R - using contrasts to compare all levels of a variable?

I am doing a statistical analysis in R. I made a lmer() model, in which a variable has 4 levels (1,2,3,4). The script sets up a contrast matrix for these levels. Basically, The main hypothesis is set up as:

Contrast:
4>3
4>2
4>1


As my study was exploratory, I was also curious of the remaining couples, and I "switched" the contrasts in order to get information about:

3>2
3>1
2>1


When I say that I "switched" the contrasts, I mean that I run the exactly same analysis by "substituting" some levels in the contrast matrix above. This because I noticed that different matrices didn't produce any change for the same contrasts, so I thought it didn't introduce any error.

Can I do that?

Best Luca

• Obviously, you can do what you are doing. The question is what you are doing with the result. If you are interested in p-values, you should only do the planned contrasts. – Roland May 6 '19 at 14:11
• Thank you @Roland! Can you extend a little your explanation? I can understand that the acknowledged method is to do just the planned contrast, but I can't understand why. And I don't know what other alternative there are for a level-to-level comparison without going into post-hoc analysis. – TakeMeToTheMoon May 6 '19 at 14:19
• stats.stackexchange.com/a/63668/11849 – Roland May 6 '19 at 14:25
• @Roland, the explanation in the link you provided is only partially satisfying. The thing is that using a contrast between different groups, the analysis tells me what is the probability one group is going to perceive a difference between the two levels tested in comparison to another group. The classical post-hoc analysis (e.g. Tukey's correction) does not provide me with that information, and provides me only with the information of how those levels are perceived within one group. – TakeMeToTheMoon May 6 '19 at 14:38
• To be clearer: I am interested to understand the differences in the levels of my aimed variable, depending on its interaction with other variables (groups, and others). – TakeMeToTheMoon May 6 '19 at 14:41