In the case of 3 groups, you can apply the logic of Fisher's LSD: I.e., you can carry out all pair-wise comparisons with no adjustment to alpha provided that the omnibus F-test for that variable is statistically significant. See this thread for more info and references:

https://www.researchgate.net/post/When-do-we-use-the-Fisher-LSD-significance-with-one-way-ANOVA-test

Someone may be able to help you with the mechanics if you say what software you use.

One other thing, when you say ANCOVA, I take that to mean that your model includes the first order effects of the factor (or group) variable and the quantitative variable (i..e, the covariate), but does not include the interaction between them. Is that what you mean?

HTH.

See the attached which should of assistance. However I don't recommend your approach. Why do an ANCOVA IF IF YOU YOU WISH TO. TEST ALL PAIRWISE COMBINATIONS OF SUB GROUP. WHAT'S THE ANCOVA FOR.? suggest you.rethink this after looking at Montgomery's Design and Analysis of Experiments, the ANCOVA Section. Good luck with your research, David Booth

BTW These methods are normally used with factorial designs (see the above refs), the purpose of which is to learn about interactions so why would you. Ignore higher order terms. Either I don't understand your question or you seem to be doing something strange. Summary advise: see a statistical consultant at your university.. Mea culpa if I misunderstood Best David Booth

David Eugene Booth wrote: "Why do an ANCOVA IF IF YOU YOU WISH TO. TEST ALL PAIRWISE COMBINATIONS OF SUB GROUP. WHAT'S THE ANCOVA FOR.?"

For the approach that I suggested in my earlier post--i.e., making all pair-wise comparisons using (a variation on) Fisher's LSD--it would be to get the error term from the ANCOVA model, which is needed in the denominator or the 3 pair-wise t-tests.

David, I can only assume that whatever approach you have in mind does not require that error term. Is that right?

No a factorial model which presumably is used has the residuals for both full and reduced models. This is discussed about factorial models in most DOE or linear models texts. I assume that is what you mean by error term is the the residual statistics which should be easily calculated for any way to model this experiment. BTW I was was not critical of your approach Bruce. I was criticizing the original question. Why do all PAIRWISE COMBINATIONS if you don't have to do that. Note that GLMs are designed to help you get away from all pairwise combinations. Which is not usually a good thing because of multiple testing this is I understand the problem in Microarray analysis in nucleic acids. Steen Knudsen wrote a very nice book on that as have others. BTW these multiple testing approaches are in my attachment. Again if I have misunderstood any of the above I would like to know about it mean culpa in that case. Best wishes to all, David Booth

Thank you David Eugene Booth and Bruce Weaver

Let me clarify: Our ANCOVA includes the main factor (3 levels) as well as 2 metric covariates. We are interested in the main effect of the factor and hence the differences between all 3 groups AS WELL AS the interaction of the factor with the 2 covariates. Would an ANCOVA with all pairwise post-hoc tests (alpha corrected) be the correct procedure for this?

Thanks in advance!

Well you really to need to model the experiment Not not just a subpart of it cause the whole experiment is what was done to the subjects. See Montgomery's Design and Analysis of Experiments for full discussion of factorial designs.and ANCOVA. It is only reasonable to .look at reduced after the full model has been considered. This is a well known principal of experimental design. Please be aware of these things prior to data collection if this was human subjects I am surprised that it was approved. Anyway please study experiment design prior to doing one. As they say proper prior planning prevents poor performance. Best wishes, David Booth

Hello Jana Schöppe. Some authors reserve the name ANCOVA for a model that does not include any covariate x factor interactions. There is nothing wrong with including such terms in your model, but I would advise you to not call it an ANCOVA model to avoid confusing readers for whom ANCOVA means a model with no such terms. Just call it it a regression model or a general linear model.

Also, when you include covariate x factor variable interactions, comparisons of group means become more complicated, because the differences among group means will depend on the values of the two covariates. When one has the group x covariate interaction for just one covariate, it is common to compare the group means at low, medium and high values of the covariate. With two covariates, one possibility would be to generate 9 combinations of covariate values (low-low, low-med, low-high, med-low, med-med, med-high, high-low, high-med, high-high) at which to examine group differences. But depending on the relationship between the two covariates, some of those combinations may not be realistic. I would look at the relationship between the two covariates in a scatter-plot to get some sense of that.

HTH.

Thanks Bruce for a nice summary of the situation. Best wishes, David Booth