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.
