Control variables vs mediated moderation?

#1
Hi everybody,

I have a question concerning the inclusion of control variables into my research. I have data from an experimental, randomly distributed social protection program.
I want to test whether a moderating variable influences the relationship between treatment and outcome. Also, I want to test for other confounds. However, the experimental design should eliminate the effect of all third variables, right? But in this case, I want to focus on the moderating variable, not the treatment itself. Is it ok to include control variables or is it rather a mediated moderation?

Thanks,
m
 
#2
Are you asking because your experiment results don't hold with added controls? If so, perhaps you should look deeper and try to understand which specific control(s) influences your estimated interaction coefficient.

On a side note, what's your sample size?