# Presentation: 160435

## FMRI Analysis

**Group Analysis**

- Individual Subject Analysis

- Pre-Processing

- Post-Processing

**FMRI Analysis**

- Experiment Design

- Scanning

## Group Analysis

- 3dttest, 3dANOVA/2/3,
-  3dRegAna, GroupAna

- Design

- Program

- Contrasts

- MTC

- Clusters

- Conjunction

- ANOVA

- Cluster Analysis

- AlphaSim,
- 3dFDR

- 3dmerge,
- 3dclust

- 3dcalc

- Connectivity Analysis

- Simple Correlation

- Context-Dependent Correlation

- Path Analysis

## Group Analysis: Types
Fixed effect
Only a few subjects as case study: can’t generalize to whole population
Simple approach: T = ∑ti/sqrt(n)
Sophisticated approach: vi = variance for coefficient bi
B = ∑(bi/√vi)/∑(1/√vi), T = B∑(1/√vi)/√n
B = ∑(bi/vi)/∑(1/vi), T = B√[∑(1/vi)]
Concatenate individual subject data
Random effect
Individual subject and group analysis: separate
Assumption: within-subject variation is negligible compared to between-subjects
Focus of this talk
Mixed effect
Ideally analyze with all subjects’ data combined, but not computationally feasible
Bring within-subject variances to group analysis, but still not easy to do currently

- Fixed effect
- Only a few subjects as case study: can’t generalize to whole population
- Simple approach: *T* = ∑*t**i*/sqrt(*n*)
- Sophisticated approach: *v**i* = variance for coefficient *b**i*
*B* = ∑(*b**i*/√*v**i*)/∑(1/√*v**i*), *T* = *B*∑(1/√*v**i*)/√*n*
*B* = ∑(*b**i*/*v**i*)/∑(1/*v**i*), *T* = *B*√[∑(1/*v**i*)]
- Concatenate individual subject data
- Random effect
- Individual subject and group analysis: separate
- Assumption: within-subject variation is negligible compared to between-subjects
- Focus of this talk
- Mixed effect
- Ideally analyze with all subjects’ data combined, but not computationally feasible
- Bring within-subject variances to group analysis, but still not easy to do currently

## Group Analysis: Programs in AFNI
Parametric Tests: assumption of Gaussian distribution; 10+ subjects
3dttest  (one-sample, unpaired and paired t)
3dANOVA (one-way between-subject)
3dANOVA2 (one-way within-subject, 2-way between-subjects)
3dANOVA3 (2-way between-subjects, within-subject and mixed, 3-way between-subjects)
3dRegAna (regression/correlation, hi-way or unbalanced ANOVA, ANCOVA)
GroupAna (Matlab script for up to 5-way ANOVA)
Non-Parametric Analysis
No assumption of normality; Statistics based on ranking
Appropriate when number of subjects too few (< 10)
Programs
3dWilcoxon (~ paired t-test)
3dMannWhitney (~ two-sample t-test)
3dKruskalWallis (~ between-subjects with 3dANOVA)
3dFriedman (~one-way within-subject with 3dANOVA2)
Permutation test
plugin on AFNI under Define Datamode /  Plugins /
C program by Tom Holroyd
Can’t handle complicated designs
Less sensitive to outliers (more robust) and less flexible than parametric tests

- Parametric Tests: assumption of Gaussian distribution; 10+ subjects
**3dttest**  (one-sample, unpaired and paired *t*)
**3dANOVA **(one-way between-subject)
**3dANOVA2 **(one-way within-subject, 2-way between-subjects)
**3dANOVA3 **(2-way between-subjects, within-subject and mixed, 3-way between-subjects)
**3dRegAna** (regression/correlation, hi-way or unbalanced ANOVA, ANCOVA)
- GroupAna (Matlab script for up to 5-way ANOVA)
- Non-Parametric Analysis
- No assumption of normality; Statistics based on ranking
- Appropriate when number of subjects too few (< 10)
- Programs
**3dWilcoxon** (~ paired *t*-test)
**3dMannWhitney** (~ two-sample *t*-test)
**3dKruskalWallis** (~ between-subjects with **3dANOVA**)
**3dFriedman** (~one-way within-subject with **3dANOVA2**)
- Permutation test
- plugin on AFNI under Define Datamode /  Plugins /
- C program by Tom Holroyd
- Can’t handle complicated designs
- Less sensitive to outliers (more robust) and less flexible than parametric tests

## Group Analysis: Overview
How many subjects?
Power/efficiency: proportional to √n; n > 10
Balance: Equal number of subjects across groups if possible
Input
Common brain in tlrc space (resolution doesn’t have to be 1x1x1 mm3 )
% signal change (not statistics) or normalized variables
HRF magnitude: Regression coefficients
Contrasts
Design
Number of factors
Number of levels for each factor
Within-subject or repeated-measures vs. between-subjects
Fixed (factors of interest) vs. random (subject)
Nesting: Balanced? 
Which program?
Contrasts and trend analysis: 
Thresholding: One- or two-tail?

- How many subjects?
- Power/efficiency: proportional to √*n*; *n* > 10
- Balance: Equal number of subjects across groups if possible
- Input
- Common brain in tlrc space (resolution doesn’t have to be 1x1x1 mm3 )
- % signal change (**not** statistics) or normalized variables
- HRF magnitude: Regression coefficients
- Contrasts
- Design
- Number of factors
- Number of levels for each factor
- Within-subject or repeated-measures vs. between-subjects
- Fixed (factors of interest) vs. random (subject)
- Nesting: Balanced?
- Which program?
- Contrasts and trend analysis:
- Thresholding: One- or two-tail?

