Can all possible pairs of comparison be planned comparisons in ANOVA? Let's say we have three intervention groups (condition A, condition B, and condition C/control) to be analyzed in ANOVA, and we are theoretically interested in the difference between each pair of all the possible comparisons (i.e., A and B, B and C, and A and C). Since the three comparisons are according to the hypotheses, I thought that it would be ok to describe this as planned comparisons. However, the planned comparisons do look like post-hoc tests (that test all possible comparisons for exploratory purposes). Is it still acceptable to consider it as planned comparisons without the necessity to adjust the p values? Or should I regard it as post-hoc tests and adjust the p values for multiple testing?
Summary of the suggestions:

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*I am starting to understand that what I described is not really how planned comparisons should be done. When I run planned contrasts, I may start from comparing intervention groups (A & B) vs. control group (C), followed by the comparison of the two intervention groups (A vs. B). Alternatively, I can focus on a specific pair, although the maximum number of contrasts should be k-1, as BruceET has suggested. (15/Sep/2021)

*Thank you so much for your brilliant insights, Tanner! It is important to adjust significance level to avoid false findings when running multiple tests. Together with COOLSerdash's critical suggestions, I may not adjust the significance level when I have a specific hypothesis for each comparison (17/Sep/2021).


The need for P-value adjustments is not due to "planning vs. post-hoc" but about alpha inflation. If I understand your analysis plan correctly, you would like to do pairwise tests comparing the relationship between each pair: AB, BC, AC.
At an alpha of 0.05 (i.e. p-value threshold of .05) you are excepting a 5% risk of there NOT actually being a statistically significant difference between the groups even though you said there was. So if you run three tests, you are actually taking a 5% risk three times, and your "true" risk level is no longer 5%, it's closer to 15%.
This has nothing to do with whether you planned these tests ahead of time or not-- it is simple a matter of re-testing the same data 3 times. So, yes, you should use p-value adjustments.
Note: the true test risk is not exactly 15%. It can be calculated with the binomial distribution, but the intuition seemed sufficient to answer this question.
