What post-hoc test to use with 2x2 repeat measures ANOVA

#1
I believe this question should be relatively simple. I have a 2x2 repeat measures anova for a performance task. My two factors are presence and absence of an observer and presence and absence of music playing in the background, therefore my 4 conditions are (1)no observer-no music, (2)observer-no music, (3)no observer-music, and (4)observer-music. For my measure, (after a significant anova test) I would like to use a post-hoc contrast to find out if conditions 1 and 2 are different from 3 and 4, and if conditions 1 and 3 are different from conditions 2 and 4. What test should I use and what controls do I need?

Thanks for any help!
 
#2
I am not a stats expert but I will give my opinion that I hope it might be useful (and, hopefully, confirmed by someone with more knowledge).
since you do only have 4 comparisons, type I error is not a major concern and you could use almost any posthoc (although I would not recommend using LSD fisher even in such a short number of comparisons). I usually perform Tukey HSD test because it is quite restrictive and should lead to few false positive results (for a comparison with other post hoc tests, see https://pages.uoregon.edu/stevensj/posthoc.pdf). In fact, I have read (https://stats.stackexchange.com/que...key-hsd-test-correct-for-multiple-comparisons) that this test maintains alpha at the specified level (i.e. 0.05) across multiple comparisons and, therefore, makes unnecessary to introduce additional corrections when comparing several pairs of means.