolved model
To find a region responsive to complex tapping AND simple tapping, we can correlate the convolved model predictor with each voxel time course
fMRI signal

14. Statistical Analyses: Basic Correlation
Correlation analysis
voxels with time course correlated with reference function
can incorporate hemodynamic response function (HRF) to predict time course more accurately (compared with simple shifting of the function in t-tests)
value of fMRI signal
volumes
For each voxel:
Find the correlation between the predictor and the MR signal
Extract the correlation (r value) and find the corresponding p value.
Determine whether it is statistically significant
In this example, similar in spirit to a t-test.
Remember r2 is the proportion of variance accounted for by our predictor, e.g., if r = .7, r2 = .5 = 50%

15. Problems with t-tests and correlations
How do we evaluate runs with different orders?
Right now, we could average our two runs done in Order1 together, and also average our two runs done in Order2 together and then do stats on the two orders separately. There is no way to collapse between orders. If there is an artifact on part of one run, we have to exclude the whole run.
2) If we test more subjects, how can we evaluate the subjects together?
As with the single subject runs, we could average all the subjects together (after morphing them into a common brain space) but that still means we have to run all of them in the same order.
2) We can get nice hemodynamic predictors for simple vs. complex finger tapping but how can we compare them accurately?
convolved model
If this predictor is significant, we won’t know if it’s because complex>simple OR because complex>rest
Design Matrix
Stay tuned next week for the solution: General Linear Model

16. Two approaches: ROI A. ROI approach MT
Do (a) localizer run(s) to find a region (e.g., show moving rings to find MT)
Extract time course information from that region in separate independent runs
See if the trends in that region are statistically significant
Because the runs that are used to generate the area are independent from those used to test the hypothesis, liberal statistics can be used
Example study: Tootell et al, 1995, Motion Aftereffect
Localize “motion area” MT in a run comparing moving vs. stationary rings
Extract time courses from MT in subsequent runs while subjects see illusory motion (motion aftereffect) MT
Source: Tootell et al., 1995

17. Two Approaches: Whole Brain Stats
B. Whole volume statistical approach
Make predictions about what differences you should see if your hypotheses are correct
Decide on statistical measures to test for predicted differences (e.g., t-tests, correlations, GLMs)
Determine appropriate statistical threshold
See if statistical estimates are significant
Statistics available
t-test
correlation
Fourier modelling (not discussed here – popular in the Stanford group – see brief description in Buxton Ch 18)
General Linear Model
-overarching statistical model that lets you perform many types of statistical analyses (including correlations, ANOVAs)
Source: Tootell et al., 1995

18. Comparing the two approaches
Region of Interest (ROI) Analyses
Gives you more statistical power because you do not have to correct for the number of comparisons
Hypothesis-driven
ROI is not smeared due to intersubject averaging
Easy to analyze and interpret
Neglects other areas which may play a fundamental role
Popular in North America
Whole Brain Analysis
Requires no prior hypotheses about areas involved
Includes entire brain
Can lose spatial resolution with intersubject averaging
Can produce meaningless “laundry lists of areas” that are difficult to interpret
Depends highly on statistics and threshold selected
Popular in Europe
NOTE: Though different experimenters tend to prefer one method over the other, they are NOT mutually exclusive. You can check ROIs you predicted and then check the data for other areas.
Source: Tootell et al., 1995