I researched Google's algorithm a while back and a a fairly strong ranking factor IS how long they spend on your page/site (whether you have GA or not) but that can backfire. (I know that Google's exact algorithm is unknown but it's based on experiments by SEO sites)
Here's how I understood it to work:
If a user finds you on a Google search and then clicks the link, Google times how long it takes for you to come back to the search results. So if you immediately backed out of the page they would take that as meaning the result was crap and they took that into account in their algorithm. The thinking being that it was an irrelevant result.
However, that counts against sites that provide the answer you want right at the top of the page so that when you open the page, the answer is staring you in the face... so obviously you are going to back out again as you have your answer.
This was from around two years ago when I was researching building an indexer and search engine for kicks so my memory of how it worked is fuzzy.
Also, it may have changed.