> long suspected that google would rank sites with Adsense higher than a website without
Google says that they don't do that. I don't believe Google based on personal experience and it's interesting to see that you had some experimental confirmation.
It is definitely hard to compare one site ranking vs another and definitively conclude that AdSense made one rank higher than just Analytics, but in every case AdSense+Analytics sites correlated with a better ranking/.
All of the cases were sites that were doing SEO (on- and off-site). There were lots of differences between them, so never an apples to apples, but Analytics + AdSense > AdSense only > Analytics only.
It was very compelling results. Never did a GA ONLY site improve better than an AS only or an AS + GA.
Google says that they don't do that. I don't believe Google based on personal experience and it's interesting to see that you had some experimental confirmation.