Hojat Vaheb wrote:
> Are vectors a=[1 1 1 0 0 0 0]’ and b=[0 0 0 1 1 1 1]’ contrasts or regressors?
Regressors, aka explanatory variables, aka design matrix columns,
*not* contrasts. For my two-sample t-test example, the contrast would
be a two-element vector (X=[a b] is a two-column matrix).
E.g. [1 -1]' for A>B or [-1 1] for B>A (or an F-contrast of either,
for a two-tailed test of A~=B).
> for example for fMRI data we expect that the observed data (Y) be similar to
> a linear combination of regressors which are convolution of temporal basis
> functions with stimulus functions.
Right, a first level fMRI design models the time-series with stimuli
convolved with the HRF.
A second level fMRI design, or e.g. a structural MRI comparison of
groups of subjects, might model the response of different subjects as
having different levels for the different groups. This is what a
two-sample t-test is -- a model that the two groups have different
means (and the same variance, usually, but not always).
The two design matrix columns a and b model these means (beta will be
a two-element vector of the means) and the contrast [-1 1] tests
whether the difference in means/betas is large compared to its
standard error.
>>response y = [a1 a2 a3 b1 b2 b3 b4]'
> regressor a = [1 1 1 0 0 0 0 ]'
> regressor b = [0 0 0 1 1 1 1 ]'
> design X = [a b]
The above uses the Matlab convention that x' is transpose(x), so [1 1]
is a row vector, while [1 1]' is a column vector, X above is a 7-by-2
matrix.
All clear?
Ged.
|