On Fri, Apr 13, 2012 at 11:31 AM, Daniel Ferreira <[log in to unmask]> wrote:
> Dear all,
>
> I want to study the global effect of Age (with three levels) over the GM volumen. So, I thought to perform an one-way ANOVA using the following F-contrast:
>
> [1 -1 0 ; 0 1 -1]
>
> Is it actually correct? Beacuse these two contrast vectors are non-orthogonal, whereas typical ANOVA's would use a full set of orthogonal contrasts to divide the "treatment" SS, e.g. [1 -1 0; 1 1 -2].
It depends on what the three columns are in the model. If each column
has 1s and 0s, where 1s indicate membership in a single group. Then
the contrast is correct. If one of the columns are all 1s, then you'd
need a different contrast as the meaning of the columns is different.
>
> My second question is, if this F-contrast is definitely correct and I obtain a significant effect of Age, then I try to evaluate the following post-hoc contrasts:
>
> [1 -1 0] [1 0 -1] [0 1 -1]
>
> and the reverse contrasts:
> [-1 1 0] [-1 0 -1] [0 -1 1]
>
> So, how should I correct these multiple comparisons in order to avoid the type 1 error.
The most conservative approach would be to divide the threshold by 3
or multiple the p-values by 3 and use a typical threshold. There are
other approaches, such as testing the most significant test a/n, then
the next at a/(n-1), but I am not sure if they have been implemented
in imaging yet due to the issue of mulitple voxels.
The type 1 error rate due to 3 tests is probably a lot smaller that
due to testing thousands of voxels. It is definitely a concern that
needs to be addressed by the field, but so far has largely been
ignored.
Also, you can mask the post-hoc tests in only regions where the F-test
was significant. In this way, you know that at least 1 of the three
tests should be significant.
>
> Thank you very much in advance
>
> Daniel Ferreira
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