While Facebook insights provide demographic details and interactions on the fan pages but are still limited as compared to Google Analytics. Yes, you can set up Google Analytics for your facebook fan page and get all the details that a analytics account provides you.
Here is how you need to do it:
You need to include include Google Analytics as an image instead of setting the standard Javascript in your code. This method tracks every visitor to the custom facebook pages on Google Analytics. It requires a combination of server side cookie management and an additional <img> tag to the bottom of the facebook fan page. Here are the steps to get Google Analytics working on your facebook fan page.
1) Setup Google Analytics account. If you already have one, create a new website profile. You can name it facebook.com or facebook.com/your_page_name. You will finally get your tracking code which looks like this UA-3123123-2
3) Add the entire custom image html tag from step 2 to the bottom of each Facebook fan page that you need to track.
That is all you need to do! Google Analytics is not real-time, so you will need to give it some time…approximately a day.
Via – Webdigi

July 28, 2010 at 8:58 pm
I never knew the fact the google analytics would be available for face book as well. This upholds my perception of facebook being an incredible marketing tool, apart from all its socializing.