1. 2nd Level Analysis Methods for Dummies 2010/11 - 2nd Feb 2011
Fiona McNab & Jen Marchant

2. 2nd Level Analysis Standard template Motion correction Smoothing
kernel
Spatial
normalisation
Standard
template
fMRI time-series
Statistical Parametric Map
General Linear Model
Design matrix
Parameter Estimates

3. Group Analysis: Fixed vs Random
 In SPM known as random effects (RFX)

4. Group Analysis: Fixed-effects
specific to cases in your study
can NOT make inferences about the population
only takes into account within-subject variance
useful if only have a few subjects (eg case studies)
Because between subject variance not considered, you may get larger effects

5. Fixed-effects Analysis in SPM
multi-subject 1st level design
no 2nd level
each subjects entered as separate sessions
create contrast across all subjects
e.g. condition A>B
c = [ ]
perform one sample t-test
Subject 1
Subject 2
Subject 3
Subject 4
Subject 5
Multisubject 1st level :
5 subjects x 1 run each

6. Group analysis: Random-effects
CAN make inferences about the population
takes into account between-subject variance

7. Methods for Random-effects
Hierarchical model
Estimates subject & group stats at once
Variance of population mean contains contributions
from within- & between- subject variance
Iterative looping  computationally demanding
Summary statistics approach  SPM uses this!
2 levels (1st = within-subject ; 2nd = between-subject)
1st level design must be the SAME
Only sample means brought forward to 2nd level
Computationally less demanding
Good approximation, unless subject extreme outlier
Friston et al. (2004) Mixed effects and fMRI studies, Neuroimage

8. Random-effects Analysis in SPM
Session 1
Session 2
Session3
Session 4
Session 5
Random-effects
1st level design per subject
generate contrast image per subject (con.*img)
images MUST have same dimensions & voxel sizes
con*.img for each subject entered in 2nd level analysis
perform stats test at 2nd level
Single subject 1st level :
1 subject x 5 runs

9. Random-effects Analysis in SPM
1st level design per subject
generate contrast image per subject (con.*img)
images MUST have same dimensions & voxel sizes
con*.img for each subject entered in 2nd level analysis
perform stats test at 2nd level
NOTE: if 1 subject has 4 sessions but everyone else has 5, you need to adjust your contrast!
Subject #1 x 5 runs (1st level)
Subject #2 x 5 runs (1st level)
Subject #3 x 5 runs (1st level)
Subject #4 x 5 runs (1st level)
Subject #5 x 4 runs (1st level)
contrast = [ ]
contrast = [ ]
contrast = [ ]
contrast = [ ]
contrast = [ ] * (5/4)

10. 2nd Level Analysis FIRST LEVEL (per person)
Data Design Contrast
Matrix Image
SECOND LEVEL Group analysis
SPM(t)
One-sample
2nd level

11. Stats tests at the 2nd Level
Choose the simplest 2nd level : one sample t-test
Compute within-subject 1st level
Each contrasts you compute generates a con*.img
Enter 1 con*.img for each person into model
Can also model covariates across the group
- vector containing 1 value per con*.img,
e.g. Compare responses between conditions A and B:
1st level design: A1 B1 A2 B2 A3 B3 A4 B4
1st level contrast A>B: [ ]  A>B con*.img
Enter A>B con*.img into 2nd level 1 sample t-test
2nd level contrast A>B: [ 1 ]
2nd level contrast A<B: [ -1 ]
1 column because it’s a one sample t-test without covariates
1 row per con*.img
(ie per subject)

12. Stats tests at the 2nd Level
If you have 2 subject groups: two sample t-test
Same design matrices for all subjects in a group
Enter con*.img for each group member
Not necessary to have same no. subject in each group
Assume measurement independent between groups
Assume unequal variance between each group
e.g. between group effect: c = [ 1 -1]  Group 1 > Group 2
c = [-1 1]  Group 1 < Group 2 1 3 2 4 5 6 8 7 9 10 11 12
Group Group 1
black
value = 0
white: value = 1
1st column models group 1
2nd column models group 2

