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.

• Do you have a sense of what SPSS means by "conditional effect of predictor at values of the moderator"? I have an idea but I'd rather not base my answer on a guess. Statistics terminology can get pretty dicey. Also... plot your data. Always plot your data. You are smarter than a test statistic. Jul 1, 2014 at 4:45
• Okay not sure if this is what you mean but: i think spss means that it is showing the effect of the predictor on the dv at different values of the moderator.
– Red
Jul 1, 2014 at 5:08
• That's what I thought. I've never heard of calculating standard errors for something like that. Do you know how they're derived? I'm pretty sure I know how to answer your question but I don't want to lead you wrong. Jul 1, 2014 at 5:41
• You might find helpful this answer: stats.stackexchange.com/a/79785/35989
– Tim
Dec 10, 2014 at 8:00

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.

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.

• Thank you, but i have a pretty basic understandimg of stats and im not really going to be doing much more analysis (maybe a mediation) as the data is collected and i need to report and interpret this analysis. I think ill leave it at: "the predicted effect is there but the interaction is insignificant, therefore aggression is higher at high narcissism and at high rumination, however there is no significant interaction between the independant variables (so high aggression can be strongly predicted independently by each one)"
– Red
Jul 1, 2014 at 5:19
• Also they are measured like this narcissism 1-6 scale, rumination 1-4 scale, aggression 1-5 scale.
– Red
Jul 1, 2014 at 5:28
• Sounds fair, I would at least take a moment to explore the direct relationship between Narcissism and Rumination. This could be as simple as a jittered scatterplot of the responses. I would do this so if there is a strong relationship, you can be a bit more nuanced with statements like can be strongly predicted independently by each one. Jul 1, 2014 at 18:35