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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