Our entry in the
Functional Imaging
Analysis contest
Jonathan Taylor
Stanford
Keith Worsley
McGill
What is functional Magnetic
Resonance Imaging (fMRI) data?






Time series of ~200 “frames”, 3D images of
brain “activity”, taken every ~2.5s (~8min)
Meanwhile, subject receives stimulus or
external task (e.g on/off every 10s)
Several (~4) time series (“runs”) per session
Several (~2) sessions per subject
Several (~15) subjects
Statistics problem: find the regions of the
brain activated by the stimulus or task
Why a Functional Imaging
Analysis Contest (FIAC)?






Competing packages produce slightly
different results, which is “correct”?
Simulated data?
Real data, compare analyses
“Contest” session at 2005 Human Brain Map
conference
9 entrants
Results in a special issue of Human Brain
Mapping in May, 2006
The main participants






SPM (Statistical Parametric Mapping, 1993),
University College, London, “SAS”, (MATLAB)
AFNI (1995), NIH, more display and
manipulation, not much stats (C)
FSL (2000), Oxford, the “upstart” (C)
….
FMRISTAT (2001), McGill, stats only (MATLAB)
BRAINSTAT (2005), Stanford/McGill, Python
version of FMRISTAT
Effect of stimulus on brain response
Alternating hot and warm stimuli separated by rest (9 seconds each).
2
1
0
-1
0
50
100
150
200
250
300
350
Hemodynamic response function: difference of two gamma densities
Stimulus is
delayed and
dispersed by ~6s
0.4

0.2
0
Modeled by convolving
the stimulus with the
“hemodynamic
response function”
-0.2
0
50
Responses = stimuli * HRF, sampled every 3 seconds
2
1
0
-1
0
50
100
150
200
Time, seconds
250
300
350
fMRI data, pain experiment, one slice
First scan of fMRI data
Highly significant effect, T=6.59
1000
hot
rest
warm
890
880
870
500
0
100
200
300
No significant effect, T=-0.74
820
hot
rest
warm
0
800
T statistic for hot - warm effect
5
0
-5
T = (hot – warm effect) / S.d.
~ t110 if no effect
0
100
0
100
200
Drift
300
810
800
790
200
Time, seconds
300
How fMRI differs from other
repeated measures data





Many reps (~200 time points)
Few subjects (~15)
Df within subjects is high, so not worth
pooling sd across subjects
Df between subjects low, so use spatial
smoothing to boost df
Data sets are huge ~4GB, not easy to use R
directly
FMRISTAT / BRAINSTAT
statistical analysis strategy

Analyse each voxel separately


Break up analysis into stages


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

Borrow strength from neighbours when needed
1st level: analyse each time series separately
2nd level: combine 1st level results over runs
3rd level: combine 2nd level results over subjects
Cut corners: do a reasonable analysis in a
reasonable time (or else no one will use it!)
MATLAB / Python
1st level:
Linear model with AR(p) errors

Data



Model



Yt = fMRI data at time t
xt = (responses,1, t, t2, t3, … )’ to allow for drift
Yt = xt’β + εt
εt = a1εt-1 + … + apεt-p + σFηt,
ηt ~ N(0,1) i.i.d.
Fit in 2 stages:


1st pass: fit by least squares, find residuals,
estimate AR parameters a1 … ap
2nd pass: whiten data, re-fit by least squares
Higher levels:
Mixed effects model

Data

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
Model

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Ei = effect (contrast in β) from previous level
Si = sd of effect from previous level
zi = (1, treatment, group, gender, …)’
Ei = zi’γ + SiεiF + σRεiR (Si high df, so assumed fixed)
εiF ~ N(0,1) i.i.d. fixed effects error
εiR ~ N(0,1) i.i.d. random effects error
Fit by ReML

Use EM for stability, 10 iterations
Where we use spatial
information

1st level: smooth AR parameters to lower
variability and increase “df”

Higher levels: smooth Random / Fixed effects
sd ratio to lower variability and increase “df”

Final level: use random field theory to correct
for multiple comparisons
1st level: Autocorrelation
AR(1) model: εt = a1 εt-1 + σFηt
 Fit the linear model using least squares
 εt = Y t – Y t
 â1 = Correlation (εt , εt-1)
 Estimating errort’s changes their correlation structure
slightly, so â1 is slightly biased:

