  Randomization (a.k.a. permutation) inference is typically interpreted as
testing Fisher's "sharp" null hypothesis that all effects are exactly zero.
This hypothesis is often criticized as uninteresting and implausible. We show,
however, that many randomization tests are also valid for a "bounded" null
hypothesis under which effects are all negative (or positive) for all units but
otherwise heterogeneous. The bounded null is closely related to important
concepts such as monotonicity and Pareto efficiency. Inverting tests of this
hypothesis yields confidence intervals for the maximum (or minimum) individual
treatment effect. We then extend randomization tests to infer other quantiles
of individual effects, which can be used to infer the proportion of units with
effects larger (or smaller) than any threshold. The proposed confidence
intervals for all quantiles of individual effects are simultaneously valid, in
the sense that no correction due to multiple analyses is needed. In sum, we
provide a broader justification for Fisher randomization tests, and develop
exact nonparametric inference for quantiles of heterogeneous individual
effects. We illustrate our methods with simulations and applications, where we
find that Stephenson rank statistics often provide the most informative
results.