## Group Analysis : 3dttest
Basic usage
One-sample t
One group: simple effect
Example: 15 subjects under condition A with H0: μA = 0
Two-sample t
Two groups: Compare one group with another
~ 1-way between-subject (3dANOVA)
Unequal sample sizes allowed
Assumption of equal variance across groups
Example: 15 subjects under A and 13 other subjects under B - H0: μA = μB
Paired t
Two conditions of one group: Compare one condition with another 
~ one-way within-subject (3dANOVA2 -type 3)
~ one-sample t  on individual contrasts
Example: Difference between conditions A and B for 15 subjects with H0: μA = μB
Output: 2 values (% and t) at each voxel
Versatile program: Most tests can be done with 3dttest -piecemeal vs. bundled

- Basic usage
- One-sample *t*
- _One group_: simple effect
- Example: 15 subjects under condition *A *with* H**0*:* **μ**A** *= 0
- Two-sample *t*
- _Two groups_: Compare one group with another
- ~ 1-way between-subject (**3dANOVA**)
- Unequal sample sizes allowed
- Assumption of equal variance across groups
- Example: 15 subjects under *A* and 13 other subjects under *B - H**0*:* **μ**A** = **μ**B*
- Paired *t*
- _Two conditions of one group_: Compare one condition with another_ _
- ~ one-way within-subject (**3dANOVA2 -type 3**)
- ~ one-sample *t*  on individual contrasts
- Example: Difference between conditions A and B for 15 subjects with *H**0*:* **μ**A** = **μ**B*
- Output: 2 values (% and *t*) at each voxel
- Versatile program: Most tests can be done with **3dttest** -piecemeal vs. bundled

## Group Analysis: 3dANOVA
Generalization of two-sample t-test
One-way between-subject
H0: no difference across all levels (groups) 
Examples of groups: gender, age, genotype, disease, etc.
Unequal sample sizes allowed
Assumptions
Normally distributed with equal variances across groups
Results: 2 values (% and t)
3dANOVA vs. 3dttest
Equivalent with 2 levels (groups)
More than 2 levels (groups): Can run multiple two-sample t-test

- Generalization of two-sample *t*-test
- One-way between-subject
*H**0*: no difference across all levels (groups)
- Examples of groups: gender, age, genotype, disease,* etc.*
- Unequal sample sizes allowed
- Assumptions
- Normally distributed with equal variances across groups
- Results: 2 values (% and *t*)
**3dANOVA** vs. **3dttest**
- Equivalent with 2 levels (groups)
- More than 2 levels (groups): Can run multiple two-sample *t*-test

## Group Analysis: 3dANOVA2
Designs
One-way within-subject (type 3)
Major usage
Compare conditions in one group
Extension and equivalence of paired t
Two-way between-subjects (type 1)
1 condition, 2 classifications of subjects
Similar to two-sample t
Unbalanced designs not allowed: Equal number of subjects across groups
Output
Main effect (-fa): F
Interaction for two-way between-subjects (-fab): F
Contrast testing
Simple effect (-amean)
1st level (-acontr, -adiff): one-sample or paired t among factor levels 
2nd level (interaction) for two-way between-subjects 
2 values per contrast: % and t

- Designs
- One-way within-subject (**type 3**)
- Major usage
- Compare conditions in one group
- Extension and equivalence of paired *t*
- Two-way between-subjects (**type 1**)
- 1 condition, 2 classifications of subjects
- Similar to two-sample *t*
- Unbalanced designs not allowed: Equal number of subjects across groups
- Output
- Main effect (**-fa**): *F*
- Interaction for two-way between-subjects (**-fab**): *F*
- Contrast testing
- Simple effect (**-amean**)
- 1st level (**-acontr, -adiff**): one-sample or paired t among factor levels
- 2nd level (interaction) for two-way between-subjects
- 2 values per contrast: % and *t*

## Group Analysis: 3dANOVA3
Designs
Three-way between-subjects (type 1)
3 categorizations of groups
Two-way within-subject (type 4): Crossed design AXBXC
Generalization of paired t-test
One group of subjects
Two categorizations of conditions: A and B
Two-way mixed (type 5): Nested design BXC(A)
Nesting factor: ≥ 2 groups of subjects (Factor A): subject classification, e.g., gender
One category of condition (Factor B)
Nesting: balanced 
Output
Main effect (-fa and -fb) and interaction (-fab): F
Contrast testing
1st level: -amean, -adiff, -acontr, -bmean, -bdiff, -bcontr
2nd level: -abmean, -aBdiff, -aBcontr, -Abdiff, -Abcontr
2 values per contrast : % and t

- Designs
- Three-way between-subjects (**type 1**)
- 3 categorizations of groups
- Two-way within-subject (**type 4**): Crossed design AXBXC
- Generalization of paired *t*-test
- _One_ group of subjects
- _Two_ categorizations of conditions: A and B
- Two-way mixed (**type 5**): Nested design BXC(A)
- _Nesting factor:_ ≥ 2 groups of subjects (Factor A): subject classification, e.g., gender
- _One_ category of condition (Factor B)
- Nesting: balanced
- Output
- Main effect (**-fa and -fb**) and interaction (**-fab**): *F*
- Contrast testing
- 1st level: **-amean, -adiff, -acontr, -bmean, -bdiff, -bcontr**
- 2nd level: **-abmean, -aBdiff, -aBcontr, -Abdiff, -Abcontr**
- 2 values per contrast : % and *t*

