Models, Methods and Network Topology: Experimental Design for the Study   of Interference
  How should a network experiment be designed to achieve high statistical power? Ex- perimental treatments on networks may spread. Randomizing assignment of treatment to nodes enhances learning about the counterfactual causal effects of a social network experiment and also requires new methodology (ex. Aronow and Samii 2017a; Bow- ers et al. 2013; Toulis and Kao 2013). In this paper we show that the way in which a treatment propagates across a social network affects the statistical power of an ex- perimental design. As such, prior information regarding treatment propagation should be incorporated into the experimental design. Our findings justify reconsideration of standard practice in circumstances where units are presumed to be independent even in simple experiments: information about treatment effects is not maximized when we assign half the units to treatment and half to control. We also present an exam- ple in which statistical power depends on the extent to which the network degree of nodes is correlated with treatment assignment probability. We recommend that re- searchers think carefully about the underlying treatment propagation model motivat- ing their study in designing an experiment on a network. 
Jake Bowers, Bruce A. Desmarais, Mark Frederickson, Nahomi Ichino,   Hsuan-Wei Lee, Simi Wang
stat.ME