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Fisherian randomization inference is often dismissed as testing anuninteresting and implausible hypothesis: the sharp null of no effectswhatsoever. We show that this view is overly narrow. Many randomization testsare also valid under a more general "bounded" null hypothesis under which alleffects are weakly negative (or positive), thus accommodating heterogenouseffects. By inverting such tests we can form one-sided confidence intervals forthe maximum (or minimum) effect. These properties hold for alleffect-increasing test statistics, which include both common statistics such asthe mean difference and uncommon ones such as Stephenson rank statistics. Thelatter's sensitivity to extreme effects permits detection of positive effectseven when the average effect is negative. We argue that bounded nulls are oftenof substantive or theoretical interest, and illustrate with two applications:testing monotonicity in an IV analysis and inferring effect sizes in a smallrandomized experiment.

Beyond the Sharp Null: Randomization Inference, Bounded Null Hypotheses, and Confidence Intervals for Maximum Effects