1. SPSS meets SPM All about Analysis of Variance
Introduction and definition of terms
One-way between-subject ANOVA: An example
One-way repeated measurement ANOVA
Two-way repeated measurement ANOVA:
Pooled and partitioned errors
How to specify appropriate contrasts to test main effects
and interactions

2. SPSS meets SPM

3. Analysis of Variance Two-sample t-test Paired-sample-t-test
Single Measures
Repeated Measures
Two-sample t-test Paired-sample-t-test
ANOVA Repeated ANOVA
between-subject ANOVA within-subject ANOVA
F-test F-test
Factors
Levels
K1 x K2 ANOVA
Two Factors
with K1 levels of one factor and
K2 level of the second factor

4. 2 x 2 repeated measurement ANOVA Within-subject Factor
Two-way ANOVA
2 x 2 ANOVA
Factor A
Factor A
Level 1 2
Level 1
Group 3 4
Level 1 2
Level 1
Subj.
1….12
Factor B
Factor B
Mixed Design
Factor A
Within-subject Factor
Drug
Placebo
Patient
Subj.
1…12
Control
Imaging
Designs
Factor B
Between-subject
Factor

5. 2 x 2 repeated measurement ANOVA
2 x 2 ANOVA
Factor A
Factor A
Fearful
Neutral
Implicit
Group 1 2
Explicit 3 4
Fearful
Neutral
Implicit
Subj.
1….12
Explicit
Factor B
Main Effect B
Factor B
Main Effect A
Interaction A X B
3 x 2 ANOVA
Fearful
Neutral
Fearful
Neutral
Happy
Implicit
Explicit
Implicit Explicit
Contrasts

6. One-way between-subject ANOVA
An individual score is specified by
Grand mean
Treatment effect
Residual error

7. General Principle of ANOVA
FULL MODEL
REDUCED MODEL
Data represent a random variation around the grand mean
Is the full model a significantly better model
then the reduced model?

8. Partitions of Sums of Squares
Total Variation (SStotal)
Treatment effect (SStreat)
Error
(SSerror)

9. One-way ANOVA between subjects
1st levels betas from one voxel in amygdala 2. 3. 4. 5.
____________________________________
4-different drug treatments (Factor A with p levels)
_____________________________________
Sums(Ai)
Means(Ai)
One factor with p levels; i = 1…4
M subjects with n subjects per level
Number of total observations = 20

10. Do the drug treatments relate to the mean activation in the amygdala?
One way ANOVA
Multiple Regression
Do the drug treatment affect differently mean activation in the amygdala ?
Do the drug treatments relate to the mean activation in the amygdala?
____________________________________
Drug treatment (Factor A with p levels)
Dependent variable = 1st level betas extracted from the amygdala
1st level betas
Drug treatments 2 1 3 4 5 6 8 7 10 1 2 3 4 1 y = a X
+ b

11. Do the drug treatments relate to the mean activation in the amygdala?
One way ANOVA
Multiple Regression
Do the drug treatment affect differently mean activation in the amygdala ?
Do the drug treatments relate to the mean activation in the amygdala?
____________________________________
Drug treatment (Factor A with p levels)
Dependent variable = 1st level betas extracted from the amygdala
1st level betas
Drug treatments 2 1 3 4 5 6 8 7 10 1 y x1 x2 x3 x4

12. Do the drug treatments relate to the mean activation in the amygdala?
One way ANOVA
Multiple Regression
Do the drug treatment affect differently mean activation in the amygdala ?
Do the drug treatments relate to the mean activation in the amygdala?
____________________________________
Drug treatment (Factor A with p levels)
Dependent variable = 1st level betas extracted from the amygdala
1st level betas
Drug treatments 2 1 3 4 5 6 8 7 10 1 Y =
b1x1 +
b2x2 +
b3x3 +
b4x4 + b0

13. Do the drug treatments relate to the mean activation in the amygdala?
One way ANOVA
Multiple Regression
Do the drug treatment affect differently mean activation in the amygdala ?
Do the drug treatments relate to the mean activation in the amygdala?
____________________________________
Teaching Methods (Factor A with p levels)
Dependent variable = reading score 11 21 31 41 51 12 . 44 54 b1 b2 b3 b4 b0
y = * +

14. Repeated ANOVA Two-sample t-test Paired-sample-t-test
Repeated Measures
Single Measures
Two-sample t-test Paired-sample-t-test
ANOVA Repeated ANOVA
between-subject ANOVA within-subject ANOVA
F-test F-test
Drug 1
Drug 2
Drug 3
Placebo
Subj.1
Subj. 2
Subj. 3 ….
…..
Drug 1
Drug 2
Drug 3
Placebo
Group 1
Group2
Group3
Group4
Assumptions
Homogeneity of Variance
Normality
Independence of observations
Assumptions
Homogeneity of Variance
Homogeneity of Correlations
Normality

15. One-way between-subject One-way within-subject
ANOVA
One-way within-subject
ANOVA
An individual score is specified by
An individual score is specified by
Grand mean
Grand mean
Subject effect
Residual error
Treatment effect
(within-subject effect)
Treatment effect
Residual error

16. Partitions of Sums of Squares
Total Variation (SStotal)
Total Variation (SStotal)
Subj. x Treat & Error
Within subj.
(SSwithin)
Treatment effect (SStreat)
Residual
(SSres)
Between subj (SSbetween)
Subject effects
Treatment effect (SStreat)
Error
(SSerror)

17. * * y = y = + + + Between Subjects Within subjects p1 p2 p3 p4 p5 b1
Drug 1
Drug 2
Drug3
Placebo p1 p2 p3 p4 p5
y = * 11 21 31 41 51 12 . 44 54 + b1 b2 b3 b4 b0 11 21 31 41 51 12 . 44 54 b1 b2 b3 b4 b0
y = * + +

18. Between Subjects Within subjects 1 1 1 2 3 4 Drug 1 Drug 2 Drug3
Placebo 1 1

19. 2 x 2 Repeated Measurement ANOVA
Factor A
Level 1 2
Level 1
Subj.
1….12
Factor B
Pooled Error
Interaction between
effect and subject
Partitioned Error

20. Within-Subjects Two-Way ANOVA
Fear-implicit neutral-implicit fear-explicit neutral-explicit 1

21. Repeated Measurement ANOVA in SPM
Pooled errors
One way ANOVA = 1st level betas 2nd level + subjects effects
Partitioned errors
Two way ANOVA = 1st level
differential effects between
levels of a factors
for main effects
differences of differential effects for interactions
2nd level (T-test for 2x2 ANOVA
F-test for 3x3 ANOVA)

22. What contrast to take from 1st level?
Two way ANOVA (2*2) with repeated measured
Factor A
Fearful
Neutral
Implicit
Explicit
Factor B
Fear/
implicit
Fear/ explicit
Neutral/ implicit
Neutral/ explicit

23. What contrast to take from 1st level?
Two way ANOVA (3*3) with repeated measured
Factor A
semantic
perception
Imagery
Picture
Words
Sounds
Factor B