Post-hoc comparisons can increase the rate of [[Type I Error]] because researchers can find associations in the sample resulting from randomness rather than true relationships in the population. This is related to [[p-hacking]].
There is no agreed upon method for controlling for inflated Type I Error in post-hoc comparisons, but the Tukey method and Bonferroni correction are most common.
In one example from the book Failure to Heal, a journal (the Lancet) requested that the author of a medical study conduct additional analysis to identify which groups in the study benefitted most from taking daily aspirin. The author, Richard Peto, knew enough to know that doing so would increase the probability of spurious results. He included the astrological signs of each patient and found that Capricorns benefit most from aspirin. To troll the journal editors, he insisted this finding be included along with any other post-hoc findings they requested.