Dear Karli & others
I also think Karli and Roland are right here, but this depends on the
question that Karli is asking.
Firstly, I am assuming that the design works as follows: AB are the levels
of one factor and 12 the levels of the 2nd, then [(A1-A2)-(B1-B2)] is
1 -1 -1 1 and [(B1-B2)-(A1-A2)] is -1 1 1 -1. If this is the case then these
are indeed interaction tests.
What these interaction tests show are regions in which the effects of AB
differ according to 12 or vice versa, ie 'differences between differences'
in factors. They will not show give you directly the subset of those regions
that show interactions *but no main effect*. The former is a perfectly valid
and indeed traditional interaction contrast, but as interactions and main
effects are orthogonal it does not address the latter question, which
involves an inference about both main effects and interactions.
I would therefore say that whether the reviewer is correct depends on what
inference you are wishing to make about your 'interaction' regions:
1/ If you just need to know that the effect of AB depends on the level of 12
(or vice versa) then your analysis will do this. The reviewer's suggestion
of a 2nd level ANOVA will also do this.
2/ If, however, you wish to isolate regions with interactions *but no main
effect*, you could 'discount' main effect regions from your interaction map,
this could be done by exclusively masking the interaction map with the main
effect map at the 2nd level, perhaps at a liberal threshold such as .05
uncorrected for the mask, as you are effectively trying to make an inference
about an effect (the interaction) and a null effect (the absence of a main
effect). Because one of the effects is effectively a null effect I don't
think a formal conjunction procedure will work, but someone will I am sure
correct me if I am wrong)
3/ If the purpose of the study is not to show that the effects of AB differ
according to 12 in certain regions, but just to show a 'simple' main effect
of AB at either 1 or 2, this is again a different test.
As far as I can see, however, the reviewer is incorrect in suggesting that a
2nd level ANOVA (as opposed to taking 1st level interaction contrasts to
t-tests at the 2nd level, as you have done) is going to produce a different
kind of interaction. It will not - the interaction columns and main effect
columns are orthogonal, so estimating one should not affect estimates of the
other. The difference is that the 'full' 2nd level ANOVA tests the
interaction agains a 'pooled' error term for all the contrasts, whereas the
2nd level t-test tests the interaction against its own error term. The
former method means taking account of nonsphericity at the 2nd level; the
latter does not. For more on this see the note by Rik Henson & Will Penny on
ANOVAs in SPM - see Roland's email! (I would also say that t-tests are fine
and that the direction of an interaction *is* important - for example A1-B1
= something and A2-B2 = nothing much)
Hope this helps,
Alexa
| -----Original Message-----
| From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]]On
| Behalf Of Roland Marcus Rutschmann
| Sent: 14 November 2005 13:16
| To: [log in to unmask]
| Subject: Re: [SPM] reviewer demands 2-way ANOVA
|
|
| Hi,
|
| now I am confused because I think Karli is right.
|
| On Saturday 12 November 2005 15:40, Alle Meije Wink wrote:
| > Dear Karli,
| >
| > >I did an fMRI study that involved a group of subjects doing a task that
| > >that varied along factors A and B and along factors 1 and 2, and I'm
| > >interested in the interaction effect. To address this, I ran
| individual
| > >t-tests of the type [(A1-A2)-(B1-B2)] and [(B1-B2)-(A1-A2)] and
| > >then did a second level random effects analysis.
| > >However, the person reviewing my paper is insisting that I do an ANOVA,
| > >and claims that the t-tests I ran are not true interaction
| maps, and that
| > >they will identify brain regions showing two main effects and no
| > >interaction. Here is his/her example:
| > >
|
| I hope I read this correctly as 2 Factors (let's call them F1, F2) with 2
| levels each (F1(1) F1(2) F2(1) F2(2)) and you build contrasts
| [F1(1)-F1(2)]-[F2(1)-F2(2)]?
|
| Why don't you take the F contrast over that contrast instead of 2
| T-contrasts
| (the "direction" of an interaction term is pretty hard to
| interpret, isn't
| it?). But other than that I don't see the incorrectness.
|
| > So the maps you made are
| > 1. [(A1-A2)-(B1-B2)] = main effect AB + main effect 12 together in a map
| > 2. [(B1-B2)-(A1-A2)] = main effect BA + main effect 12 together in a map
|
| This is interaction: If the difference between cond1 and cond2 is
| different in
| condA then condB, the maineffect(1-2) depends on the other effect
| (A-B). This
| is exactly the 3rd coloumn in fig 7 of Rick Hanson's excellent technical
| guide to Anova.
| http://www.fil.ion.ucl.ac.uk/~wpenny/publications/rik_anova.pdf
|
| > I don't think you can conclude anything about interactions from those.
| > What you need is a repeated measures ANOVA, set up in the following way:
|
| Like I said, I think he's right. Can someone enlighten us?
|
| Regards,
|
| Roland
|
| --
| Dr. Roland Marcus Rutschmann
| <[log in to unmask]>
| Institute for Experimental Psychology, University of Regensburg
| Universitätsstraße 31, 93053 Regensburg, Germany
| Tel: +49 941 943 2533, Fax: +49 941 943 3233
| http://www.psychologie.uni-regensburg.de/Rutschmann
|
|