  Randomization inference (RI) is typically interpreted as testing Fisher's
"sharp" null hypothesis that all unit-level effects are exactly zero. This
hypothesis is often criticized as restrictive and implausible, making its
rejection scientifically uninteresting. We show, however, that many
randomization tests are also valid for a "bounded" null hypothesis under which
the unit-level effects are all non-positive (or all non-negative) but are
otherwise heterogeneous. In addition to being more plausible a priori, bounded
nulls are closely related to substantively important concepts such as
monotonicity and Pareto efficiency. Reinterpreting RI in this way also
dramatically expands the range of inferences possible in this framework. We
show that exact confidence intervals for the maximum (or minimum) unit-level
effect can be obtained by inverting tests for a sequence of bounded nulls. We
also generalize RI to cover inference for quantiles of the individual effect
distribution as well as for the proportion of individual effects larger (or
smaller) than a given threshold. The proposed confidence intervals for all
effect quantiles are simultaneously valid, in the sense that no correction for
multiple analyses is required, and are thus a "free lunch" added to
conventional RI. In sum, our reinterpretation and generalization provide a
broader justification for randomization tests and a basis for exact
nonparametric inference for effect quantiles. We illustrate our methods with
simulations and applications, finding that Stephenson rank statistics can
provide more informative results than the more common Wilcoxon rank or
difference-in-means statistics. We also provide an R package RIQITE
implementing the proposed approach.
