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Subject:

Re: fixed effects analysis across two sessions

From:

"MCLAREN, Donald" <[log in to unmask]>

Reply-To:

MCLAREN, Donald

Date:

Thu, 24 Feb 2011 15:42:24 -0500

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (69 lines)

Israr,

Let me start of on the issue of means, sd, r, and t-statistics (basic ideas).
(1) beta ~ weight of a particular IV (e.g. column)
(2) sd ~ weight of overall variance based on covariance of betas
(3) beta=sd(XY)/var(X); r=beta*sd(x)/sd(y) {for linear regression, for
multiple linear regression and general linear models, you compute
partial correlations}
(4) r=sqrt(t^2/(t^2+df) OR t=beta-0/sd

The beta and residual of the model form the basis of the r, not the
other way around. Everything is test against a mean of 0. Since fMRI
values are non-zero, a constant is included to account for the
non-zero mean of the data. It is the betas (not r) that are compared
statistically.

Contrasts:
Run1-C1 Run1-C2 Run2-C1 Run2-C2 Run3-C1 Run3-C2 Run4-C1 Run4-C2
1 -1 1 -1 0 0 0 0 tests C1>C2 for pretreatment
0 0 0 0 1 -1 1 -1 tests C1>C2 for postreatment
1 -1 1 -1 -1 1 -1 1 tests  (C1>C2 for pretreatment) > (C1>C2 for postreatment)

1 means you add the beta, -1 means you subtract the beta, AND it is
the sum of the added and subtracted betas that give you the value to
compare against 0.

T-statistic (matrix notation not included):
T=Contrast*beta/(ResMS*Contrasts*covbeta*Contrasts)
which can be thought of as effect-mean (effect-0) divided by the variance.

Now, if you have multiple subjects, you take the Contrast*beta part of
the T-statistic(con_* images) to the second level modelling.

Let me know if that clarified the issue.

Best Regards, Donald McLaren
=================
D.G. McLaren, Ph.D.
Postdoctoral Research Fellow, GRECC, Bedford VA
Research Fellow, Department of Neurology, Massachusetts General
Hospital and Harvard Medical School
Office: (773) 406-2464
=====================
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On Thu, Feb 24, 2011 at 2:54 PM, Israr Ul Haq <[log in to unmask]> wrote:
> Thanks a lot, This makes sense, particularly the second explanation. although the runs1 and 2 I specified were from the same subject and the whole analysis is being done for each subject separately but I suppose in a way its the same thing and is taking into account the variability across runs. My model is actually an overt naming task, the experimental condition includes a semantic process of interest whereas the control condition has all but that.
>
> Thinking about this though, how is the direction of the change from pre to post treatment (in a voxel) taken into account? I computed a pre - post treatment contrast to check whether it will give me the same voxels (worried that the areas included both positive and negative change over the two sessions in my first contrast) and was relieved to see different voxels. However, if its not too cumbersome, can you please explain how the eventual t statistic is being computed in such a multi session analysis with two independent conditions? Heres what I understand; for each voxel, a correlation coefficient (r) is calculated for each stimulus of a specified condition, and all the r values in a run give a distribution for that condition, with a mean and standard deviation. These are then utilized in the t tests of no significant difference, where the linear t contrasts between two conditions are setup such that whether for that particular voxel, one condition had significantly different signal than the other, using the mean and sd of the r values. What i am trying to wrap my head around is how based on the weightings that we specificy (i.e +1 or -1), the t statistic is calculated for exp > control vs control > exp, since in both cases, what we are essentially inputting is the difference between the means. Intuitively it would seem that it would give a voxel as significant only if the condition weighted +1 also has the higher mean of the two conditions being contrasted. But if so, how would this apply to multiple runs and sessions, or more specifically what would be the sequence of computations in my design? Theres a plus one weighting in both pre and post treatment runs, albeit for different conditions.
>
> Thanks
> Israr
>
>
>
>

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