Raw autocorrelation Smoothed 12.4mm
~ -0.05
Bias corrected â1
~0
0.3
0.2
0.1
0
-0.1
How much smoothing?
• Variability in
acor lowers df
• Df depends
on contrast
• Smoothing acor
brings df back up:
(
dfacor = dfresidual
1
1
dfeff = dfresidual+
Hot stimulus
FWHMacor2
2
+1
2
FWHMdata
2 acor(contrast of data)2
dfacor
FWHMdata = 8.79
Residual df = 110
0
100
Target = 100 df
Contrast of data, acor = 0.61
dfeff
0
10
20
FWHM = 10.3mm
Hot-warm stimulus
Residual df = 110
100
Target = 100 df
50
)
3/2
Contrast of data, acor = 0.79
50
dfeff
30
FWHMacor
0
0
10
20
FWHM = 12.4mm
30
FWHMacor
Higher order AR model? Try AR(3):
a1
a2
a3
0.3
0.2
AR(1) seems
to be adequate
0.1
0
… has little effect on the T statistics:
No correlation
AR(1), df=100
AR(2), df=99
-0.1
AR(3), df=98
5
0
-5
biases T up ~12% → more false positives
2nd level: 4 runs, 3 df for random effects sd
Run 1
Run 2
Run 3
Run 4
2nd level
Effect,
Ei
1
0
… very noisy sd:
-1
0.2
Sd,
Si
0.1
… and T>15.96 for P<0.05 (corrected):
0
5
T stat,
E i / Si
0
… so no response is detected …
-5
Solution:
Spatial smoothing of the sd ratio
• Basic idea: increase df by spatial smoothing
(local pooling) of the sd.
• Can’t smooth the random effects sd directly,
- too much anatomical structure.
• Instead,

sd = smooth
random effects sd
 fixed effects sd
fixed effects sd
)
which removes the anatomical structure
before smoothing.
^

Average Si
Random effects sd, 3 df
Fixed effects sd, 440 df
Mixed effects sd, ~100 df
0.2
0.15
0.1
0.05
divide
Random sd / fixed sd
0
multiply
Smoothed sd ratio
1.5
1
0.5
random
effect, sd
ratio ~1.3
How much smoothing?
(
dfratio = dfrandom
FWHMratio2
2
+1
2
FWHMdata
)
1
1
1
=
+
dfeff dfratio dffixed
3/2
dfrandom = 3,
dffixed = 4  110
= 440,
FWHMdata = 8mm:
fixed effects
analysis,
dfeff = 440
400
300
dfeff
Target = 100 df
random effects
analysis,
dfeff = 3
200
FWHM
= 19mm
100
0
0
20
40
FWHMratio
Infinity
Final result: 19mm smoothing, 100 df
Run 1
Run 2
Run 3
Run 4
2nd level
Effect,
Ei
1
0
… less noisy sd:
-1
0.2
Sd,
Si
0.1
… and T>4.93 for P<0.05 (corrected):
0
5
T stat,
E i / Si
0
… and now we can detect a response!
-5
Final level: Multiple comparisons correction
Bonferroni
4.7
4.6
Gaussianized threshold
4.5
True
4.4
4.3
4.2
T, 10 df
Random Field Theory
T, 20 df
Discrete Local Maxima (DLM)
4.1
Gaussian
4
3.9
3.8
3.7
0
Low FWHM:
use Bonferroni
1
2
3
4
5
6
7
8
FWHM of smoothing kernel (voxels)
In between: use Discrete
Local Maxima (DLM)
9
10
High FWHM: use
Random Field Theory
0.12
Gaussian
T, 20 df
T, 10 df
0.1
Random Field Theory
Bonferroni
P-value
0.08
0.06
0.04
True
DLM can ½ P-value
when FWHM ~3 voxels
0.02
0
Discrete Local Maxima
0
Low FWHM:
use Bonferroni
1
2
3
4
5
6
7
FWHM of smoothing kernel (voxels)
In between: use Discrete
Local Maxima (DLM)
8
9
10
High FWHM: use
Random Field Theory
FIAC paradigm
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16 subjects
4 runs per subject
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4 conditions per run
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2 runs: event design
2 runs: block design
Same sentence, same speaker
Same sentence, different speaker
Different sentence, same speaker
Different sentence, different speaker
3T, 191 frames, TR=2.5s
Response

Events
0.4
0.2
0
-0.2
0
50
100
150
200
250
300
350
400
450
500
350
400
450
500
Beginning of block/run

