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

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

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

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

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 = [ 1 -1 1 -1 1 -1 1 -1 1 -1 ] perform one sample t-test Subject 1 Subject 2 Subject 3 Subject 4 Subject 5 Multisubject 1st level : 5 subjects x 1 run each

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

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

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

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 = [ 1 0 1 0 1 0 1 0 1 0] contrast = [ 1 0 1 0 1 0 1 0 1 0] contrast = [1 0 1 0 1 0 1 0 1 0] contrast = [1 0 1 0 1 0 1 0 1 0] contrast = [ 1 0 1 0 1 0 1 0 ] * (5/4)

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

Stats tests at the 2nd Level Choose the simplest analysis @ 2nd level : one sample t-test Compute within-subject contrasts @ 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: [ 1 -1 1 -1 1 -1 1 -1 ]  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)

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 2 Group 1 black value = 0 white: value = 1 1st column models group 1 2nd column models group 2

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 = [ 1 1 -1 -1] ; c = [ 1 -1 1 -1 ] ; c = [ 1 -1 -1 1] 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 = [ 1 1 -1 -1] c= [ 1 -1 1 -1] c = [ 1 -1 -1 1]

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

SPM 2nd Level: How to Set-Up

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

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)

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

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

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 = -1 (-ve effect of 1st level contrast) Select desired contrast 1 row per con*.img

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 = 0.001  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

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

2nd Level Analysis & thanks to Ged Ridgway Methods for Dummies slides 2009/10 http://www.fil.ion.ucl.ac.uk/spm/doc/mfd/2009/ Will Penny’s SPM May 2009 slides http://www.fil.ion.ucl.ac.uk/spm/course/slides09/ SPM8 Manual http://www.fil.ion.ucl.ac.uk/spm/doc/spm8_manual.pdf Human Brain Function (eds. Frackowiak et al.) http://www.sciencedirect.com/science/book/9780122648410 & thanks to Ged Ridgway