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SPM  June 2008

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Subject:

Re: A statistical question, probably easy to answer

From:

Thilo Kellermann <[log in to unmask]>

Reply-To:

Thilo Kellermann <[log in to unmask]>

Date:

Wed, 11 Jun 2008 15:58:41 +0200

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Dear Henrike,

your F-contrast is in principle correct, but maybe that you loose one degree 
of freedom (but it might be that SPM automatically looks for linear 
dependencies in your f-contrast). The "typical" F-contrast would look like 
this:
1 -1 0
0 1 -1
Of course you should get at least almost the same results. (The comparison 
between group one and three is implicitly modelled by this contrast, i.e. the 
additional vector [1 0 -1] is not linear independent from the other two 
rows).
Question 1 and 2: Your model is appropriate and your interpretation of your 
F-contrast is right.

You are right that t-contrasts as such are not suitable to be used as post hoc 
tests. But what you can do is making use of the "Mask with other 
contrasts"-feature, i.e. choose "Yes" here and enter your F-contrast at your 
desired significance level as mask. But still you will have to figure out 
first which group has the bigger contrast estimate of the two.

However, the answer to question 3 is not that easy (are any other clusters 
showing up in a t-contrast "statistically real" or not?). Generally a single 
t-contrast is more sensitive because these are directional tests. In contrast 
F test look for differences as such no matter which group has "more". When we 
want to be conservative and our priority is to keep our type I error 
probability at the specified level (usually 5% but actually I do not know the 
threshold you used) you are right when keeping the null hypothesis for the 
other clusters while rejecting it only for the cluster showing up in the 
F-contrast.

Chances are, however, that you commit a type II error (keeping the null while 
the alternative is true) although we cannot determine the exact probability 
without some further information. To keep it at least a little short: It 
depends on your willingness to commit a type I error.

On the other hand if you have some prior information w.r.t. the question which 
of the groups should activate more than another, then it makes sense to 
report the t-contrast. (Although it should be noted that your type I error 
rate inflates with the the number of contrasts you look at).

QUESTION 3: HHMMMMM......!?

Question 4:
When you have only one cluster to be described it is probably the best way to 
make a plot of the contrast estimates comparing the groups visually. Here I 
would chosse the option "Contrast estimates and 90% C.I." and choose your 
F-contrast in the next step. This gives you "nice" (my taste) and 
interpretable plots for the groups with 90% confidence limits.

Hope this makes sense....

Thilo


On Wednesday 11 June 2008 14:58, Henrike Hemingway wrote:
> Dear colleagues,
>
> unfortunately, I am sort of naive, from a statistical point of view. Some
> simple questions:
>
> The experiment is the following: three different groups performed a
> standard encoding task. I am interested in activation differences between
> these groups. For that, I used a ANOVA design, 1 factor with 3 levels
> (group 1, group 2, group 3). QUESTION 1: Is that appropriate?
>
> To look at general group differences, I used the following F-contrast
>    1 -1 0
>    1 0 -1
>    0 1 -1
> This gave one nice cluster. In my opinion, this means that at least two
> groups have activation differences in this cluster. QUESTION 2: Is that the
> correct interpretation?
>
> Now I wanted to find out which groups differ. I used, as post-hoc t-tests,
> simple t-contrasts and found out that group 1 has more activity than group
> 3 in the nice cluster from above. However, these t-contrasts showed also
> other activation differences between the groups. I assume however that I am
> not allowed to take these differences as "statistical real" since they did
> not appear in the ANOVA F-contrast. QUESTION 3: Is that correct?
>
> At last, I still did not know how to interpret these group differences. It
> might be that - both groups have activation, one more than the other.
> - both groups have deactivation, one more than the other.
> - one group has activation, the other deactivation.
> This is probably not unimportant to know.
> I tried several options:
> 1.) I used the "plot button", fitted response, against scan/time. This
> showed me nicely that group 1 differs from group 3, but I had a bad
> feeling: I did not know whether to use the "adjusted" or "fitted" response,
> I did not know how to extract the data from the graph, I did not know what
> SPN does to the data, etc. 2.) I used the "eigenvariate button" to extract
> the first eigenvariate from all voxels within my cluster. This gave totally
> different results. Does it only work when I want to look at a real time
> series? 3.) I decided to go back to the raw data, extracted the mean
> intensity value in the cluster from the con-images of all subjects. Again,
> I got different results QUESTION 4: what is the right way to proceed?
>
>
> Best wishes,
> Henrike

-- 
Thilo Kellermann
Department of Psychiatry and Psychotherapy
RWTH Aachen University
Pauwelsstr. 30
52074 Aachen
Tel.: +49 (0)241 / 8089977
Fax.: +49 (0)241 / 8082401
E-Mail: [log in to unmask]

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