Can a 16-year old move from her parent’s home without being forced to go back?

Why do you need to move? Are you being abused? If so you need to call please the police and tell your teachers at school ASAP.  If you are doing it because you just don't want to follow the rules, you may not realize the legal consequences.  The "age of majority" is 18; this is the age when you legally become an adult.  until then you are a "minor" and subject to your parents authority and control (but not abuse).  Therefore you can't simply move out, run away, etc.

The only method a minor can live on their is when they are legally "emanicipated" by the court.  A minor can become emancipated before their 18th birthday if several ways; it varies from state-to-state.  Some common ways are they: join the military, get married, or obtain a court order granting emancipation.  With respect to emancipation, in order to successfully petition the court a minor would have to show, among other things that, they have a safe place to stay, they can financially provide for themselves, and they are stable and mature enough to handle the responsibilities of adulthood.  However, courts do not routinely grant emancipation. 

At this point you need to speak with a responsible adult (minister, teacher, aunt, etc) and go over your reasons for wanting to leave. From there, possibly they can help you find out exactly what the requirements are to become emancipated in your state.