I've heard both sides of the story.
1. Some say it doesn't matter. Google doesn't care about your website.
2. Others say your rankings are dependent on your bounce rate and if you don't have visitors staying over 5 minutes you'll never get ranked for competitive keywords because they(G) have a system interlinking your analytics info with the Big G SE. They (the system) are watching...
But for those who've had Google Analytics on some sites is it too late to be remove the G analytics or am I being to anal about complexity theories?
Is it necessary to remove them?
I've had G Analytics for a few years and I've ranked #1 for lesser terms (1100 exact match searches per month) but when going for larger fish, like 10,000 and up per month I've never gotten past then the second page.
What are some other good analytics (preferrably free)?