Interaction insignificant, main effects significant I am using modprobe syntax on SPSS to test an interaction between narcissism and rumination on a dependent variable, aggression.
I get a significant effect of rumination (b = .6450, t = 2.32, p = .0216) and significant effect of narcissism (b = .5646, t = 2.5, p = .0135).
The interaction is not significant (b = -.069, t = -.824, p =. 4114).  
I'm not really sure how to interpret this. Can I still look at the plot and slopes? Or are they now meaningless as they are insignificant? (Or should I look at them and try to see why it is insignificant, e.g., because narcissism lines are too close together at +1 SD of rumination?)
The modprobe output has a section called: 'conditional effect of predictor at values of the moderator'
So:
Rumination -1sd:  narcis=2.25.   B=  .49.    T= 4.19. P=  .000
Rumination  Mean: narcis=3.21.       .42.       4.69.     .000
Rumination  +1sd: narcis=4.17.   B=  .36.    T= 2.86. P=  .0048

Since all these are significant, doesn't this make the interaction significant? Basically, I'm not sure what the significance in the above table represents since the main effects' and interaction's significances are already shown elsewhere.
Secondly, is it possible that the interaction is not significant because of the high p at +1 SD? 
All I really want to know is how to report this output, but I'm trying to grasp some understanding of it while I'm at it.
 A: Your interaction is not significant. What the modprobe output is showing you are your simple slopes for the effect of rumination on aggression, at different levels of narcissism (-1 SD, average, and +1 SD). It's okay that all of your simple slopes are significant, and that your interaction is not. This is because all of your simple slopes are in the same direction and roughly the same magnitude: B = .49 (-1 SD narcissism), .42, (average narcissism), and .36 (+1 SD narcissism), respectively. For there to be a significant interaction, the association between X & Y (in this case, rumination and aggression) must change depending on the level of the moderating variable, and in this case, it very clearly doesn't.
A: It looks as if Narcissism and Rumination are measured on some kind of scale.  If so, did you consider any non-linearities (assuming you have enough data to support that exploration)?  Off the bat, I would assume what you're seeing are non-linear interactions.  The linear interaction term was not significant, but the conditional effect was for certain values. 
If you wanted to get all proper, I'd recommend something like a two dimensional spline, such as a thin-plate-spline.  My personal choice for fitting those would be the mgcv package in R.  That package (or any other appropriate model) should provide a heat-map type view of the relationship.
Also be sure to understand any relationship directly between Narcissism and Rumination so you're not drawing insight from a very sparsely populated area of the feature space.
As for the heart of your question, I'd say it depends on how many observations you have.  If you've got 50 or less, I'd just say there wasn't a strong interaction effect.  If you've got a few hundred, then I'd be sure to explore all the non-linearities.  Anything in-between is a bit of a grey area that should have been addressed with power calculations prior to any analysis.
All of the above are of course my own suggestions.  Best of luck.
