I have a bunch of variables organized into 10 different levels of a grouping factor. I'm doing some ANCOVA on particular variables and also plotting the data using boxplots. I'd like to add 84% confidence intervals to all the groups (since non-overlapping 84% CIs indicate a significant difference at alpha .05 - at least for two groups). I can do all this quite easily in R.
My question is - should I be applying a "family-wise" 84% CIs to all the groups? In other words, just as one would devalue an alpha level by the number of groups to obtain a family-wise alpha, should I inflate the CI a reciprocal amount to achieve a family-wise interval? This seems reasonable to me, but I haven't seen this discussed in the literature.
If alpha were CI were interchangeable for two or more groups the the family-wise 84% CI would be 99.5%, but i've read that alpha and CI are only interchangable for 1-sample situations. If this is the case, how would I go about calculating the family-wise confidence intervals for 10 (or any number) groups?
Any advice would be welcome.