## Group Analysis: GroupAna
Multi-way ANOVA
Matlab script package for up to 5-way ANOVA
Requires Matlab plus Statistics Toolbox
GLM approach (slow): regression through dummy variables
Powerful: Test for interactions
Downside
Difficult to test and interpret simple effects/contrasts
Complicated design, and compromised power
Heavy duty computation: minutes to hours
Input with lower resolution recommended 
Resample with adwarp -dxyz # or 3dresample
Can handle both volume and surface data
Can handle following unbalanced designs (two-sample t type):
3-way ANOVA type 3: BXC(A)
4-way ANOVA type 3: BXCXD(A)
4-way ANOVA type 4: CXD(AXB)
See http://afni.nimh.nih.gov/sscc/gangc for more info
Alternative: 3dRegAna

- Multi-way ANOVA
- Matlab script package for up to 5-way ANOVA
- Requires Matlab plus Statistics Toolbox
- _GLM_ approach (slow): regression through dummy variables
- Powerful: Test for interactions
- Downside
- Difficult to test and interpret simple effects/contrasts
- Complicated design, and compromised power
- Heavy duty computation: minutes to hours
- Input with lower resolution recommended
- Resample with **adwarp -dxyz # **or **3dresample**
- Can handle both volume and surface data
- Can handle following _unbalanced_ designs (two-sample *t* type):
- 3-way ANOVA type 3: BXC(A)
- 4-way ANOVA type 3: BXCXD(A)
- 4-way ANOVA type 4: CXD(AXB)
- See _http://afni.nimh.nih.gov/sscc/gangc_ for more info
- Alternative: **3dRegAna**

## Group Analysis: Example 
Design
4 conditions (TM, TP, HM, HP) and 8 subjects
2-way within-subject: 2x2x8
A (Object), 2 levels: Tool vs Human
B (Animation), 2 levels: Motion vs Point
C (subject), 8 levels
AxBxC: Program? 3dANOVA3 -type 4
Main effects (A and B): 2 F values
Interaction AXB: 1 F
Contrasts
1st order: TvsH, MvsP
2nd order: TMvsTP, HMvsHP, TMvsHM, TPvsHP
6 contrasts x 2 values/contrast = 12 values
Logistic
Input: 2x2x8 = 32 files (4 from each subject)
Output: 18 sub-bricks 

- Design
- 4 conditions (TM, TP, HM, HP) and 8 subjects
- 2-way within-subject: 2x2x8
- A (Object), 2 levels: Tool vs Human
- B (Animation), 2 levels: Motion vs Point
- C (subject), 8 levels
- AxBxC: Program? **3dANOVA3 -type 4**
- Main effects (A and B): 2 *F* values
- Interaction AXB: 1 *F*
- Contrasts
- 1st order: TvsH, MvsP
- 2nd order: TMvsTP, HMvsHP, TMvsHM, TPvsHP
- 6 contrasts x 2 values/contrast = 12 values
- Logistic
- Input: 2x2x8 = 32 files (4 from each subject)
- Output: 18 sub-bricks

## Group Analysis: Example
Script

3dANOVA3 -type 4  -alevels 2  -blevels 2  -clevels 8 \

-dset 1 1 1 ED_TM_irf_mean+tlrc \
-dset 1 2 1 ED_TP_irf_mean+tlrc \
-dset 2 1 1 ED_HM_irf_mean+tlrc \
-dset 2 2 1 ED_HP_irf_mean+tlrc \
...
-adiff    1  2 TvsH1 \ (indices for difference)
-acontr   1 -1 TvsH2 \ (coefficients for contrast)
-bdiff    1  2 MvsP1 \ 
-aBdiff   1  2 : 1 TMvsHM \ (indices for difference)
-aBcontr  1 -1 : 1 TMvsHM \ (coefficients for contrast)
-aBcontr -1  1 : 2 HPvsTP \ 
-Abdiff   1 : 1  2 TMvsTP \ 
-Abcontr  2 : 1 -1 HMvsHP \ 

-fa  ObjEffect \ 
-fb  AnimEffect \
-fab ObjXAnim \

-bucket Group 

- Script
**3dANOVA3 -type 4  -alevels 2  -blevels 2  -clevels 8 \**
**-dset 1 1 1 ED_TM_irf_mean+tlrc \**
**-dset 1 2 1 ED_TP_irf_mean+tlrc \**
**-dset 2 1 1 ED_HM_irf_mean+tlrc \**
**-dset 2 2 1 ED_HP_irf_mean+tlrc \**
**...**
**-adiff    1  2 TvsH1 \ ***(indices for difference)*
**-acontr   1 -1 TvsH2 \ ***(coefficients for contrast)*
**-bdiff    1  2 MvsP1 \ **
**-aBdiff   1  2 : 1 TMvsHM \ ***(indices for difference)*
**-aBcontr  1 -1 : 1 TMvsHM \ ***(coefficients for contrast)*
**-aBcontr -1  1 : 2 HPvsTP \ **
**-Abdiff   1 : 1  2 TMvsTP \ **
**-Abcontr  2 : 1 -1 HMvsHP \ **
**-fa  ObjEffect \ **
**-fb  AnimEffect \**
**-fab ObjXAnim \**
**-bucket Group **

- Model type, number of
- levels for each factor

- Input for each cell in
- ANOVA table:
- totally 2X2X8 = 32

- 1st order Contrasts,
- paired *t* test

- Main effects &
- interaction *F* test;
- Equivalent to contrasts

- Output: bundled

- 2nd order Contrasts,
- paired *t* test

## Group Analysis: Example  
Alternative approaches
GroupAna
3dRegAna
Paired t: 6 tests
Program: 3dttest -paired 
For TM vs HM: 16 (2x8) input files (β coefficients: %) from each subject

 3dttest -paired -prefix TMvsHM    			\
 -set1 ED_TM_irf_mean+tlrc ... ZS_TM_irf_mean+tlrc 	\
 -set2 ED_HM_irf_mean+tlrc ... ZS_HM_irf_mean+tlrc

One-sample t : 6 tests
Program: 3dttest
For TM vs HM: 8 input files (contrasts: %) from each subject

