Thanks again, Eugene, may I clarify my concept again.....

F-tests investigate several contrasts to see whether any combination of them is significantly non-zero. In this 1-factor 4-level ANOVA, there are 4 EVs: D, A-D, B-D, C-D. Contrasts of the last 3 EVs are included in ANOVA F-test. 

Based on your explanation, for example, you mean F-test not only examine "(A-D) + (B-D)" but also examine "(A-D) - (B-D)"? In my understanding I thought it only examined "(A-D) + (B-D)"...........If it did examine "-" between EVs, in the "F-tests" example in the manual (3 groups of subjects, Contrast 1=mean of group 1, Contrast 2=mean of group 2, etc), the question to be addressed is not always "is any group activating on average?" (group 1; group 2; group 3; group 1+2; group 2+3; group 1+3; group 1+2+3) but should be "is any group combination activating on average?"(for example, group 2-3, group 1-2-3, etc)...... 

And the final puzzle for me is, in this 8-subject design, why the EV1 fitting condition D is

1

1

1

1

1

1

1

1

? Isn't this representing the group mean of the 8 inputs? Or does it just shift the mean of D to the group mean and make "relative" comparisons between other levels? 

Really appreciate for your help!

Mark

2012/9/29 Eugene Duff <[log in to unmask]>

I may not have been completely clear.  Put a different way: An F-test across evs tests whether any combination of the evs explains a significant effect.  The contrasts you mention can be described in terms of a combination of the three evs used.  E.g A-B = (A-D)-(B-D).  So the F-test is implicitly testing for that effect, as well as the others.

Cheers,

Eugene

On 29 September 2012 16:16, 曾tmt <[log in to unmask]> wrote:

Hi Eugene,

Yes ANOVA detects difference between levels. One point that confuses me is that, why the other rest 3 differences, i.e. A-B, B-C, A-C, are not evaluated in this contrast setting? Must be some point I don't understand well in this stats model setting I guess.....

Mark

2012/9/29 Eugene Duff <[log in to unmask]>

Hi Mark - 

On 29 September 2012 13:19, Mark Tseng <[log in to unmask]> wrote:

Hi,

I'm a beginner of fsl and hope someone could help me to figure our this simple question......

http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FEAT/UserGuide#Group_Statistics

In the ANOVA 1-factor 4-levels session, the example in this guide explains:

"We have 8 subjects and 1 factor at 4 levels A, B, C and D. The first two inputs are subjects in condition A, the next two are B etc. To compare a level with another we could just have one EV per level. However, if we want to ask the ANOVA question - where is there any treatment effect then we can do the following. EV1 fits condition D (it is the only nonzero EV during condition D). EV2 fits A relative to this, i.e. represents A-D (see below for explanation). The F-test then tests for any deviation - ie any difference between the levels, and corresponds exactly to the standard ANOVA test."

My question is, why is the EV for Condition D not:

  0

  0

  0

  0

  0

  0

  1

  1


  ?

Also, in ANOVA, the test is significant if the difference of any combination of the 4 levels is different, isn't it? But the contrasts only contain A-D, B-D and C-D, without containing A-B, B-C, A-C....

Hi Mark - 

An ANOVA is only interested in identifying any differences between levels.  When there are four levels, if there are any differences between levels, at least one of the three contrasts, A-D B-D and C-D must show an effect.  The specific design provides on EV for each of these differences.  Therefore, F-test across these differences provides the standard ANOVA test.

Cheers,

Eugene

 

Thanks for any clarification of my concept.

Mark