Hi Danny,
The cosine of the angle between the vectors should be equal to the
correlation (consider the fact that the angle between two vectors is not
affected by removing the mean of each of the two vectors). I will let
others speak to the implementation in SPM2 vs. SPM99 though, sounds like
perhaps the formula in SPM2 may not be correct.
Regards,
Vince
> -----Original Message-----
> From: SPM (Statistical Parametric Mapping)
> [mailto:[log in to unmask]] On Behalf Of Daniel H. Mathalon
> Sent: Thursday, February 19, 2004 8:34 AM
> To: [log in to unmask]
> Subject: orthogonality estimates in SPM2 vs SPM99
>
> Dear SPMers,
>
> We have noticed that the orthogonality values produced by SPM99 and
> SPM2 are different for the same event-related experimental design.
> On further investigation, this seems to depend on whether the design
> matrix and regressors are generated in SPM99 or SPM2.
>
> In SPM'99, the regressor representing a given condition has a mean of
> zero, whereas in SPM2, the regressor for the same condition does not
> have a mean of zero. In calculating the orthogonality between two
> conditions, the documentation in the MATLAB code indicates that the
> estimate is based on taking the cosine of the angle between the
> vectors representing the two regressors. We are further told that
> only when the regressor is centered on zero (i.e., has a mean of
> zero) does the cosine of the angle equal the correlation between the
> regressors. Indeed, when we subtract the mean out of the regressors
> generated by SPM2, the resulting regressors show identical
> orthogonality values (i.e. correlations) as those generated in SPM'99
> for the same conditions.
>
> Why do the coding of the regressors in SPM'99 and SPM2 differ
> in this way?
> Why does the orthogonality calculation rely on a formula that is
> sensitive to whether the regressors have a mean of zero (i.e., why
> not simply calculate the correlation coefficients between the
> regressors, which would be insensitive to linear transformations of
> the regressors such as subtracting out the mean value)?
>
> Any insights would be greatly appreciated.
>
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