 3dttest -prefix TMvsHM             	\
 -base1 0				\
 -set2 ED_TMvsHM_irf_mean+tlrc ... ZS_TMvsHM_irf_mean+tlrc

- Alternative approaches
- GroupAna
**3dRegAna**
- Paired *t*: 6 tests
- Program: **3dttest ****-paired**** **
- For TM vs HM: 16 (2x8) input files (β coefficients: %) from each subject
**	**
** ****3dttest ****-paired**** -prefix TMvsHM    ****	****	****	****\**
** ****-set1 ED_TM_irf_mean+tlrc ... ZS_TM_irf_mean+tlrc ****	****\**
** ****-set2 ED_HM_irf_mean+tlrc ... ZS_HM_irf_mean+tlrc**
- One-sample *t *: 6 tests
- Program: **3dttest**
- For TM vs HM: 8 input files (contrasts: %) from each subject
** ****3dttest -prefix TMvsHM             ****	****\**
** ****-base1 0****	****	****	****	****\**
** ****-set2 ED_TMvsHM_irf_mean+tlrc ... ZS_TMvsHM_irf_mean+tlrc**

## Group Analysis: ANCOVA (ANalysis of COVAriances)
Why ANCOVA?
Subjects might not be an ideally randomized representation of a population
If no controlled, cross-subject variability will lead to loss of power and accuracy
Direct control through experiment design: balanced selection of subjects
Indirect (statistical) control: untangling covariate effect
Factor of no interest - covariate: uncontrollable/confounding variable, usually continuous
Age, IQ, Cortex thickness
Behavioral data, e.g., response time, correct rate
Gender 
ANCOVA = Regression + ANOVA
Assumption: linear relation between % signal change and the covariate
GLM approach
Can model interaction between covariate and other factors
Centralize covariate so that it would not confound with other effects
3dRegAna
Flexible program that can run all sorts of group analysis
Miserable to write script, but hopeful: python scripting in future

- Why ANCOVA?
- Subjects might not be an ideally randomized representation of a population
- If no controlled, cross-subject variability will lead to loss of power and accuracy
- Direct control through experiment design: balanced selection of subjects
- Indirect (statistical) control: untangling covariate effect
- Factor of no interest - covariate: uncontrollable/confounding variable, usually continuous
- Age, IQ, Cortex thickness
- Behavioral data, e.g., response time, correct rate
- Gender
- ANCOVA = Regression + ANOVA
- Assumption: linear relation between % signal change and the covariate
- GLM approach
- Can model interaction between covariate and other factors
_**Centralize**_ covariate so that it would not confound with other effects
- 3dRegAna
- Flexible program that can run all sorts of group analysis
- Miserable to write script, but hopeful: python scripting in future

## Group Analysis: ANCOVA Example
Example: Running ANCOVA
Two groups: 15 normal vs. 13 patients
Analysis: comparing the two groups
Running what test?
Two-sample t with 3dttest 
Controlling age effect
GLM model 
Yi = β0 + β1X1i + β2X2i + β3X3i + εi, i = 1, 2, ..., n (n = 28)
Demean covariate (age) X1
Code the factor (group) with a dummy variable
                  0, when the subject is a patient;     X2i = {                1, when the subject is normal. 
With covariate X1 centralized: 
   β0 = effect of patient; β1 = age effect (correlation coef); β2 = effect of normal
X3i = X1i X2i models interaction (optional) between covariate and factor (group)
   β3 = interaction

- Example: Running ANCOVA
- Two groups: 15 normal vs. 13 patients
- Analysis: comparing the two groups
- Running what test?
- Two-sample *t* with **3dttest**
- Controlling age effect
- GLM model
*Y**i** = β**0** + β**1**X**1i** + β**2**X**2i** +* *β**3**X**3i** +* *ε**i**, i* = 1, 2, ..., *n *(*n* = 28)
- Demean covariate (age) *X**1*
- Code the factor (group) with a dummy variable
-                   0, when the subject is a patient;     *X**2i* = {                1, when the subject is normal.
- With covariate *X**1* centralized:
*   **β**0* = effect of patient; *β**1* = age effect (correlation coef); *β**2* = effect of normal
*X**3i** *= *X**1i **X**2i *models interaction (optional) between covariate and factor (group)
*   **β**3* = interaction

## Group Analysis: ANCOVA Example
     3dRegAna -rows 28 -cols 3 \ 
     -workmem 1000 \ 
     -xydata 0.1 0 0 patient/Pat1+tlrc.BRIK \-xydata 7.1 0 0 patient/Pat2+tlrc.BRIK \...
     -xydata 7.1 0 0 patient/Pat13+tlrc.BRIK \-xydata 2.1 1 2.1 normal/Norm1+tlrc.BRIK \-xydata 2.1 1 2.1 normal/Norm2+tlrc.BRIK \...
    -xydata -8.9 1 -8.9 normal/Norm14+tlrc.BRIK \-xydata 0.1 1 0.1 normal/Norm15+tlrc.BRIK \
     -model 1 2 3 : 0 \
     -bucket 0 Pat_vs_Norm \
     -brick 0 coef 0 ‘Pat’ \-brick 1 tstat 0 ‘Pat t' \-brick 2 coef 1 'Age Effect' \-brick 3 tstat 1 'Age Effect t' \-brick 4 coef 2 'Norm-Pat' \-brick 5 tstat 2 'Norm-Pat t' \-brick 6 coef 3 'Interaction' \-brick 7 tstat 3 'Interaction t' 
     See http://afni.nimh.nih.gov/sscc/gangc/ANCOVA.html for more information

