To follow from Jim's detailed response -- the issue of interpreting 'overlap' in CI's in terms of 'significance' (in the statistical sense), is illustrated by means of a simple numerical example in the following:

viewtopic.php?f=1&t=3987&p=13190&hilit=overlapping#p13189As Jim suggests, its important to realize that the approach you take would depend largely on whether you're trying to compare difference between groups in a single analysis (Jim's first suggestion using a offset-intercept design matrix), or if you have two separate estimates from two separate analyses, where the CONTRAST approach might work for you.

More 'conceptually', it might also be worth considering the important distinction between 'statistical' significance and 'biological' significance. One of the important ideas the Burnham & Anderson tomes reminded everyone of was the idea that statistical significance at some nominal alpha level can be (and often is) fairly arbitrary (why is alpha=0.05 any better than, say, alpha=0.025, or 0.1?). Rather, an alternative (and IMO, often better) approach is to specify a priori how big a difference at minimum you think is 'biologically' important, and why, and then use the statistical tools to determine if the differences between groups (as in your example, say) is bigger than your designated minimum critical (important) difference, and if based on the CI for that difference, does it bound this minimum threshold? This concept is discussed in some detail in the MARK book - chapter, 6, section 6.13:

http://www.phidot.org/software/mark/doc ... ap6.pdf#68Of course, if the issue at hand is 'difference between psi estimates', the challenge might be to determine what a 'biological significant difference' might be.