Can the influence of a different factor on a known effect be analyzed directly? If I am trying to analyse wether a known effect is inhibited by another factor, is it a fallacy to analyse the influence of the factor on the effect size directly? I.e. can I just use a statistical test between the effect sizes for different conditions, or do I have to do a full interaction model?
Here is the setup. In each condition I am measuring two variables X_1 and X_2. The difference between the variable X_1 and X_2 gives the effect size I am interested in.
Now I also have two conditions C_1 and C_2 and my hypothesis is, that the effect size for C_2 will be smaller than for C_1. One way I could test this, is by calculating all the effect sizes in condition C_1 from the appropriate X_1 and X_2 and comparing all these with the effects calculated for C_2.
However what I am analysing could also be seen as an interaction effect between the conditions and the factor which went into producing X_1 and X_2. So I could also use an 2x2 interaction model, to see if my conditions have a significant influence on the effect size.
What would be the problem with an direct analysis of the effect size? In the final plot I would like to show only the conditions versus effect sizes, because this will reduce a lot of complexity.
 A: It sounds as if you prefer simply to show the difference between the results under c_1 and c_2, but that you have the nagging feeling you "should" develop an interaction model. I have no idea where that feeling is coming from, but, if done well, such a model will tell you not only the magnitude of the difference but also the p-value associated with it. In other words, it will tell how rare such a difference would be if condition didn't truly matter, and if chance alone were at work in creating the difference you obtained for your samples. Is such a piece of probabilistic information useful to you, or to the audience for your study?  The answer to that "should" determine whether you run such a test or whether you stick with the descriptive findings.
EDIT:  I'm rethinking my answer after reading your comment and rereading your question.  There is no "factor which went into producing X_1 and X_2" -- the difference score is simply one minus the other, and this doesn't depend on any factor.  I see nothing with which the condition variable can interact.  If you want to run an inferential procedure, the t-test is the one, as long as you have looked into its usual assumptions.  There's no "flaw" to it, and there's nothing wrong with plotting 2 difference score means as opposed to 4 pre-differencing means. I think the situation is simpler than you have been envisioning.