*     **3dRegAna -rows 28 -cols 3 \ *
*     **-workmem 1000 \ *
*     **-xydata 0.1 0 0 patient/Pat1+tlrc.BRIK \**-xydata 7.1 0 0 patient/Pat2+tlrc.BRIK \**...*
*     **-xydata 7.1 0 0 patient/Pat13+tlrc.BRIK \**-xydata 2.1 1 2.1 normal/Norm1+tlrc.BRIK \**-xydata 2.1 1 2.1 normal/Norm2+tlrc.BRIK \**...*
*    **-xydata -8.9 1 -8.9 normal/Norm14+tlrc.BRIK \**-xydata 0.1 1 0.1 normal/Norm15+tlrc.BRIK \*
*     **-model 1 2 3 : 0 \*
*     **-bucket 0 Pat_vs_Norm \*
*     **-brick 0 coef 0 ‘Pat’ \**-brick 1 tstat 0 ‘Pat t' \**-brick 2 coef 1 'Age Effect' \**-brick 3 tstat 1 'Age Effect t' \**-brick 4 coef 2 'Norm-Pat' \**-brick 5 tstat 2 'Norm-Pat t' \**-brick 6 coef 3 'Interaction' \**-brick 7 tstat 3 'Interaction t' *
-      See _[http://afni.nimh.nih.gov/sscc/gangc/ANCOVA.html](http://afni.nimh.nih.gov/sscc/gangc/ANCOVA.html)_ for more information

- Model parameters: 28 subjects,
- 3 independent variables

- Memory

- Input: Covariates, factor levels,
- interaction, and input files

- Specify model for F and R2

- Output: #subbriks = 2*#coef + F + R2

- Label output subbricks for *β**0*,* **β**1*,* **β**2*,* **β**3*

## Group Analysis: A Sophisticated ANCOVA Example
     	3 groups (col. 1-2), 13 subjects (col. 6-41) in each group; 2 conditions (col. 3); 1 covariate (col. 42)
	3dANOVA3 –type 5 if no covariate

	3dRegAna  -workmem 2000  -rows 78  -cols 42 \ 
	-xydata 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 121 gs.acw.cf+tlrc \ 
	-xydata 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 96 ew.acw.cf+tlrc \ 
	... \ 
	-xydata 1 0 1 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 115 kb.acw.cf+tlrc \

	-xydata 1 0 -1 -1 -0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 121 gs.aril.cf+tlrc \
	-xydata 1 0 -1 -1 -0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 96 ew.aril.cf+tlrc \ 
	... \ 
	-xydata 1 0 -1 -1 -0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 115 kb.aril.cf+tlrc \ 

	-xydata 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 bd.acw.cf+tlrc \
	-xydata 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 106 05.acw.cf+tlrc \ 
	... \ 
	-xydata 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 78 dw.acw.cf+tlrc \ 

	-xydata 0 1 -1 -0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 bd.aril.cf+tlrc \
	-xydata 0 1 -1 -0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 106 05.aril.cf+tlrc \ 
	... \ 
	-xydata 0 1 -1 -0 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 78 dw.aril.cf+tlrc \ 

	-xydata -1 -1 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 86 pw.acw.cf+tlrc \ 
	-xydata -1 -1 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 109 an.acw.cf+tlrc \ 
	...\ 
	-xydata -1 -1 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 91 jf.acw.cf+tlrc \ 

	-xydata -1 -1 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 86 pw.aril.cf+tlrc \ 
	-xydata -1 -1 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 109 an.aril.cf+tlrc \ 
	... \ 
	-xydata -1 -1 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 91 jf.aril.cf+tlrc \ 
	-model 1 2 : 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 \ 
	-bucket 0 GrpEff 

-      	3 groups (col. 1-2), 13 subjects (col. 6-41) in each group; 2 conditions (col. 3); 1 covariate (col. 42)
- 	3dANOVA3 –type 5 if no covariate
- 	3dRegAna  -workmem 2000  -rows 78  -cols 42 \
- 	-xydata 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 121 gs.acw.cf+tlrc \
- 	-xydata 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 96 ew.acw.cf+tlrc \
- 	... \
- 	-xydata 1 0 1 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 115 kb.acw.cf+tlrc \
- 	-xydata 1 0 -1 -1 -0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 121 gs.aril.cf+tlrc \
- 	-xydata 1 0 -1 -1 -0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 96 ew.aril.cf+tlrc \
- 	... \
- 	-xydata 1 0 -1 -1 -0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 115 kb.aril.cf+tlrc \
- 	-xydata 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 bd.acw.cf+tlrc \
- 	-xydata 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 106 05.acw.cf+tlrc \
- 	... \
- 	-xydata 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 78 dw.acw.cf+tlrc \
- 	-xydata 0 1 -1 -0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 bd.aril.cf+tlrc \
- 	-xydata 0 1 -1 -0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 106 05.aril.cf+tlrc \
- 	... \
- 	-xydata 0 1 -1 -0 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 78 dw.aril.cf+tlrc \
- 	-xydata -1 -1 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 86 pw.acw.cf+tlrc \
- 	-xydata -1 -1 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 109 an.acw.cf+tlrc \
- 	...\
- 	-xydata -1 -1 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 91 jf.acw.cf+tlrc \
- 	-xydata -1 -1 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 86 pw.aril.cf+tlrc \
- 	-xydata -1 -1 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 109 an.aril.cf+tlrc \
- 	... \
- 	-xydata -1 -1 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 91 jf.aril.cf+tlrc \
- 	-model 1 2 : 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 \
- 	-bucket 0 GrpEff

