  Many causal questions involve interactions between units, also known as
interference, for example between individuals in households, students in
schools, or firms in markets. In this paper, we formalize the concept of a
conditioning mechanism, which provides a framework for constructing valid and
powerful randomization tests under general forms of interference. We describe
our framework in the context of two-stage randomized designs and apply our
approach to a randomized evaluation of an intervention targeting student
absenteeism in the School District of Philadelphia. We show improvements over
existing methods in terms of computational and statistical power.
