Dear McLaren,
Many thanks to your enlightening discussion and suggestion. I agree that both the main effect and conjunction results should be reported for the neuroimaging data.
As to the last issue you have mentioned about the repeated-measures ANOVA, I am now indeed using the repeated-measures ANOVA model (i.e. flexible factorial model) to deal with both ERP and fMRI data. Therefore, I would like to ask more about it if it is not too boring for you.
For example, my data were from a 2 by 2 design and both factors were within-group factor. There were totally 4 conditions: A1B1, A1B2, A2B1, A2B2. I built a flexible factorial model in SPM8 based on an article titled "contrast weights in flexible factorial design with multiple groups of subjects" by Jan Glascher and Darren Gitelman. The model included a between-subjects factor "subject" (independence-yes, variance-equal) and two within-subjects factors "A" and "B" (independence-no, variance-equal). The contrasts I set were listed as below (all F contrasts):
(1) 'Main effect of A', [0.5 0.5 -0.5 -0.5];
(2) 'Main effect of B', [0.5 -0.5 0.5 -0.5];
(3) 'Interact between A & B', [0.5 -0.5 -0.5 0.5];
(4) 'A1, B1 vs B2', [1 -1 0 0];
(5) 'A2, B1 vs B2', [0 0 1 -1];
(6) 'B1, A1 vs A2', [-1 0 1 0];
(7) 'B2, A1 vs A2', [0 -1 0 1];
If I am going to report main effects, interaction effects and conjunction results, should I report both (1) and (2) for main effects of A/B, (3) for their interaction effects, [(4) AND (5)] for the "common" effect of factor B, [(6) AND (7)] for the "common" effect of factor A?
Bests,
--------------
Delin
>The two analysis are asking two different questions. Here are my
>thoughts on the issue.
>(1) Statistical theory says its okay to interpret main effects in the
>absence of an interaction. This is becuase the two levels are not
>different. This has been done for a number of years in a number of
>fields. You can, however, use a more liberal definition of
>significance for the interaction if you want to me more conservative.
>(2) I like using the logical AND as it shows where two things are both
>significant. However, these are routinely falsely interpreted by the
>neuroscience field (Nieuwenhuis et al. 2011, Erroneous analyses of
>interactions in neuroscience: a problem of significance). The main
>issue is that when A is significant and B is not significant,
>researchers conclude that A and B are different. As one can see from
>point #1, this is not necessarily true.
>
>Thus, it is probably important to report both the main effect and
>conjunction to properly characterize the results.
>
>The other issue to be careful about is to make sure you have properly
>modelled the repeated-measure effects, if this is a repeated-measures
>ANOVA.
>
>Best Regards, Donald McLaren
>=================
>D.G. McLaren, Ph.D.
>Postdoctoral Research Fellow, GRECC, Bedford VA
>Research Fellow, Department of Neurology, Massachusetts General Hospital and
>Harvard Medical School
>Website: http://www.martinos.org/~mclaren
>Office: (773) 406-2464
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>
>On Tue, Apr 24, 2012 at 1:31 AM, Sun Delin <[log in to unmask]> wrote:
>> Dear SPMers,
>>
>> ? ?I am considering whether we should report the results of conjunction analyses but NOT those of ANOVA main effects.
>> ? ?For example, a 2 by 2 design, conditions are listed as below
>> ? ? ?A1B1 ? A1B2
>> ? ? ?A2B1 ? A2B2
>> ? ?An 2-way ANOVA model is recruited to show the significant main and interaction effects of neuroimaging data (both fMRI and ERP). The main effect is often used to show the "common" effect of some factor whilst the interaction effect is often used to show the manipulation of a factor on another factor.
>> ? ?I have no doubts on reporting the significant interaction effect [(A1B1-A1B2)-(A2B1-A2B2)] because it really reflects the manipulation of factor A on factor B. However, I am some confused about the main effect of both factor A [0.5*(A1B1+A1B2)-0.5*(A2B1+A2B2)] and factor B [0.5*(A1B1+A2B1)-0.5*(A1B2+A2B2)] since the fomula of main effect just neglects the difference between different conditions. That is, if the intensity of a voxel is found significant for an interaction effect, e.g. [(A1B1-A1B2)>(A2B1-A2B2)], we know that (A1B1-A2B1) is something different from (A1B2-A2B2), and so that the main effect of factor A is reflected more by a larger difference of (A1-A2) when B1 than a smaller difference when B2. Therefore, It may elicit confusion to show a main effect where there is a significant interaction effect because the main effect does not mean the "common" effect. Moreover, I think it is also not appropriate to show a main effect even there is no significant interaction effect. The reason is that we recruit very high height threshold (p < 0.001 uncorrected or more strict threshold set by multiple correction algorithm) to limit the output. Thus, no significant interaction effect does not mean that factor A is not manipulated by factor B here, it only means that such manipulation is not above the threshold (e.g. p = 0.0011). Therefore, reporting a significant main effect where there is no significant interaction effect can also be misleading.
>> ? ?I think there should be two ways to deal with the question to look for "common" results:
>> 1) to look for significant (e.g. p < 0.001) main effect where the interaction effect is indeed small (e.g. p > 0.05);
>> 2) recruit conjunction analysis to find the "common" effects, e.g. [(A1B1-A2B1) AND (A1B2-A2B2)] to look for the common effect of factor A under both levels of factor B.
>>
>> ? ?I am not sure whether this idea is appropriate and I will greatly appreciate for any comments.
>>
>>
>> Bests,
>> Delin
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