1. Contrast and Inferences
Joy Geng
Beatriz Calvo

2. Remember, what do we use fMRI for:
Functional specialisation:
Identification of regionally specific effects that can be attributed to changing stimuli or task conditions
Functional integration:
Identification of interactions among specialised cortical areas and how these interactions depend upon context
The main aim of functional neuroimaging is to elucidate the neural correlates of a particular cognitive, sensory or motor process. There are several types of experimental design that can be employed to achieve this aim.
Choose design according our aim!

3. Before starting the experiment we need to have clear…
Hypothesis / Question
when making inferences about activations, we can have an…
Anatomically closed hypothesis:
(hypothesis driven)
we can report uncorrected p value
Anatomically open hypothesis:
(we have to use correction methods)

4. Before starting the experiment we need to have clear…
Hypothesis / Question
Design that help me to answer my question
How I am going to build my SPM model
How I am going to analyse my data
I am going to use, Inference / contrast / Statistic
What contrasts and inferences are made is dependent on choice of experimental design
theoretical review
how SPM does it

5. What I can use... (some examples)
Can be used with event related or block designs.
Cognitive subtraction (subtractions designs)
Cognitive conjunction
Interactions, main /simple effects
(factorial designs)

6. Cognitive subtraction
Conceptual framework very used in psychology
Definition: the difference between two task can be formulate as a separable cognitive or sensorimotor component
Then, regionally specific differences in haemodynamic response, evoked by the two task, identify the corresponding functionally specialised area
Many subtraction designs relay on the assumption of pure insertion

7. the pure insertion problem
Pure insertion: A new cognitive (A) component is added to a task, the implementation of the pre-existing components (e.g., B) remains unaffected.
Pure insertion requires that an extra cognitive component can be introduced without affecting the expression of existing components
If this were not the case the difference between tasks that did, and did not, include component B would depend on the presence of component A.
Pure insertion discounts both functional and psychological interactions and therefore represent a very restricted precondition for cognitive subtraction

8. Assumptions of cognitive subtraction
The experimental task and baseline/ control task must be identical in every way except for the process of interest B A
Region(s) involved in the cognitive/ sensorimotor
process of interest
Baseline/control task
identical to A except for process of interest
Activation task involving process of interest

9. An example… Task A Task B Regions involved in biological motion?
Question: areas for biological motion?
Task A
Task B
Regions involved in biological motion?
Activation task
Point light display movie
Baseline / control task
Point light display static image
MT / V5
STS
Frontal eye fields
Cerebellum
Parietal cortex
My area of interest is the rol of inferotemporal cortex in the semantic processing
How to solve the problem, you have to improve your paradigm, for example include a verbal response also in the task b, with no semantic processing.
Violates assumption 1: task A and B identical but the process of interest
Many processes in addition to presence of biological motion in A including visual motion and eye movements

10. An example… Task A Task B Regions involved in biological motion?
Question: areas for biological motion?
Task A
Task B
Regions involved in biological motion?
Activation task
Point light display moves
Baseline / control task
Random dots moves
MT / V5
STS
Frontal eye fields
Cerebellum
Parietal cortex
My area of interest is the rol of inferotemporal cortex in the semantic processing
How to solve the problem, you have to improve your paradigm, for example include a verbal response also in the task b, with no semantic processing.
A better baseline to answer this question….

11. Assumptions of cognitive subtraction
2. There must be no implicit processing of the component of interest in the baseline/control task B A
Region(s) involved in the cognitive/ sensorimotor
process of interest
Baseline/control task
identical to A except for process of interest
Activation task involving process of interest

12. An example… Task A Task B Regions involved in semantic processing?
Question: is inferotemporal cortex involve in the semantic processing?
Task A
Task B
Regions involved in semantic processing?
Activation task
read words aloud
Baseline / control task
look at words
My area of interest is the rol of inferotemporal cortex in the semantic processing
How to solve the problem, you have to improve your paradigm, for example include a verbal response also in the task b, with no semantic processing.
Violates assumption 2:
Not implicit processing of the component of interest in the baseline task
difficult not to read (silently) a visually presented word, and if this is the case there will be semantic processing due to implicit reading of words in B

13. So, when using substraction design, remember!
The experimental task and baseline/ control task must be identical in every way except for the process of interest
2. There must be no implicit processing of the component of interest in the baseline task

14. Conjunctions
Cognitive conjunctions can be an extension of the subtraction technique
Cognitive conjunctions combine a series of subtractions with the aim of isolating a process that is common to two (or more) task pairs
The assumption of pure insertion can be avoided by extracting the presence of a main effect in the absence of an interaction
Conjunctions have the advantage of testing the effect independently of the task context, thereby controlling for influences of the effect on the context.
Cognitive conjunctions, can be an extension of the subtraction technique.
Conjunctions analysis allow one to demonstrate the context invariant nature of regional responses

