**Three Groups (One Factor/Three Levels), No Covariates**

This models the input as three separate offsets/intercepts/means, one for each group. The two groups can be thought of as three levels of a single discrete factor (eg, Normal, Mild Cognitive Impairment (MCI), and AD). There is not continuous covariate. These results hold for DODS or DOSS.

Contents

# FSGD File (g3v0.fsgd)

GroupDescriptorFile 1 Title OSGM Class Normal Class MCI Class AD Input subject1 Normal Input subject2 MCI Input subject3 AD

Nclasses = 3

Nvariables = 0

# Regressors

NregressorsDODS = Nclasses*(Nvariables+1) = 3*(0+1) = 3

NregressorsDOSS = Nclasses + Nvariables = 3+0 = 3

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

Regressor2: ones for subjects in Group 3, 0 otherwise. Codes intercept/mean for Group 3

# 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 normal-mci.mtx

Null Hypothesis: is there a difference between the normals and MCI means?

1 -1 0

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

## Contrast 2 normal-ad.mtx

Null Hypothesis: is there a difference between the normals and AD means?

1 0 -1

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

## Contrast 3 mci-ad.mtx

Null Hypothesis: is there a difference between the MCI and AD means?

0 1 -1

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

## Contrast 4 group.effect.mtx

Null Hypothesis: is there a difference between any of the group means? Is there an effect of group (diagnosis)?

1 -1 0 1 0 -1

This is a F-test and so unsigned. The contrast matrix is constructed from the contrast matrices testing Normals-vs-MCI and Normals-vs-AD. Note that one does NOT include a third row for MCI-vs-AD. This is because if Normals==MCI AND Normals==AD, then it MUST be the case that MCI==AD. Inclusion of the third row will actually cause an error.

## Contrast 5 normal+mci-vs-ad.mtx

Null Hypothesis: does the average of Normal and MCI equal AD?

0.5 0.5 -1

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

## 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 g3v0 \ --y y.mgh \ --fsgd g3v0.fsgd \ --C normal-mci.mtx \ --C normal-ad.mtx \ --C mci-ad.mtx \ --C group.effect.mtx \ --C normal+mci-vs-ad.mtx