## Group Analysis

- Design

- Program

- Contrasts

- ANOVA

- 3dttest, 3dANOVA/2/3,
-  3dRegAna, GroupAna

- Connectivity Analysis

- Simple Correlation

- Context-Dependent Correlation

- Path Analysis

## Cluster Analysis: Multiple testing correction
Two types of errors
What is H0 in FMRI studies?
Type I  = P (reject H0|when H0 is true) = false positive = p value 
   Type II = P (accept H0|when H1 is true) = false negative = β  
Usual strategy: controlling type I error
   (power = 1- β = probability of detecting true activation)
Significance level α: p < α
Family-Wise Error (FWE)
Birth rate H0: sex ratio at birth = 1:1
What is the chance there are 5 boys (or girls) in a family?	 (2)5 ~ 0.03
In a community with 100 families with 5 kids, expected #families with 5 boys =? 
	100X(2)5 ~ 3
In fMRI H0: no activation at a voxel
What is the chance a voxel is mistakenly labeled as activated (false +)?
 Multiple testing problem: With n voxels, what is the chance to mistakenly label at least one voxel? Family-Wise Error: αFW = 1-(1- p)n →1 as n increases
Bonferroni correction: αFW = 1-(1- p)n ~ np, if p << 1/n 
   Use p=α/n as individual voxel significance level to achieve αFW = α

- Two types of errors
- What is *H**0* in FMRI studies?
- Type I  = P (reject *H**0*|when *H**0* is true) = false positive = *p* value
-    Type II = P (accept *H**0*|when *H**1* is true) = false negative = *β*
- Usual strategy: controlling type I error
-    (power = 1- *β* = probability of detecting true activation)
- Significance level *α*: *p < **α*
- Family-Wise Error (FWE)
- Birth rate *H**0*: sex ratio at birth = 1:1
- What is the chance there are 5 boys (or girls) in a family?	 (2)5 ~ 0.03
- In a community with 100 families with 5 kids, expected #families with 5 boys =?
- 	100X(2)5 ~ 3
- In fMRI *H**0*: no activation at a voxel
- What is the chance a voxel is mistakenly labeled as activated (false +)?
-  Multiple testing problem: With *n* voxels, what is the chance to mistakenly label at least one voxel? _*Family-Wise Error*_*: **α*FW = 1-(1- *p*)*n* →1 as *n* increases
- Bonferroni correction: *α*FW = 1-(1- *p*)*n* ~ *np*, if *p* << 1/*n*
*   *Use *p*=*α*/*n* as individual voxel significance level to achieve *α*FW = *α*

## Cluster Analysis: Multiple testing correction
Multiple testing problem in fMRI: voxel-wise statistical analysis
Increase of chance at least one detection is wrong in cluster analysis
3 occurrences of multiple testings: individual, group, and conjunction
Group analysis is the most concerned
Two approaches
Control FWE: αFW = P (≥ one false positive voxel in the whole brain)
Making αFW small but without losing too much power
Bonferroni correction too consersative: p=10-8~10-6
*Too stringent and overly conservative: Lose statistical power
Something to rescue? Correlation and structure!
*Voxels in the brain are not independent
*Structures in the brain
Control false discovery rate (FDR)
FDR = expected proportion of false + voxels among all detected voxels
Concrete example: individual voxel p = 0.001 for a brain of 25,000 EPI voxels 
Uncorrected → 25 false + voxels in the brain
FWE:  corrected p = 0.05 → 5% false + hypothetical brains for a fixed voxel location
FDR: corrected p = 0.05 → 5% voxels in those positively labeled ones are false + 

- Multiple testing problem in fMRI: voxel-wise statistical analysis
- Increase of chance at least one detection is wrong in cluster analysis
- 3 occurrences of multiple testings: individual, group, and conjunction
- Group analysis is the most concerned
- Two approaches
- Control FWE: _*α*__FW__ = __*P*__ (≥ one false positive voxel in the whole brain)_
- Making *α*FW small but without losing too much power
- Bonferroni correction too consersative: *p*=10-8~10-6
- *Too stringent and overly conservative: Lose statistical power
- Something to rescue? Correlation and structure!
- *Voxels in the brain are not independent
- *Structures in the brain
- Control false discovery rate (FDR)
- _FDR = expected proportion of false + voxels among all __detected__ voxels_
- Concrete example: individual voxel *p* = 0.001 for a brain of 25,000 EPI voxels
- Uncorrected → 25 false + voxels in the brain
- FWE:  corrected *p* = 0.05 → 5% false + hypothetical brains for a fixed voxel location
- FDR: corrected *p* = 0.05 → 5% voxels in those positively labeled ones are false +

## Cluster Analysis: AlphaSim
FWE: Monte Carlo simulations
Named for Monte Carlo, Monaco, where the primary attractions are casinos 
Program: AlphaSim
Randomly generate some number (e.g., 1000) of brains with white noise
Count the proportion of voxels are false + in all brains
Parameters: 
* ROI - mask
* Spatial correlation - FWHM
* Connectivity - radium
* Individual voxel significant level - uncorrected p
Output 
* Simulated (estimated) overall significance level (corrected p-value) 
* Corresponding minimum cluster size 
Decision: Counterbalance among 
* Uncorrected p
* Minimum cluster size
* Corrected p

- FWE: Monte Carlo simulations
- Named for Monte Carlo, Monaco, where the primary attractions are casinos
- Program: **AlphaSim**
- Randomly generate some number (e.g., 1000) of brains with white noise
- Count the proportion of voxels are false + in all brains
- Parameters:
- * ROI - mask
- * Spatial correlation - FWHM
- * Connectivity - radium
- * Individual voxel significant level - uncorrected *p*
- Output
- * Simulated (estimated) overall significance level (corrected *p*-value)
- * Corresponding minimum cluster size
- Decision: Counterbalance among
- * Uncorrected *p*
- * Minimum cluster size
- * Corrected *p*

