I have a general question on whether effect sizes need to be corrected for multiple comparisons. I need to conduct 8 t-tests, in order to test whether values from 8 different conditions different significant from 0. I know that are procedures that allow an adjustment of the p-value according to the number of tests conducted (e.g., Bonferroni). I was wondering whether a similar approach needs to be employed for effect sizes, and if so which would be the best option.
The 8 conditions I am testing reflect the cells of my 2x2x2 within-subject design. The issue with the multiple comparison appears twice: 1. When conducting an ANOVA, I find a 3-way interaction and need to conduct post-hoc comparisons. I know how to adjust the p-values, but not the effect size estimate (indeed, I asked whether this is in principle possible at all); 2. When I want to test whether each of 8 conditions (2x2s2) is significantly different from zero. For both options I should then just adjust the CI, but not the estimates?