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I'm having trouble interpreting the result of a moderation analysis using the PROCESS macro in SPSS. The following is the structure of the data:

Predictor, outcome, and moderator are all continuous. All assumptions verified. Initially I conducted a single moderator analysis in one group of a fourth categorical variable (n = 56). The interaction was significant. My original hypothesis was that this moderation would differ between groups (3 level categorical variable), so at first I repeated the simple moderation within each group (i.e., 3 times). The other two groups did not show a significant moderation effect.

However, I eventually figured out I should be examining this question with a moderated moderation by looking at whether the original simple moderation is moderated by the three-level categorical variable. Once I ran that, the highest-order three-way interaction was not significant.

I'm having trouble interpreting this since the two-way interaction (i.e., simple moderation) appears to be different across the three categorical groups (significant in one, not significant in the other two), but the three way interaction is not significant. If it is the case that there are qualitative differences in the two-way effect, but they are not statistically significant, then can the significant simple moderation (two way interaction) in one of the groups be interpreted as a finding or is it meaningless without a significant three-way interaction?

Thank you

John
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  • This is a question you can expand beyond the confines of PROCESS. Placing PROCESS how you do front and center may turn some people off if they do not know what PROCESS is. Take two effects, A and B. Simple response is that if A > 0, but we are not able to distinguish B from 0, it does not mean we can distinguish B from A. Even if B > A > 0, if B is a very noisy effect, B versus A and B versus 0 might not be statistically significant, while A versus 0 is statistically significant. – Heteroskedastic Jim Aug 02 '18 at 18:56
  • In my experience two-way interactions are significant more often than three-way interactions. (That is to say, you are not the first person to wonder about this.) That may be because the three-way effects are truly smaller, it may be that power to detect even important three-way effects is not as great, or (most likely) some of each. // There may also be four-way interactions with any of a dozen factors not controlled in your design; they are hiding in the error term(s), thus making other interactions of lesser orders more difficult to detect. // One expt cannot settle everything. – BruceET Aug 02 '18 at 21:34

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