🔍 Built on BFP (2013): What Was Known

Bowers, Fredrickson, and Panagopoulos (2013, Reasoning about interference between units: A general framework, Political Analysis 21(1):97–124; henceforth BFP) demonstrated that Fisher's randomization-based hypothesis testing framework can be used to assess counterfactual causal models of treatment propagation and spillover across social networks. That framework framed sharp null hypotheses about interference and used randomization inference to evaluate them.

🧪 How the Test Was Improved

This research note introduces two modest but practical changes that increase statistical power for testing interference models while staying within BFP's framework:

• Replace the original Kolmogorov–Smirnov–style test statistic with a test statistic based on a sum of squared residuals (SSR).
• Incorporate information about the fixed network structure into the simple Kolmogorov–Smirnov test statistic (following Hollander 1999, section 5.4) that BFP originally used.

📊 What This Achieves

• Improved statistical inference for the kinds of counterfactual causal models of treatment propagation and spillover considered by BFP.
• A straightforward, implementable alternative statistic (SSR) that draws on residual variation to gain power.
• A way to make the simple KS-based approach more informative by explicitly using the known network topology.

⚖️ Scope and Limits

This note offers an incremental improvement to the application of BFP's "reasoning about interference" approach rather than a general theory of test statistics. It does not provide general results about optimal test statistics for multi-parameter causal models on social networks. The modifications are presented to encourage further, deeper work on test statistics and sharp hypothesis testing in settings with interference.