## Cluster Analysis: AlphaSim
See detailed steps at http://afni.nimh.nih.gov/sscc/gangc/mcc.html
Example
AlphaSim \
-mask MyMask+orig \
-fwhmx 4.5 -fwhmy 4.5 -fwhmz 6.5 \ 
-rmm 6.3 \
-pthr 0.0001 \
-iter 1000 

Output: 5 columns
Focus on the 1st and last columns, and ignore others
1st column: minimum cluster size in voxels
Last column: alpha (α), overall significance level (corrected p value)

Cl Size       Frequency      Cum Prop      p/Voxel         Max Freq        Alpha2                  1226           0.999152     0.00509459        831             0.859
    5                    25             0.998382     0.00015946        25               0.137
   10                     3             1.0               0.00002432          3               0.03
May have to run several times with different uncorrected p: uncorrected p↑↔ cluster size↑

- See detailed steps at http://afni.nimh.nih.gov/sscc/gangc/mcc.html
- Example
- AlphaSim \
- -mask MyMask+orig \
- -fwhmx 4.5 -fwhmy 4.5 -fwhmz 6.5 \
- -rmm 6.3 \
- -pthr 0.0001 \
- -iter 1000
- Output: 5 columns
- Focus on the 1st and last columns, and ignore others
- 1st column: minimum cluster size in voxels
- Last column: alpha (*α*), overall significance level (corrected *p* value)
- Cl Size       Frequency      Cum Prop      p/Voxel         Max Freq        Alpha2                  1226           0.999152     0.00509459        831             0.859
-     5                    25             0.998382     0.00015946        25               0.137
-    10                     3             1.0               0.00002432          3               0.03
- May have to run several times with different uncorrected *p*: uncorrected p↑↔ cluster size↑

- Program

- Restrict correcting region: ROI

- Spatial correlation

- Connectivity: how clusters are defined

- Uncorrected *p*

- Number of simulations

## Cluster Analysis: 3dFDR

Definition: 
	FDR = proportion of false + voxels among all detected voxels

Doesn’t consider 
spatial correlation
cluster size
connectivity
Again, only controls the expected % false positives among declared active voxels
Algorithm: statistic (t)  p value  FDR (q value)  z score
Example: 
    3dFDR -input ‘Group+tlrc[6]'      \
     -mask_file mask+tlrc           \
     -cdep -list                    \
     -output test 

- Definition:
- 	FDR =_ proportion of false + voxels among all detected voxels_
- Doesn’t consider
- spatial correlation
- cluster size
- connectivity
- Again, only controls the _**expected**_ % false positives among declared active voxels
- Algorithm: statistic (*t*)  *p* value  FDR (*q* value)  *z* score
- Example:
-     **3dFDR -input ‘Group+tlrc[6]'      \**
**     ****-mask_file mask+tlrc           \**
**     ****-cdep -list                    \**
**     ****-output test**

|  | Declared Inactive | Declared Active |  |
| --- | --- | --- | --- |
| Truly Inactive | Nii | Nia (I) | Ti |
| Truly Active | Nai (II) | Naa | Ta |
|  | Di | Da |  |

- Output

- Arbitrary distribution of *p*

- ROI

- One statistic

## Cluster Analysis: FWE or FDR?
Correct type I error in different sense
FWE: αFW = P (≥ one false positive voxel in the whole brain)
Frequentist’s perspective: Probability among many hypothetical activation brains
Used usually for parametric testing
FDR = expected % false + voxels among all detected voxels
Focus: controlling false + among detected voxels in one brain
More frequently used in non-parametric testing
Fail to survive correction? 
At the mercy of reviewers
Analysis on surface
Tricks
One-tail?
ROI – cheating?
Many factors along the pipeline
Experiment design: power?
Sensitivity (power) vs specificity (small regions)
Poor spatial alignment among subjects

- Correct type I error in different sense
- _FWE: __*α*__FW__ = __*P*__ (≥ one false positive voxel in the whole brain)_
- Frequentist’s perspective: Probability among many hypothetical activation brains
- Used usually for parametric testing
- _FDR = expected % false + voxels among all detected voxels_
- Focus: controlling false + among detected voxels in one brain
- More frequently used in non-parametric testing
- Fail to survive correction?
- At the mercy of reviewers
- Analysis on surface
- Tricks
- One-tail?
- ROI – cheating?
- Many factors along the pipeline
- Experiment design: power?
- Sensitivity (power) vs specificity (small regions)
- Poor spatial alignment among subjects

## Cluster Analysis: Conjunction analysis
Conjunction analysis: HM vs TM
Common activation area
Exclusive activations 
Double/dual thresholding with AFNI GUI
Tricky
Only works for two contrasts
Common but not exclusive areas
Conjunction analysis with 3dcalc 
Flexible and versatile
Heaviside unit (step function) 
   defines a On/Off event

- Conjunction analysis: HM vs TM
- Common activation area
- Exclusive activations
- Double/dual thresholding with AFNI GUI
- Tricky
- Only works for two contrasts
- Common but not exclusive areas
- Conjunction analysis with **3dcalc **
- Flexible and versatile
**Heaviside unit (****step function**)
-    defines a *On/Off* event

## Cluster Analysis: Conjunction analysis
Example with 3 contrasts: A vs D, B vs D, and C vs D
Map 3 contrasts based on binary system: A: 001(1); B: 010(2); C: 100(4)
Create a mask with 3 subbricks of t (threshold = 4.2)

  3dcalc -a func+tlrc'[5]' -b func+tlrc'[10]' -c func+tlrc'[15]‘ \
  -expr 'step(a-4.2)+2*step(b-4.2)+4*step(c-4.2)' \
  -prefix ConjAna

