Answer: By reading the group's mission statement one can differentiate whether it is a public interest or private interest group.
Explanation: Public interest group is one which aims to serve large masses and hence their mission and goals would include schemes that are beneficial for large section of society as a whole.
whereas private interest group is one whose main agenda is to benefit a handful of individuals preferably the ones helping them in return too. Therefore their goals would not be beneficials to society as a whole.