There was in interesting psychological study done by researchers at Purdue regarding sports performance, including a specific experiment in putting performance with targets of different perceived sizes. More detailed info is found at http://pss.sagepub.com/content/23/4/397 but here's a short version.
An experiment was set up where test subjects putted at a golf hole, but an overhead projector was used to make the hole appear larger than it actually was. Putting performance was improved with the subjects perceiving that the size of the hole was larger than it actually was. The researchers hypothesize that the reason is that the subject has more confidence with a larger hole, and were more relaxed and focused on making a good putt rather than worrying about how small the hole is.
Another thing discussed in their study is the concept of "quiet eyes", where it has been shown in multiple sports that keeping ones eye focused on the target and not moving it around much has improved performance; this is seen in basketball free throw shooting, putting, etc. One of the things that Dave Stockton talks about in his putting instruction is to keep your eyes focused on the target and line and not be looking all over the place; he doesn't refer to the quiet eye concept, but he's essentially saying the same thing.
I've been following Stockton's advice for a few month and have found my putting has noticeably improved. I think I'll start experimenting with visualizing a larger hole next and see what that does.