Very simply, the entire stats engine that powers WordPress.com is Google Analytics. The stats you get in Dashboard | Blog Stats are the number crunched by GA. Don’t believe? When you visit your blog next time, pay attention to the browser Status Bar and you may see ‘www.GoogleAnalytics.com’ load. I’ve seen it numerous times but sometimes it doesn’t show.
By the way – please consider linking your user name to your blog as explained in the sticky at the top of the forum:
Go into your dashboard -> users -> your profile -> then scroll down to ‘contact info’. In the spot where it says ‘website’ fill in the address of your blog and save the changes.
Now… when you comment here and on other blogs, your name will link to your blog. If you do this before you post your request for help, it will allow forum volunteers to be able to help you quicker since they won’t have to ask you for a link and wait until you come back to post one.
So, if you want to have full control (in this case Google Analytics) you need to install WordPress on your own (or rented) server. Such as GoDaddy, or whatever. And e.g. use a Google Analytics plugin to easily(?) get GA stats for your blog. Right?