Exact P-values for Network Interference

Abstract

We study the calculation of exact p-values for a large class o f non- sharp null hypotheses about treatment effects in a setting wi th data from experiments involving members of a single connected ne twork. The class includes null hypotheses that limit the effect of on e unit’s treatment status on another according to the distance betwe en units; for example, the hypothesis might specify that the treatmen t status of immediate neighbors has no effect, or that units more than two edges away have no effect. We also consider hypotheses concerning t he valid- ity of sparsification of a network (for example based on the st rength of ties) and hypotheses restricting heterogeneity in peer effe cts (so that, for example, only the number or fraction treated among neigh boring units matters). Our general approach is to define an artificia l experi- ment, such that the null hypothesis that was not sharp for the original experiment is sharp for the artificial experiment, and such t hat the randomization analysis for the artificial experiment is val idated by the design of the original experiment.