Interaction significant but simple slopes not significant?

#1
I have run a forum search and an internet search, and tried posting this question on other forums, but have been unable to find an answer to my specific problem. My question concerns interpretation of simple slopes generated from moderation analysis.

I have conducted a moderation analysis as follows:

X (continuous independent variable, centered), M (continuous moderator, centered),
Y (dependent variable).

Standard deviation for X is 3.8, and for M is 2.

I first entered X and M into a multiple regression analysis, and both were significantly associated with Y (beta X=0.23, beta M=0.21, both significant at p less than 0.05), with the model significant as well (R-squared=0.14). For the next step, I entered X, M, and the product of X and M (X*M, interaction factor) into a regression analysis, and got a small but significant R-squared change (of 0.001), with significant regression coefficients for X (beta X=0.273), for M (beta M=0.215) and for X*M (beta X*M=-0.034), all p less than 0.05. The interaction factor did have a sign opposite the main effects. I understand that this means that M is a significant moderator of the relationship between X and Y.

However, when I try to plot simple slopes at high (+1SD) and low (-1SD) levels of M, both slopes are nonsignificant (unstandardized slope 0.029, t=0.314 and p=0.89 for high M, and unstandardized slope 0.1349, t=0.902 and p=0.37 for low M). I believe this means neither slope is different from zero.

My question is, does this invalidate my interaction? Should I therefore not consider M a significant moderator of Y on X, despite significant interaction coefficient and significant R-squared change? If the interaction is still valid, how do I report the results of the simple slope analysis?

Thanks in advance!
 
#2
First, the interaction is not about the slopes themselves, but about the difference in the slopes. So, the test of the slopes is irrelevant.

Second, don't get too hung up on significance. The interaction would be valid even if it was not significant.

Third, I wouldn't report simple slope analysis at all. In fact, the presence of an interaction means that the simple slope analysis is invalid.

Finally, to examine the importance (as opposed to the significance) of the interaction, I would calculate the predicted values of Y at various values of X and M.
 

hlsmith

Less is more. Stay pure. Stay poor.
#3
The part that you may be missing is that X relationship may is conditional on the value or M. So Y(x|m) is what you are looking at and reporting x not given m would be inappropriate, thus you keep the main effects of x and m in the model but only interpret the interaction term because of the conditional relationship.