Effect size - is correction for multiple comparison needed? 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?

What people typically refer to as 'the effect size' for some data is a point estimate.  Just as you can get a point estimate of a regression slope and a confidence interval around that, you can get an interval estimate for an effect size.  For example, from the data for a t-test, you can compute a standardized mean difference, and you can get a 95% CI around it.
If you have multiple comparisons, there are several ways you can think about the individual comparisons within the set.  You can treat them individually, or you might be concerned about the probability of Type I errors within the set as a whole (or some gradation in between).  If the latter were your situation, you might use something like a Bonferroni correction.  This could be done to alpha, your threshold for significance, or you could do it to the p-value itself.  You can also use the adjusted thresholds to compute a Bonferroni-adjusted 95% CI.
If you are computing interval estimates for multiple effect sizes, and you are worried about the potential for multiplicity to influence the larger picture, you can make exactly the same kind of Bonferroni-adjusted 95% CI for the effect sizes.  For instance, if you had 2 effect sizes, a 97.5% (1-.05/2) CI would be the Bonferroni-adjusted 95% CI.
