心智科學大型研究設備共同使用服務計畫身體 心靈與文化整合影像研究中心 fmri 教育講習課程 I Hands-on (2 nd level) Group Analysis to Factorial Design 黃從仁助理教授臺灣大學心理學系 trhuang@ntu.edu.tw
Analysis So+ware h"ps://goo.gl/ctvqce
Where are we?
Where are we?
500-page SPM 12 Manual h"p://www.fil.ion.ucl.ac.uk/spm/doc/manual.pdf
Dataset h"p://www.fil.ion.ucl.ac.uk/spm/data/
Face Dataset for Today Download & run: face_rfx_spm12_batch.m
Analysis of Behavioral vs. fmri Data Same set of stafsfcal methods applied to different effect sizes (accuracy, RT, contrast, etc.) One-Sample T-test Two-Sample T-test ANOVA Fixed-Effects vs. Random-Effects Models MulFlevel/Hierarchical Models
1 st -level GLM FSL Course Slides
1 st -level GLM FSL Course Slides
2 nd -level GLM: One Sample Brainvoyager User s Guide
FSL Course Slides 2 nd -level GLM: Two Samples
2 nd -level GLM: Paired Samples Easiest: 1-sample t-test on pair differences FSL Course Slides
Fixed vs. Random Effects FE (FFX in SPM) for the same subj (on runs & sessions) ME (RXF in SPM) for different subjects FSL Course Slides
Fixed Effects (1/3) FSL Course Slides
Fixed Effects (2/3) The same voxel from two subjects: Effect size, c ~ 4 Within-subject variability, s w ~1.1 Effect size, c ~ 2 Within-subject variability, s w ~1.5 SPM Course Slides
Fixed Effects (3/3) N=12 Fme series are concatenated (i.e., no 2 nd level) as if we had one subject with N=12x50=600 scans. c = [3, 4, 2, 1, 1, 2, 3, 3, 3, 2, 4, 4] s w = [0.9, 1.2, 1.5, 0.5, 0.4, 0.7, 0.8, 2.1, 1.8, 0.8, 0.7, 1.1] Mean effect, m=2.67 Average within subject variability (stand dev), s w =1.04 Standard Error Mean (SEM W ) = s w /sqrt(n)=0.04 Standard Error Mean (SEM W ) = s w /sqrt(n)=0.04 Is effect significant at voxel v? t=m/sem W =62.7, p=10-51 SPM Course Slides
Fixed vs. Random Effects FE for the same subject (on runs & sessions) ME (RXF in SPM) for different subjects FSL Course Slides
Mixed Effects (MulTlevel Models) FSL Course Slides
Huge Mixed-Effects GLM See SPM 12 manual Chapter 33 FSL Course Slides
Summary StaTsTcs Approach (1/3) See SPM 12 manual Chapter 32 FSL Course Slides
Summary StaTsTcs Approach (2/3) 12 Fme series, each has 50 scans: c = [3, 4, 2, 1, 1, 2, 3, 3, 3, 2, 4, 4] s w = [0.9, 1.2, 1.5, 0.5, 0.4, 0.7, 0.8, 2.1, 1.8, 0.8, 0.7, 1.1] Mean effect, m=2.67 Average within subject variability (stand dev), s w =1.04 Standard Error Mean (SEM W ) = s w /sqrt(n)=0.04 Between subject variability (stand dev), s b =1.07 Standard Error Mean (SEM b ) = s b /sqrt(n)=0.31 Is effect significant at voxel v? t=m/sem b =8.61, p=10-6 SPM Course Slides
Summary StaTsTcs Approach (3/3) T First level Second level c ˆ α t = T Data Design Matrix Contrast Images Var ˆ ( c ˆ) α SPM(t) One-sample t-test @ 2 nd level SPM Course Slides
1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 Design Matrix (1/2) Choose the simplest analysis @ 2 nd level : one sample t-test Compute within-subject contrasts @ 1 st level Enter con*.img for each person Can also model covariates across the group - vector containing 1 value per con*.img, 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 Group 2 Group 1 Marchant & Dekker, 2010
