How to determine if a change in F value when introducing a covariate, is significant?

Question

My question may be very basic but I hope that you can help me. I have got two groups (A and B). I am measuring two continuous biological measures (X and Y) which are significantly positively correlated. Theoretically it is clear that X can influence Y but not vice versa. Y has been measured two times (Y1 and Y2) and should be analyzed by repeated measurements analysis. The effect of group on X is strong and significant (ANOVA). The effect of group on Y is also significant (repeated measurements ANOVA) but when introducing X as a covariate (repeated measurements ANCOVA), it is very small and not significant anymore. To my opinion, this probably means that group is influencing Y only indirectly.

I would like to know if the difference in p values and/or effect sizes between the group effect on Y with and without X as a covariate, is significant. Is there a way to test this?

Answer 1

Yes there is an appropriate F test comparing the hierarchical models lower order model without X compared with the higher order model with X included. Alternatively you can test to see whether or not the coefficient for X is significantly different from 0. This is done with a t test. Normailty of residuals is assumed for this.