13. Stats tests at the 2nd Level
If you have no other choice: ANOVA
Designs are much more complex
e.g. within-subject ANOVA need covariate per subject 
BEWARE sphericity assumptions may be violated, need to account for
Better approach:
generate main effects & interaction contrasts at 1st level
c = [ ] ; c = [ ] ; c = [ ]
use separate t-tests at the 2nd level 
Subject 10
Subject 11
Subject 1
Subject 2
Subject 3
Subject 4
Subject 5
Subject 6
Subject 7
Subject 8
Subject 9
Subject 12
2x2 design
Ax Ao Bx Bo
One sample t-test equivalents:
A>B x>o A(x>o)>B(x>o)
con.*imgs con.*imgs con.*imgs
c = [ ] c= [ ] c = [ ]

14. Stats tests at the 2nd Level
Canonical Temporal Dispersion
Example of when you might want to use an ANOVA
Chosen an informed basis set at 1st level:
canonical + temporal & dispersion derivatives
Set independence option to ‘NO’ to take into account covariance between images 
Use F- & T-tests to determine if the derivative bring any additional information to the design
F-test
eye(3)
Greyscale
shading indicates covariance
Plotting betas for selected voxel for each column of the 1x3 design:
1st column Canonical carries most info
Temp & Disp also significant info

15. SPM 2nd Level: How to Set-Up

16. SPM 2nd Level: Set-Up Options
Directory
- select directory to write out SPM
Design
- select 1st level con.*img
- several design types
- one sample t-test
- two sample t-test
- paired t-test
- multiple regression
- full or flexible factorial
- additional options for PET only
- grand mean scaling
- ANCOVA

17. SPM 2nd Level: Set-Up Options
Covariates
- covariates & nuisance variables
- 1 value per con*.img
Options:
- Vector (X-by-1 array)
- Name (string)
- Interaction
- Centring
Masking
- 3 masks types:
- threshold (voxel > threshold used)
- implicit (voxels = ?? are excluded)
- explicit (image for implicit mask, voxels with NaN or zero omitted)

18. SPM 2nd Level: Set-Up Options
Global calculation  for PET only Global normalisation  for PET only
Specify 2nd level Set-Up ↓
Save 2nd level Set-Up
Run analysis
Look at the RESULTS

19. SPM 2nd Level: Results Click RESULTS Select your 2nd Level SPM

20. SPM 2nd Level: Results 2nd level one sample t-test Select t-contrast
Define new contrast ….
c = +1 (+ve effect of 1st level contrast)
c = (-ve effect of 1st level contrast)
Select desired contrast
1 row per con*.img

21. SPM 2nd Level: Results Select options for displaying result:
Mask with other contrast
Title
Threshold (pFWE, pFDR punc)
Size of cluster
punc ***NOT corrected for multiple comparisons ***
probabliity of a false positive at each voxel
e.g. punc =  50/50000 voxels
pFDR proportion of discoveries likely to be false
e.g. pFDR = 0.1; 10% of voxels
pFWE proportion of SPMS containing FWEs
e.g. pFWE = 0.05  1 in 20 SPMs contain false positive somewhere in the image

22. SPM 2nd Level: Results Here are your results!!!
Now you can do lots of things:
Table of results [whole brain]
Look at t-value for a voxel of choice
Display results on anatomy [ overlays ]
SPM templates
mean of subjects
Small Volume Correct
significant voxels in a
small search area ↑ pFWE
1 row per
con*.img

23. 2nd Level Analysis & thanks to Ged Ridgway
Methods for Dummies slides 2009/10
Will Penny’s SPM May 2009 slides
SPM8 Manual
Human Brain Function (eds. Frackowiak et al.)
& thanks to Ged Ridgway