Interpret output - 8 (=23) scenarios:
   000(0): none; 
   001(1): A but no others; 
   010(2): B but no others; 
   011(3): A and B but not C; 
   100(4): C but no others; 
   101(5): A and C but not B;  
   110(6): B and C but not A; 
   111(7): A, B and C
Downside: no p associated conjunctions with and no MTC

- Example with 3 contrasts: A vs D, B vs D, and C vs D
- Map 3 contrasts based on binary system: A: 001(1); B: 010(2); C: 100(4)
- Create a mask with 3 subbricks of *t* (threshold = 4.2)
** **
**  ****3dcalc -a func+tlrc'[5]' -b func+tlrc'[10]' -c func+tlrc'[15]‘ \**
**  ****-expr 'step(a-4.2)+2*step(b-4.2)+4*step(c-4.2)' \**
**  ****-prefix ConjAna**
- Interpret output - 8 (=23) scenarios:
-    000(0): none;
-    001(1): A but no others;
-    010(2): B but no others;
-    011(3): A and B but not C;
-    100(4): C but no others;
-    101(5): A and C but not B;
-    110(6): B and C but not A;
-    111(7): A, B and C
- Downside: no *p* associated conjunctions with and no MTC

## Group Analysis

- Design

- Program

- Contrasts

- ANOVA

- 3dttest, 3dANOVA/2/3,
-  3dRegAna, GroupAna

- Connectivity Analysis

- Simple Correlation

- Context-Dependent Correlation

- Path Analysis

## Connectivity: Correlation Analysis 
Similarity between a seed and the rest of the brain
Says nothing about causality
Voxel-wise analysis
Both individual subject and group levels
Steps at individual subject level
Extract seed time series: 3dmaskdump 
Remove trend: 3dDetrend
Correlation analysis: 3dfim+ or 3dDeconvolve
Steps at group level
Convert correlation coefficients to Z (Fisher transformation): 3dcalc 
One-sample t test on Z scores: 3dttest
More details: http://afni.nimh.nih.gov/sscc/gangc/SimCorrAna.html

- Similarity between a seed and the rest of the brain
- Says nothing about causality
- Voxel-wise analysis
- Both individual subject and group levels
- Steps at individual subject level
- Extract seed time series: 3dmaskdump
- Remove trend: 3dDetrend
- Correlation analysis: 3dfim+ or 3dDeconvolve
- Steps at group level
- Convert correlation coefficients to Z (Fisher transformation): 3dcalc
- One-sample t test on Z scores: 3dttest
- More details: http://afni.nimh.nih.gov/sscc/gangc/SimCorrAna.html

## Connectivity: Path Analysis 
Causal model approach on a network of ROI’s
Minimizing discrepancies 
btw correlation based on data and one estimated from model

Input: Model specification, correlation matrix, residual error variances, DF
Output: Path coefficients, various fit indices

- Causal model approach on a network of ROI’s
- Minimizing discrepancies
- btw correlation based on data and one estimated from model
- Input: Model specification, correlation matrix, residual error variances, DF
- Output: Path coefficients, various fit indices

## Connectivity: Path Analysis – 1dSEM
AFNI program 1dSEM
Written in C
Not dependent on FMRI analysis platform
Two modes
Validate a theoretical model
Accept, reject, or modify the model?
Search for ‘best’ model 
Start with a minimum model (can be empty): 1
Some paths can be excluded: 0
Model grows by adding one extra path a time: 2
‘Best’ in terms of various fit criteria
Script: 1dSEM -theta testthetasfull.1D -C testcorr.1D -psi testpsi.1D -DF 30
Caveats:
Causal relationship modeled through correlation (covariance) analysis
Valid only with the data and model specified
If one critical ROI is left out, things may go awry
More details
http://afni.nimh.nih.gov/sscc/gangc/PathAna.html
1dSEM -help

- AFNI program **1dSEM**
- Written in C
- Not dependent on FMRI analysis platform
- Two modes
- Validate a theoretical model
- Accept, reject, or modify the model?
- Search for ‘best’ model
- Start with a minimum model (can be empty): 1
- Some paths can be excluded: 0
- Model grows by adding one extra path a time: 2
- ‘Best’ in terms of various fit criteria
- Script: *1dSEM -theta testthetasfull.1D -C testcorr.1D -psi testpsi.1D -DF 30*
- Caveats:
- Causal relationship modeled through correlation (covariance) analysis
- Valid only with the data and model specified
- If one critical ROI is left out, things may go awry
- More details
- _[http://afni.nimh.nih.gov/sscc/gangc/PathAna.html](http://afni.nimh.nih.gov/sscc/gangc/PathAna.html)_
- 1dSEM -help

## Need Help?
Command with “-help” 
3dANOVA3 -help
Manuals 
http://afni.nimh.nih.gov/afni/doc/manual/
Web 
http://afni.nimh.nih.gov/sscc/gangc
Examples: HowTo#5
http://afni.nimh.nih.gov/afni/doc/howto/
Message board 
http://afni.nimh.nih.gov/afni/community/board/
Appointment
Contact us @1-800-NIH-AFNI

- Command with “-help”
**3dANOVA3 -help**
- Manuals
- _[http://afni.nimh.nih.gov/afni/doc/manual/](http://afni.nimh.nih.gov/afni/doc/manual/)_
- Web
- _[http://afni.nimh.nih.gov/sscc/gangc](http://afni.nimh.nih.gov/sscc/gangc)_
- Examples: HowTo#5
- _[http://afni.nimh.nih.gov/afni/doc/howto/](http://afni.nimh.nih.gov/afni/doc/howto/)_
- Message board
- _[http://afni.nimh.nih.gov/afni/community/board/](http://afni.nimh.nih.gov/afni/community/board/)_
- Appointment
**Contact us @****1-800-NIH-AFNI**