Ram,
> Hi -
>
> Based on what was previously posted to the list, I have come to believe the
> F-test as calculated in FEAT is as follows:
>
> if the model is : y = b1x1 + b2x2 + b3x3 + b4x4 + e
>
> then an F test of {b1,b2} is testing:
>
> H0 : b1=b2=0
Yes. This is the null hypothesis we are testing.
> Ha : one of {b1,b2} is not equal to zero
>
> and the method of testing is equivalent to fitting both:
>
> full model : y = b1x1 + b2x2 + b3x3 + b4x4 + e
> reduced model: y = b3x3 + b4x4 + e
>
> and then calculating:
>
> F = [ SSE(Reduced) - SSE(Full) / dof(reduced) - dof (full) ] *
> dof(full)/SSE(full)
> SSE = Sum Squared Error
Yes:
F = [SSE(Reduced) - SSE(Full)]/ [dof(reduced) - dof (full)]
*dof(full)/SSE(full)
However, in Feat we actually calculate this using
F=b'c*inv(Var(c'b))*c'b/K
with K and n DOF, where c is a K*m contrast matrix (in your example c=[1 0
0 0; 0 1 0 0]) and n is the no of time points minus the number of
regressors (m). This is equivalent to the way you spelled out.
Cheers, Mark.
Mark Woolrich.
Oxford University Centre for Functional MRI of the Brain (FMRIB),
John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK.
Tel: (+44)1865-222782 Homepage: http://www.fmrib.ox.ac.uk/~woolrich
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