Is it a valid test to compare the endpoints of the confidence intervals between the interaction terms using the margins?
I am having a hard time accepting that the confidence intervals of my different groups (interaction of two variables) are independent?
Is it true that they are dependent and that we can interpret the results by saying that there is an effect of this interaction?
I really appreciate your help, many thanks.
Your question isn't quite clear to me, but I'll offer a few thoughts.
A) If you want to know if the interaction effect is "significant", you should probably be conducting something analogous to an analysis of variance (analysis of deviance, and so on). This should be available with good software, depending on your model.
B) It is generally acceptable to consider e.g. means with non-overlapping confidence intervals as statistically different. This result won't be exactly the same as comparing e.g. means with a statistical test, but it is a useful approach in some cases.
C) However, depending on your software, there is probably a way to directly compare e.g. means or marginal means by hypothesis tests. Often the function or option is called emmeans or EMMEANS.
It appears that you have an interaction plot showing interaction. See the attachment below. Your model is likely not correct though to test this interaction effect. See these topics under factorial design in book in the second attachment from the z-library for download. Further see the the second screen shot for the method to model the interaction effect from Montgomery book from the z-library as a regression model.
Best wishes David Booth
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