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# Two Groups (One Factor/Two Levels), One Covariates

This models the input as two separate lines (DODS), one for each group. The two groups can be thought of as two levels of a single discrete factor. The covariate can be thought of as a continuous factor (eg, Age).

### FSGD File (g2v1.fsgd)

```GroupDescriptorFile 1
Title OSGM
Class Group1
Class Group2
Variable Age
Input subject1 Group1 30
Input subject2 Group2 40```

Nclasses = 2
Nvariables = 1

### Regressors (DODS)

Nregressors = Nclasses*(Nvariables+1) = 2*(1+1) = 4
Regressor1: ones for subjects in Group 1, 0 otherwise. Codes intercept/mean for Group 1
Regressor2: ones for subjects in Group 2, 0 otherwise. Codes intercept/mean for Group 2
Regressor3: age for subjects in Group 1, 0 otherwise. Codes age slope for Group 1
Regressor4: age for subjects in Group 2, 0 otherwise. Codes age slope for Group 2

### Contrasts

The number of columns in each contrast matrix must be the same as the number of regressors (Nregressors). If there is only one row in the contrast matrix, then the result will be a t-test and will have a sign. Reversing the signs in the contrast matrix will only change the sign of the output, not its magnitude. If there is more than one row, the result will be an F-test and will be unsigned.

##### Contrast 1

Null Hypothesis: is there a difference between the group intercepts? Is there a difference between groups regressing out the effect of age?

Contrast File: g1-g2.intercept.mtx

`1 -1 0 0`

This is a t-test with Group1>Group2 being positive (red/yellow).

##### Contrast 2

Null Hypothesis: is there a difference between the group slopes? Note: this is an interaction between group and age. Note: not possible to test with DOSS.

Contrast File: g1-g2.slope.mtx

`0 0 1 -1`

This is a t-test with Group1>Group2 being positive (red/yellow).

##### Contrast 3

Null Hypothesis: does Group1 differ from Group2 in intercept or slope?

Contrast File: g1-vs-g2.mtx

```1 -1 0  0
0  0 1 -1 ```

Note: this is an F-test (and hence unsigned). Reversing the signs will have no effect.

##### Contrast 4

Null Hypothesis: does mean of group intercepts differ from 0?

Contrast File: g1g2.intercept.mtx

`0.5 0.5 0 0`

This is a t-test with (Group1+Group2)/2 > 0 being positive (red/yellow). If the mean is < 0, then it will be displayed in blue/cyan.

##### Contrast 5

Null Hypothesis: does mean of group slopes differ from 0? Is there an average affect of age regressing out the effect of group?

Contrast File: g1g2.slope.mtx

`0 0 0.5 0.5`

This is a t-test with (Group1+Group2)/2 > 0 being positive (red/yellow). If the mean is < 0, then it will be displayed in blue/cyan.

### mri_glmfit command

This is an example invocation of mri_glmfit. Depending upon your application, you may have other options as well.

```mri_glmfit \
--glmdir g2v1 \
--y y.mgh \
--fsgd g2v1.fsgd \
--C g1-g2.slope.mtx \
--C g1-vs-g2.mtx \
--C g1g2.intercept.mtx \
--C g1g2.slope.mtx```

Fsgdf2G1V (last edited 2022-01-04 14:27:33 by DougGreve)