I've used a general linear model function to run an ANCOVA, involving a categorical predictor (with two levels), a continuous predictor, and their interaction effect.
If I don't center the continuous predictor, I get a significant effect for the categorical predictor and a significant interaction effect. If I mean-center the covariate, the categorical predictor effect becomes non-significant but the other effects remain unaltered. Does anyone know why this happens? And which option is the correct one (to center or not to center?)?
Best Answer
Neither, or both, are correct.
You often cannot interpret the main effect when you have an interaction in there. The main effect is the difference between the groups when the covariate is equal to zero - if zero is meaningful, then it's interpretable. If you move where 0 is (by centering) you change the main effect of the between subjects factor. But the actual model doesn't change, you just shuffle the parameters about.
Usually a graph is sufficient to see what's going on. If you want to get more technical, you can calculate 'regions of significance', see: http://quantpsy.org/interact/
(Note that ANCOVA is multiple regression, which is why the pages refer to multiple regression.)
Here's a picture, the lines of best fit for two groups are shown. If the intercept is at the left, then group 2 has a higher score. If the intercept is on the right, then group 1 has the higher score. If you center the covariate, then the two lines are at the same height, and there's no difference.