Repeated measures ANOVA

33 Pages·2014·2.13 MB·English

by  Guillaume Flandin

Group Analyses
Guillaume Flandin
Wellcome Trust Centre for Neuroimaging
University College London
With many thanks to W. Penny, S. Kiebel, T. Nichols, R. Henson, J.-B. Poline, F. Kherif
SPM Course
Lausanne, April 2014
Image time-series
Spatial filter Design matrix Statistical Parametric Map
Realignment Smoothing General Linear Model
Statistical
RFT
Inference
Normalisation
p <0.05
Anatomical
reference
Parameter estimates
GLM: repeat over subjects
fMRI data Design Matrix Contrast Images SPM{t}

1

t
c
e
j
b
u
S

2

t
c
e
j
b
u
S

…

N

t
c
e
j
b
u
S
First level analyses :
(p<0.05 FWE)
Data from R. Henson
Fixed effects analysis (FFX)
Modelling all
Subject 1
subjects at once
Subject 2


Simple model
Subject 3

Lots of degrees of
freedom


… Large amount of
data

Assumes common
variance over
subjects at each
voxel
Subject N
Fixed effects analysis (FFX)
      Modelling all
1 1 1
y  X  
subjects at once


Simple model
X (1)  Lots of degrees of
1
freedom

y = 1 +  
X (1) 1  Large amount of
2
data

Assumes common
X (1) variance over
3
subjects at each
voxel
Fixed effects
     
1 1 1
y  X  
 Only one source of random variation (over sessions):
 measurement error
Within-subject Variance

 True response magnitude is fixed.
Random effects
     
1 1 1
y  X  
       
1 2 2 2
  X  
 Two sources of random variation:
Within-subject Variance
 measurement errors
 response magnitude
(over subjects) Between-subject Variance
 Response magnitude is random
 each subject/session has random magnitude
Random effects
     
1 1 1
y  X  
       
1 2 2 2
  X  
 Two sources of random variation:
Within-subject Variance
 measurement errors
 response magnitude
(over subjects) Between-subject Variance
 Response magnitude is random
 each subject/session has random magnitude
 but population mean magnitude is fixed.
Random effects
Probability model underlying random effects analysis