One of my websites is almost static in content and has a fairly constant stream of visitors, mainly from referring sites and the search engines. In the last months I have played around with some options to increase page load speed. I constantly monitored the page load speed mentioned in Google Webmaster Tools, and at the same time looked at the number of pages per visitor. The sample size of visitors we talk about is about 100,000 unique visitors per month, over a period of five months.
The optimizations I have done had no direct visible effect on the page layout. What I did was combining multiple images to one to reduce HTTP requests, push JavaScript to the bottom so scripts are not postponing rendering etc. I have reverted the changes on different occasions to be sure that the pages/visitor values were related to the page load speed, and not any other reasons like seasonable differences etc.
Over these five months I have seen a fairly consistent relation between the two. The faster the page loads, the more pages a visitor wants to view. My figures:
4.7 secs: 1.51 pages per visitor
3.0 secs: 1.56 pages per visitor
2.7 secs: 1.58 pages per visitor
Anyone else with statistics to share?