Facebook Insights has some interesting and somewhat useful information. It gives you analytics on your posts, likes, people talking about this and your total reach. Social media analytics can be very difficult to quantify by itself. Run alongside a separate campaign you could use this research tool more effectively.
For example, if you were running a non digital campaign to get people to like your facebook page you could test different methods and compare them to the amount of likes that you received in a given period.
Total reach can be some interesting data. This shows how many people saw your business or page in a given period of time. So if you posted and people saw it or people reposted you or tagged you, things of this nature.