Hi,

also note that F-tests have a spherical or elliptical rejection region while individual t-tests evaluate rectangular rejection regions. This leads to differences in the rejection regions: points outside an ellipse may be detected by the F-test but, if they fall within a box, the H0 may not be rejected by the t-test. See http://www.amstat.org/publications/jse/v16n3/martin.html (Tom Nichols alerted me once to Fig. 2).
It is a bit of a different plot than your example (because you are wondering about the discrepancy of positive detections) but it may be worthwhile to mention.
Cheers,
Andreas


Von: FSL - FMRIB's Software Library <[log in to unmask]> on behalf of "Anderson M. Winkler" <[log in to unmask]>
Antworten an: FSL - FMRIB's Software Library <[log in to unmask]>
Datum: Samstag, 3. Dezember 2016 um 10:49
An: <[log in to unmask]>
Betreff: Re: [FSL] Discrepancy between f- and t-test images

Hi Lisa,

Oops, my bad, it's Hayter, not Hayer: Hayter AAJ. The maximum familywise error rate of Fisher’s least significant difference test. J Am Stat Assoc. 1986 Dec;81(396):1000–4. http://www.jstor.org/stable/2289074

However you don't have to bother much with it -- it refers to differences more in the opposite direction, i.e., excess false positives as opposed to not finding results in the t-test, and also it shows that with 3 groups it's fine. The fact that you are using cluster-level inference already explains the issue: there is no guarantee that the F-test will match the t-tests even in the 3-group case.

Which to choose then? I would go for the one that has higher specificity: the t-tests. I would leave the F-test results aside.

All the best,

Anderson


On 2 December 2016 at 12:28, Lisa Kramarenko <[log in to unmask]> wrote:
Hi Anderson,

thanks for your response! Indeed, I am comparing three groups and I am using easythresh (after flameo) which performs multiple comparison correction at the cluster level!
Unfortunately I can't find the paper you're referring to, could you also tell me its name? Or maybe you can really briefly summarize what the reason for this discrepancy is?
And I have another question: would you mind giving a hint about how to interpret the not-matching results? Is it a difference to be reported or rather not?

Thanks so much for your help!


On 1 December 2016 at 10:16, Anderson M. Winkler <[log in to unmask]> wrote:
Hi Lisa,

The results may not match, particularly if:
- Spatial statistics are used (e.g., cluster, TFCE).
- The rank of the F-test diverges from 2 (e.g., if you are comparing 3 or more groups). For a reference, see Hayer (JASA, 1986).

All the best,

Anderson


On 30 November 2016 at 10:26, Lisa Kr <[log in to unmask]> wrote:
Hello,

I have some trouble understanding the discrepancy in the results of my ANOVA. While the F-stat image shows the regions with significant differences between my three groups, the individual t-tests then  show that the differences between the single groups are in regions other than these F-test has shown (see attached, red=f-test, green and blue: group differences). Is there any explanation for this? I was expecting the differences between groups to fall in the general areas indicated by the F-Test.

Thanks!!

Lisa