If I can be claimed as a dependent, should I still file my taxes myself?

I graduated college in May 2016. My parents paid for all of my college expenses.

I started living alone in August, made $16,000 or so.

When filing my taxes I noticed that my federal refund drops about 2,000 when I check the box, "can anyone claim you as a dependent".

How should I file my taxes when my refund gets close to nothing since I can be claimed as a dependent? Would it give me a bigger refund if my parents actually do claim me?