Design Matrix (2/2) Ax Ao Bx Bo If you have no other choice: ANOVA 2x2 design Subject 1 Subject 2 Subject 3 Subject 4 Subject 5 Subject 6 Subject 7 Subject 8 Subject 9 Subject 10 Subject 11 Subject 12 Designs are much more complex within-subject ANOVA need covariate per subjectè Be"er approach: generate main effects & interacfon contrasts at 1 st level: 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] use separate one-sample t-tests at the 2 nd level Marchant & Dekker, 2010
DEMO 若是自己的 1 st -level data 應將各受試者的同一個 spmt_000x* 或 con_000x* 重新命名轉放到 2 nd -level folder 範例見 SPM 12 Manual Chapter 32 與資料集中的三個資料夾
Appendix
HRF Models
T-test in SPM T-test - one dimensional contrasts SPM{t} c T = 1 0 0 0 0 0 0 0 QuesTon: box-car amplitude > 0? = β 1 = c T β> 0? β 1 β 2 β 3 β 4 β 5... Null hypothesis: H 0 : c T β=0 Test statstc: contrast of estmated parameters T = variance estmate SPM Course Slides T T T c ˆ β c ˆ β = = ~ T 2 var( c ˆ) β ˆ σ c c T T 1 ( X X ) tn p
con_???? image q For a given contrast c: T-contrast in SPM beta_???? images ˆ T 1 T β = ( X X ) X y ResMS image T ˆ ε ˆ ε ˆ σ 2 = N p c T βˆ spmt_???? image SPM{t} SPM Course Slides
1 T-test in SPM: An Example Q: activation during q Passive word listening versus rest c T = [ 1 0 0 0 0 0 0 0] listening? Null hypothesis: β 1 = 0 t= c T β / var( c T β ) SPMresults: Height threshold T = 3.2057 {p<0.001} voxel-level T ( Z ) mm mm mm p uncorrected 13.94 Inf 0.000-63 -27 15 12.04 Inf 0.000-48 -33 12 11.82 Inf 0.000-66 -21 6 13.72 Inf 0.000 57-21 12 12.29 Inf 0.000 63-12 -3 9.89 7.83 0.000 57-39 6 7.39 6.36 0.000 36-30 -15 6.84 5.99 0.000 51 0 48 6.36 5.65 0.000-63 -54-3 6.19 5.53 0.000-30 -33-18 5.96 5.36 0.000 36-27 9 5.84 5.27 0.000-45 42 9 5.44 4.97 0.000 48 27 24 5.32 4.87 0.000 36-27 42 SPM Course Slides
F-test in SPM (1/2) F-test - the extra-sum-of-squares principle Model comparison: SPM Course Slides Null Hypothesis H 0: True model is X 0 (reduced model) X 0 X 1 X 0 Test statistic: ratio of explained variability and unexplained variability (error) RSS ˆ ε 2 full RSS 0 ˆreduced ε 2 Full model? or Reduced model? ν 1 = rank(x) rank(x 0 ) ν 2 = N rank(x)
F-test - mulfdimensional contrasts SPM{F} Tests mulfple linear hypotheses: SPM Course Slides H 0 : True model is X 0 X0 F-test in SPM (2/2) H 0 : β 4 = β 5 =... = β 9 = 0 test H 0 : c T β = 0? X 0 X 1 (β 4-9 ) 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 c T = 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 SPM{F 6,322} Full model? Reduced model?
F-contrast in SPM ResMS image beta_???? images ˆ T 1 T β = ( X X ) X y T ˆ ε ˆ ε ˆ σ 2 = N p ess_???? images ( RSS 0 - RSS ) spmf_???? images SPM{F} SPM Course Slides
10 20 30 40 50 60 70 80 contrast(s) 2 4 6 8 Design matrix 10 20 30 40 50 60 70 80 contrast(s) F-test in SPM: An Example movement related effects Design matrix 2 4 6 8 SPM Course Slides
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