Blocks
0.4
0.2
0
-0.2
0
50
100
150
200
250
Seconds
300
Design matrix for block expt

B1, B2 are basis functions for magnitude and delay:
1st snt in block
S snt, S spk, B1
S snt, S spk, B2
S snt, D spk, B1
S snt, D spk, B2
D snt, S spk, B1
D snt, S spk, B2
D snt, D spk, B1
D snt, D spk, B2
Constant
Linear
Quadratic
Cubic
Spline
Whole brain avg
1st level analysis


Motion and slice time correction (using FSL)
5 conditions
3 contrasts
Beginning
of block/run
Same sent, Same sent,
same speak diff speak
Diff sent,
same speak
Diff sent,
diff speak
Sentence
Speaker
0
0
-0.5
-0.5
-0.5
0.5
0.5
-0.5
0.5
0.5
1
-1
-1
1
Interaction 0

Smoothing of temporal autocorrelation to
control the effective df
Magnitude sd (relative to error)
Efficiency
2
1.5
Sd of contrasts (lower is
better) for a single run,
assuming additivity of
responses
Event
Block
1
0.5
0
Diff sente Diff speak
• For the magnitudes,
event and block have
similar efficiency
• For the delays, event is
much better.
Interac
Delay sd (seconds)
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Event
Block
Diff sente Diff speak
Interac
2nd level analysis


Analyse events and blocks separately
Register contrasts to Talairach (using FSL)


Bad registration on 2 subjects - dropped
Combine 2 runs using fixed FX
3rd level analysis

