  Many previous causal inference studies require no interference, that is, the
potential outcomes of a unit do not depend on the treatments of other units.
However, this no-interference assumption becomes unreasonable when a unit
interacts with other units in the same group or cluster. In a motivating
application, a university in China admits students through two channels: the
college entrance exam (also known as Gaokao) and recommendation (often based on
Olympiads in various subjects). The university randomly assigns students to
dorms, each of which hosts four students. Students within the same dorm live
together and have extensive interactions. Therefore, it is likely that peer
effects exist and the no-interference assumption does not hold. It is important
to understand peer effects, because they give useful guidance for future
roommate assignment to improve the performance of students. We define peer
effects using potential outcomes. We then propose a randomization-based
inference framework to study peer effects with arbitrary numbers of peers and
peer types. Our inferential procedure does not assume any parametric model on
the outcome distribution. Our analysis gives useful practical guidance for
policy makers of the university in China.
