Ok, well, here is something that might give you a feeling for the difference.
In a regression with only a single independent variable, the standardized
beta equals r (the Pearson's correlation). This would also be true (I think)
if all the variables were totally uncorrelated in a multiple regression.
The analysis I have done is one in which I want to look at a correlation as my
statistic, and the standardized Beta coefficient is one way to report a
factor loading which takes into account that factor's covariance w/ other
factors. It would be 1 if the activity of a voxel were perfectly predictable
from that factor, and 0 if that factor had no power to predict it. So, the
reason for having it is in the _interpretation_ of the statistic.
Typically, it is computed as:
Beta = b * (sx / sy)
where
Beta: standardized regression coefficient (-1 to 1)
b: the unstandardized regression coefficient (can take any value), which is
the 'regulular' weight, sometimes confusingly referred to as beta but isn't
standardized) - probably a pe, which is equivalent to one of my copes in this
case
sx: standard deviation of the EV
xy: standard deviation of the data
Does that make any sense?
Ed
On Tuesday 12 August 2003 02:26 am, Tim Behrens wrote:
> Hi there -
>
> I'm not sure what this is ( or how to compute it ).
> If you can give us the equations describing this, we should be able to
> tell you how to compute it with the Feat output.
>
> What is it that you would like to describe with "Standardized Beta
> weights", that you can't describe with the original Betas and the t-stats?
>
> Sorry I'm no use
>
> T
>
> On Tue, 12 Aug 2003, Edward Vessel wrote:
> > No, I am referring not to a t or z score, but to a regression weight.
> > A standardized Beta weight is never greater than one. It is a 'factor
> > loading' so to speak.
> >
> > Ed
> >
> > On Tuesday 12 August 2003 01:16 am, Tim Behrens wrote:
> > > Hi there - by standardised beta weight, do you mean the t-statistic?
> > >
> > > You can get these post-hoc using Feat, by just running the
> > > contrast-manager (by selecting Post-Stats from the top right menu,
> > > clicking on the Post-Stats tab, and selecting "Edit Contrasts").
> > >
> > > If you want to get them by hand, you were nearly right, you have to
> > > divide the copes by the square root of the varcopes (i.e. the standard
> > > error on the copes).
> > >
> > > If you want them to be truly sandardised (i.e. z-scores), you have to
> > > account for the degrees of freedom, you can do this with ttoz
> > >
> > > ttoz -zout zoutput varcope cope dof
> > >
> > >
> > >
> > > Hope this answers your question
> > >
> > > cheers
> > >
> > > Tim
> > >
> > > On Mon, 11 Aug 2003, Edward Vessel wrote:
> > > > Hi folks -
> > > >
> > > > How would one go about computing a standardized beta weight (in the
> > > > regression sense) from a cope or pe?
> > > >
> > > > If I am correct, the pe's are (unstandardized) regression weights
> > > > (b's). Therefore, I'd need to multiply by the standard deviation of
> > > > the predictor and divide by the standard deviation of the data. But
> > > > I am unsure which files would correspond to this.
> > > >
> > > > The varcope seems to be not just be the deviation of the predictor,
> > > > as that should be the same for all voxels. It also isn't the
> > > > standard deviation of the data, as this would be the same for all
> > > > predictors. Is it a ratio of the two?
> > > >
> > > > If that is the case, then do I just divide the cope by the varcope to
> > > > get a standardized weight?
> > > >
> > > > I'm not interested in getting percent signal change in this case ...
> > > > it is a continuously varying parameter (from 0 to 1), so I'd like to
> > > > get a beta weight (or even part correlation).
> > > >
> > > > Ed
> > > >
> > > > --
> > > > Ed Vessel
> > > > U. of Southern California [log in to unmask]
> > > > Dept. of Neuroscience
> > > > HNB, 3641 Watt Way http://geon.usc.edu/~vessel
> > > > Los Angeles, CA 90089-2520
> > > > (213) 740-6102
--
Ed Vessel
U. of Southern California [log in to unmask]
Dept. of Neuroscience
HNB, 3641 Watt Way http://geon.usc.edu/~vessel
Los Angeles, CA 90089-2520
(213) 740-6102
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