Combine remaining 14 subjects using random FX


3 contrasts × event/block × magnitude/delay = 12
Threshold using best of Bonferroni, random field
theory, and discrete local maxima (new!)
Part of slice
z = -2 mm
Magnitude (%BOLD), diff - same sentence, event experiment
Subj 0
1
3
4
6
7
8
9
10
11
12
13
14
Mixed
effects
15
Left
2
1
0
Ef
Right
-1
Random
/fixed
effects sd
smoothed
7.0105mm
1.5
-2
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: min fMRI > 6214
1
Left
Sd
Right
271
272
271
265
264
132
270
275
269
274
248
256
264
278
1
0
0.5
5
FWHM (mm)
15
40
Left
-50
T
0
x (mm)
df
0.5
10
0
5
50
Ant.
Post.
Right
P=0.05 threshold for local maxima is +/- 5.68
-5
-40-20 0
y (mm)
0
Magnitude (%BOLD), diff - same sentence, block experiment
Subj 0
1
3
4
6
7
8
9
10
11
12
13
14
Mixed
effects
15
Left
2
1
0
Ef
Right
-1
Random
/fixed
effects sd
smoothed
7.103mm
1.5
-2
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: min fMRI > 5904
1
Left
Sd
Right
202
202
204
205
204
203
201
202
200
206
205
202
204
200
1
0
0.5
5
FWHM (mm)
15
40
Left
-50
T
0
x (mm)
df
0.5
10
0
5
50
Ant.
Post.
Right
P=0.05 threshold for local maxima is +/- 5.67
-5
-40-20 0
y (mm)
0
Delay shift (secs), diff - same sentence, event experiment
Subj 0
1
3
4
6
7
8
9
10
11
12
13
14
Mixed
effects
15
Left
0.2
0.1
0
-0.1
-0.2
Ef
Right
Random
/fixed
effects sd
smoothed
10.6778mm
1.5
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: magnitude, stimulus average, T statistic > 5
Left
0.4
Sd
1
0.2
Right
df
271
272
271
265
264
132
270
275
269
274
248
256
264
278
0
0.5
40
FWHM (mm)
15
T
0
-2
Ant.
Post.
Right
P=0.05 threshold for local maxima is +/- 4.31
-50
x (mm)
Left
2
10
0
5
50
-40-20 0
y (mm)
0
Delay shift (secs), diff - same sentence, block experiment
Subj 0
1
3
4
6
7
8
9
10
11
12
13
14
Mixed
effects
15
Left
1
0.5
0
Ef
Right
-0.5
Random
/fixed
effects sd
smoothed
8.8952mm
1.5
-1
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: magnitude, stimulus average, T statistic > 5
2
Left
1.5
Sd
1
1
0.5
Right
df
202
202
204
205
204
203
201
202
200
206
205
202
204
200
0
0.5
40
FWHM (mm)
15
T
0
-2
Ant.
Post.
Right
P=0.05 threshold for local maxima is +/- 4.3
-50
x (mm)
Left
2
10
0
5
50
-40-20 0
y (mm)
0
Event
Block
Subj 0
1
3
4
6
7
8
9
10
11
12
13
14
Magnitude (%BOLD), diff - same sentence, block experiment
Mixed
effects
15
1
3
4
6
7
8
9
10
11
12
13
14
Left
Left
0
0
Random
/fixed
effects sd
smoothed
7.0105mm
1.5
-2
1
1
Left
271
265
264
132
270
275
269
274
248
256
264
278
Sd
0.5
1
0
0.5
40
Right
Right
272
Random
/fixed
effects sd
smoothed
7.103mm
1.5
-2
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: min fMRI > 5904
Left
Sd
271
-1
Right
Right
-1
2
1
Ef
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: min fMRI > 6214
df
Mixed
effects
15
1
Ef
Magnitude
Subj 0
2
df
202
202
204
205
204
203
201
202
200
206
205
202
204
200
x (mm)
10
FWHM (mm)
15
-50
T
0
0.5
Left
Left
0
0
5
-50
T
1
40
FWHM (mm)
15
5
0.5
0
5
x (mm)
Magnitude (%BOLD), diff - same sentence, event experiment
50
1
3
4
6
7
8
9
10
11
12
13
14
-40-20 0
y (mm)
P=0.05 threshold for local maxima is +/- 5.67
Delay shift (secs), diff - same sentence, block experiment
Mixed
effects
15
Subj 0
1
3
4
6
7
8
9
10
11
12
13
14
Mixed
effects
15
Left
Left
0.2
0.1
0
-0.1
-0.2
Ef
-0.5
2
1.5
Sd
1
0.2
271
272
271
265
264
132
270
275
269
274
248
256
264
278
1
0.5
0
Right
Right
df
Random
/fixed
effects sd
smoothed
8.8952mm
1.5
-1
Left
Left
1
0.5
40
df
202
202
204
205
204
203
201
202
200
206
205
202
204
200
0
0.5
40
-2
10
T
0
2
-50
0
5
50
0
P=0.05 threshold for local maxima is +/- 4.3
Ant.
-40-20 0
y (mm)
-2
Post.
Right
Ant.
Post.
Right
P=0.05 threshold for local maxima is +/- 4.31
x (mm)
0
-50
Left
Left
T
FWHM (mm)
15
x (mm)
FWHM (mm)
15
2
0
1
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: magnitude, stimulus average, T statistic > 5
0.4
Sd
-40-20 0
y (mm)
0
Right
Right
Random
/fixed
effects sd
smoothed
10.6778mm
1.5
-5
0.5
Ef
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: magnitude, stimulus average, T statistic > 5
Delay
0
Ant.
Subj 0
5
50
Post.
Right
Delay shift (secs), diff - same sentence, event experiment
-5
Ant.
Post.
Right
P=0.05 threshold for local maxima is +/- 5.68
10
0
10
0
5
50
-40-20 0
y (mm)
0
Events vs blocks for delays
in different – same sentence



Events: 0.14±0.04s; Blocks: 1.19±0.23s
Both significant, P<0.05 (corrected) (!?!)
Answer: take a look at blocks:
Greater
magnitude
Best fitting block
Greater
delay
Different sentence
(sustained interest)
Same sentence
(lose interest)
SPM
BRAINSTAT
Magnitude increase for
 Sentence, Event
 Sentence, Block
 Sentence, Combined
 Speaker, Combined
at (-54,-14,-2)
Magnitude decrease for
 Sentence, Block
 Sentence, Combined
at (-54,-54,40)
Delay increase for
Sentence, Event
at (58,-18,2)
inside the region where all
conditions are activated
Conclusions

Greater %BOLD response for



different – same sentences (1.08±0.16%)
different – same speaker (0.47±0.0.8%)
Greater latency for

