I do have one more question regarding these results, I hope you don't mind:
Does the mathematical test in 3dLMEr, which produced the z values for my above mentioned group*time interaction effect, have a name?
Since you said chi-square results for group:time and z values for [-gltCode Int-Ctlr_over_Time 'Group : 1*Intervention -1*Control Time :'] are conceptually equivalent and it's possible to use either one, I decided to use the z values, because those also show the direction of the group*time effect.
I just want to make sure that readers of the papers know which of those values were chosen. So if I had taken the the chi-square values, I would write "Chi-square tests show that ... ". - Now that I've chose the z values instead: What is the correct phrase to use for the z values?
