  In this paper, we address the fundamental statistical question: how can you
assess the power of an A/B test when the units in the study are exposed to
interference? This question is germane to many scientific and industrial
practitioners that rely on A/B testing in environments where control over
interference is limited. We begin by proving that interference has a measurable
effect on its sensitivity, or power. We quantify the power of an A/B test of
equality of means as a function of the number of exposed individuals under any
interference mechanism. We further derive a central limit theorem for the
number of exposed individuals under a simple Bernoulli switching interference
mechanism. Based on these results, we develop a strategy to estimate the power
of an A/B test when actors experience interference according to an observed
network model. We demonstrate how to leverage this theory to estimate the power
of an A/B test on units sharing any network relationship, and highlight the
utility of our method on two applications - a Facebook friendship network as
well as a large Twitter follower network. These results yield, for the first
time, the capacity to understand how to design an A/B test to detect, with a
specified confidence, a fixed measurable treatment effect when the A/B test is
conducted under interference driven by networks.