different – same sentences (0.148±0.035 secs)
The main effects of sentence repetition (in red) and of speaker
repetition (in blue). 1: Meriaux et al, Madic; 2: Goebel et al, Brain
voyager; 3: Beckman et al, FSL; 4: Dehaene-Lambertz et al, SPM2.
z=-12
z=2
2
3
z=5
1
1,4
3
Brainstat:
combined
block and
event,
threshold
at T>5.67,
P<0.05.
3
3
1
3
Estimating the delay of the response
• Delay or latency to the peak of the HRF is approximated by
a linear combination of two optimally chosen basis functions:
delay
0.6
0.4
basis1
0.2
HRF
basis2
0
-0.2
-0.4
-5
0
shift
5
10
t (seconds)
15
20
25
HRF(t + shift) ~ basis1(t) w1(shift) + basis2(t) w2(shift)
• Convolve bases with the stimulus, then add to the linear model
• Fit linear model,
estimate w1 and w2
3
w2 / w1
2
1
• Equate w2 / w1 to estimates, then
solve for shift (Hensen et al., 2002)
w1
• To reduce bias when the magnitude
is small, use
0
w2
shift / (1 + 1/T2)
-1
where T = w1 / Sd(w1) is the T statistic
for the magnitude
-2
-3
-5
0
shift (seconds)
5
• Shrinks shift to 0 where there is little
evidence for a response.
Magnitude (%BOLD), stimulus average
0
1
3
4
6
7
Subject id, event experiment
8
9
10
11
12
13
14
15
Mixed
effects
6
4
Ef
2
0
Random
/fixed
effects sd
smoothed
10.836mm
-2
Contour is: average anatomy > 2000
2
1.5
1.5
Sd
1
1
0.5
200
200
200
200
200
100
200
200
200
200
200
200
200
200
0.5
5
FWHM (mm)
20
50
15
100
10
150
100
T
0
x (mm)
df
0
5
200
-5
P=0.05 threshold for peaks is +/- 5.1687
250
120
140
160
180
y (mm)
0
Magnitude (%BOLD), stimulus average
0
1
3
4
6
7
Subject id, block experiment
8
9
10
11
12
13
14
15
Mixed
effects
4
Ef
2
Random
/fixed
effects sd
smoothed
6.7765mm
0
Contour is: average anatomy > 2000
1
6
Sd
0.5
4
2
0
df
209
209
214
210
211
210
210
207
212
214
214
210
210
216
99
FWHM (mm)
20
20
-50
T
10
5
0
-5
P=0.05 threshold for peaks is +/- 5.9873
x (mm)
15
15
0
10
50
5
-60
-40
-20 0
y (mm)
0
Magnitude (%BOLD), diff - same speaker
0
1
3
4
6
7
Subject id, event experiment
8
9
10
11
12
13
14
15
Mixed
effects
2
1
Ef
0
-1
Random
/fixed
effects sd
smoothed
11.7848mm
1.5
-2
Contour is: average anatomy > 2000
2
1.5
Sd
1
1
0.5
df
273
271
276
281
274
136
265
293
264
268
265
264
296
270
0
0.5
5
FWHM (mm)
20
100
T
0
-5
P=0.05 threshold for peaks is +/- 5.1469
x (mm)
-50
15
0
10
50
5
-60
-40
-20 0
y (mm)
0
Magnitude (%BOLD), diff - same speaker
0
1
3
4
6
7
Subject id, block experiment
8
9
10
11
12
13
14
15
Mixed
effects
2
1
Ef
0
-1
Random
/fixed
effects sd
smoothed
11.9735mm
1.5
-2
Contour is: average anatomy > 2000
1
Sd
df
201
202
200
206
201
201
200
200
204
204
206
201
205
204
0.5
1
0
0.5
5
FWHM (mm)
20
100
T
0
-5
P=0.05 threshold for peaks is +/- 5.1666
x (mm)
-50
15
0
10
50
5
-60
-40
-20 0
y (mm)
0
Magnitude (%BOLD), interaction
0
1
3
4
6
7
Subject id, event experiment
8
9
10
11
12
13
14
15
Mixed
effects
2
1
Ef
0
-1
Random
/fixed
effects sd
smoothed
11.4737mm
1.5
-2
Contour is: average anatomy > 2000
2
1.5
Sd
1
1
0.5
df
278
278
279
280
264
126
277
287
264
272
260
277
264
264
0
0.5
5
FWHM (mm)
20
100
T
0
-5
P=0.05 threshold for peaks is +/- 5.4124
x (mm)
-50
15
0
10
50
5
-60
-40
-20 0
