Models, methods and network topology: Experimental design for the study of interference

How should a network experiment be designed to achieve high statistical power? Experimental 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, Bowers 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 experimental 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 example in which statistical power depends on the extent to which the network degree of nodes is correlated with treatment assignment probability. We recommend that researchers think carefully about the underlying treatment propagation model motivating their study in designing an experiment on a network.