15. An example… - = - = B1 A1 Baseline task Activation task Name colour
Name objects - = A2
Activation task
Looking At objects B2
Baseline task
Looking at colours - =

16. Using Conjunctions, remenber...
Baseline tasks can be high level or low level
The only restriction is that differences between the task pairs both contain the component of interest
The analysis results in any commonality in activation differences between the task pairs
The resulting region should be uniquely associated with the process of interest, not any interactions specific to each subtraction

17. Factorial Design In factorial designs there are two or more factors
The main effects of each factor identify brain areas that respond to that particular factor of interest
The interaction between factors identifies brain areas where the effect of one factor varies depending on the presence or absence of the other factor
This allows to measure the effect of one factor on the expression of the other factor

18. Factorial design 2x2 Factor A Factor B 2 SPM representation 1 2 3 4 B1

19. Main effects Factor A Factor B Main effect of factor A1 (1+3)-(2+4)
[ ]
Factor A1
BOLD signal in voxel Y
Factor A2 B1 B2

20. Main effects Factor A Factor B Main effect of factor B1 (1+2)-(3+4)
[ ]
Factor A1
BOLD signal in voxel Y
Factor A2 B1 B2

21. Interactions between factors1 2 3 4
factor B(1)
factor B(2) 1 2 3 4 A
Interaction effect (A x B)

22. Interaction between the factors (1-2)-(3-4) 1 -1 -1 1
Interactions …
Factor B
Factor A B1 A1 B2 A2 1 2 3 4
Interaction between the factors (1-2)-(3-4)
Factor A1
BOLD signal in voxel Y
Factor A2 B1 B2

23. Crossover interaction
Factor B
Factor A B1 A1 B2 A2 1 2 3 4
Interaction between the factors A1 B1 y A2 B2:
(1-2)-(3-4)
Factor A2
BOLD signal in voxel Y
Factor A1 B1 B2

24. So,
Now we have clear what comparisons we want to make… to answer our question
How do I do it in SPM?
I have my nice design matrix…
Y = X β ε
Observed data
Design matrix
Parameters
Error

25. First level (single subject): design matrix
A regressor, X, = timeseries of expected activation based on, e.g stimulus onsets for one condition of interest
session 1
Mean or constant term, X
Data, Y (e.g. swufMAO*.img filenames)
Y = X + e

26. Time series of expected activation for a regressor, X
Blocked
Event related

27. Fitting X to Y gives you one  (parameter estimate) for each column of X, a μ and e. Betas provide information about fit of regressor X to data, Y, in each voxel =
* 5
+ … +
* 50 +
Y = X1 * 1 +… Xn * μ e

28. Now we that we have our betas for every regressor for every voxel for every subject, what next? Contrast Vectors A1 A2
Each value in the contrast vector represents a weight for each beta in regression model
e.g. 2x2 exp with factor A (a1,a2) x B (b1, b2)
model has four regressors of interest: a1, a2, b1, b2
Main effect of A: [ ]
Simple effect of B in A: [ ]
Interaction of A and B: [ ]
Contrast image (con*.img): contains information about betas * contrast weights (CT ) B1 1 2 B2 3 4
Y = X1 * 1 +… Xn * μ e *
[1] [ ]

29. Now we that we have our betas for every regressor for every voxel for every subject, what next? T statistic
T statistic (spmT*.img): is activation correlated with condition A greater than that with condition B in voxel x?
Contrast vector = [ ] or [ ]
Ho: A = B
H1: A > B, B > A
One-tailed
Comparison of betas to variance in usual way,
T(df) = (CT  / SD((CT ))

30. Now we that we have our betas for every regressor for every voxel for every subject, what next? F statistic
What overall differences exist for conditions A than B? Do the treatment effects explain the data better than the subject (/grand mean) effects and residual errors?
Contrast vector: [ ; ]
compares with baseline
Ho: A = baseline = B
H1: A ≠ baseline or baseline ≠ B
Contrast vector: [ ]
gives differences in both directions (pos/neg), equivalent to two-tailed T statistic
Ho: A = B (same as B = A)
H1: A ≠ B

31. How to interpret nondirectional tests? Parameter estimates
Find coordinates of voxel of interest
Plot contrast estimates, and ‘y’ to see values per subject

32. Now we that we have our contrast images for comparisons of interest for every subject, what next? Contrasts at second level
Second level
T and F contrasts
Take contrasts images from first level relevant for analysis … start again with basic model…
Nonsphericity correction?
Replications (random/ fixed effects)
Grand mean scaling
Global normalization

34. Modelling the baseline or no?
Betas from model without baseline regressors
Betas from model with baseline regressors
Same but mean-centred
->makes a difference for “1 0” contrasts, but not “1 – 1” contrasts