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I have done an online survey for my dissertation and now I am a little bit confused: I tested the following model:

  1. Variables A -----> B (Variable A negatively correlates with Variable B).

  2. Moderating Variable: M on the relationship of A -----> B.

My results show:

  1. That the relationship between A -----> B is not statistically significant (.233).
  2. The moderating variable M is statistically significant (.025).

My Problem: How can I interpret these results? I am confused on how to argue about that the moderating variable has an impact on a non-significant relationship between A -----> B?

I mean, if the 'underlying' relationship between A ------> B is not statistically significant, how can there be a moderating impact on it?

The only explanation that comes to my mind is that the moderating variable M only would occur, if further research shows that the relationship between A ------> B is significant (e.g. because of a larger sample size - I had only 100 participants)? Am I on the right path here?

Thanks a lot!

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    $\begingroup$ I think that for this to be answerable, you need to add more details about your data, model, and the tests performed. However, note that "statistifically significant" does not mean "true" and "not significant" does not mean "false" and the difference between significant and not significant might not be significant (stat.columbia.edu/~gelman/research/published/signif4.pdf) $\endgroup$ Commented Aug 8, 2016 at 8:55
  • $\begingroup$ I don't know to what extent moderation in these sorts of models differs from interactions in a multiple regression context, so I may be wildly wrong, but is it possible that what's happening here is that there is a relationship between A and B, but it's only "strong enough" to reach statistical significance for extreme values of M? I'm thinking about possible parallels in regression/ANOVA where there's a significant interaction but no main effect. $\endgroup$
    – Ian_Fin
    Commented Aug 8, 2016 at 18:05

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I think this really ought to be a comment, but I don't have enough reputation (yet) to leave a comment. Two thoughts occur to me. (a) Are you sure you did a correct moderator analysis and entered everything correctly? (Sorry if that sounds patronising, but I don't know you.) See http://quantpsy.org/sobel/sobel.htm for a well recognised website. (b) Perhaps your AB correlation was parametric, but your moderator analysis used a nonparametric process such as resampling? If so, have a good look at whether your variables meet parametric assumptions, and be consistent in whether you use parametric or nonparametric tests.

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