y (mm)
0
Magnitude (%BOLD), interaction
0
1
3
4
6
7
Subject id, block experiment
8
9
10
11
12
13
14
15
Mixed
effects
2
1
Ef
0
-1
Random
/fixed
effects sd
smoothed
12.1993mm
1.5
-2
Contour is: average anatomy > 2000
1
Sd
df
204
200
207
200
204
205
202
203
202
204
206
201
201
200
0.5
1
0
0.5
5
FWHM (mm)
20
100
T
0
-5
P=0.05 threshold for peaks is +/- 5.1467
x (mm)
-50
15
0
10
50
5
-60
-40
-20 0
y (mm)
0
Delay shift (secs), stimulus average
0
1
3
4
6
7
Subject id, event experiment
8
9
10
11
12
13
14
15
Mixed
effects
2
1
Ef
0
-1
Random
/fixed
effects sd
smoothed
13.3482mm
1.5
-2
Contour is: magnitude, stimulus average, T statistic > 5
2
1.5
Sd
1
1
0.5
df
200
200
200
200
200
100
200
200
200
200
200
200
200
200
0
0.5
4
FWHM (mm)
20
100
-50
T
0
-2
-4
P=0.05 threshold for peaks is +/- 3.8943
x (mm)
2
15
0
10
50
5
-60
-40
-20 0
y (mm)
0
Delay shift (secs), stimulus average
0
1
3
4
6
7
Subject id, block experiment
8
9
10
11
12
13
14
15
Mixed
effects
2
1
Ef
0
-1
Random
/fixed
effects sd
smoothed
13.5901mm
1.5
-2
Contour is: magnitude, stimulus average, T statistic > 5
2
1.5
Sd
1
1
0.5
df
209
209
214
210
211
210
210
207
212
214
214
210
210
216
0
0.5
4
FWHM (mm)
20
100
-50
T
0
-2
-4
P=0.05 threshold for peaks is +/- 3.983
x (mm)
2
15
0
10
50
5
-60
-40
-20 0
y (mm)
0
Delay shift (secs), diff - same speaker
0
1
3
4
6
7
Subject id, event experiment
8
9
10
11
12
13
14
15
Mixed
effects
2
1
Ef
0
-1
Random
/fixed
effects sd
smoothed
16.9641mm
1.5
-2
Contour is: magnitude, stimulus average, T statistic > 5
2
1.5
Sd
1
1
0.5
df
273
271
276
281
274
136
265
293
264
268
265
264
296
270
0
0.5
4
FWHM (mm)
20
100
-50
T
0
-2
-4
Peaks not significant at P=0.05
x (mm)
2
15
0
10
50
5
-60
-40
-20 0
y (mm)
0
Delay shift (secs), diff - same speaker
0
1
3
4
6
7
Subject id, block experiment
8
9
10
11
12
13
14
15
Mixed
effects
2
1
Ef
0
-1
Random
/fixed
effects sd
smoothed
14.3951mm
1.5
-2
Contour is: magnitude, stimulus average, T statistic > 5
2
1.5
Sd
1
1
0.5
df
201
202
200
206
201
201
200
200
204
204
206
201
205
204
0
0.5
4
FWHM (mm)
20
100
-50
T
0
-2
-4
Peaks not significant at P=0.05
x (mm)
2
15
0
10
50
5
-60
-40
-20 0
y (mm)
0
Delay shift (secs), interaction
0
1
3
4
6
7
Subject id, event experiment
8
9
10
11
12
13
14
15
Mixed
effects
2
1
Ef
0
-1
Random
/fixed
effects sd
smoothed
16.9013mm
1.5
-2
Contour is: magnitude, stimulus average, T statistic > 5
2
1.5
Sd
1
1
0.5
df
278
278
279
280
264
126
277
287
264
272
260
277
264
264
0
0.5
4
FWHM (mm)
20
100
-50
T
0
-2
-4
P=0.05 threshold for peaks is +/- 3.8306
x (mm)
2
15
0
10
50
5
-60
-40
-20 0
y (mm)
0
Delay shift (secs), interaction
0
1
3
4
6
7
Subject id, block experiment
8
9
10
11
12
13
14
15
Mixed
effects
2
1
Ef
0
-1
Random
/fixed
effects sd
smoothed
14.4178mm
1.5
-2
Contour is: magnitude, stimulus average, T statistic > 5
2
1.5
Sd
1
1
0.5
df
204
200
207
200
204
205
202
203
202
204
206
201
201
200
0
0.5
4
FWHM (mm)
20
100
-50
T
0
-2
-4
Peaks not significant at P=0.05
x (mm)
2
15
0
10
50
5
-60
-40
-20 0
y (mm)
0
STAT_SUMMARY example: single run, hot-warm
Detected by BON and
DLM but not by RFT
Detected by DLM,
but not by BON or RFT