Inference for Group Interaction Experiments

Working paper with Jiawei Fu and Cyrus Samii

Why this paper matters

Group interaction experiments—such as deliberation studies, classroom experiments, group therapy sessions, and lab coordination games—are widely used across political science, economics, psychology, and public health. Yet researchers often analyze these designs using off-the-shelf methods (individual-level regressions, cluster-robust standard errors, or simple difference-in-means) without clarity on what estimand these procedures recover or when they are valid. A central difficulty is that groups may be pre-existing or randomly formed, and outcomes may exhibit interference within groups—meaning a person’s outcome depends not only on their group’s treatment assignment but also on their group members’ identities and attributes. These features fall outside the settings covered by standard cluster inference, creating widespread confusion about whether researchers are estimating the ATE, a spillover-contaminated quantity, or something else. This paper fills that gap by providing a general, design-based, super-population framework that characterizes the correct estimand, variance estimation, and sampling distribution of the commonly used estimators, such as difference-in-means, under all relevant design × interference scenarios.

What the approach contributes

The paper shows that the same estimator can converge to different estimands depending on (1) whether groups are fixed or randomly formed, and (2) whether interference within groups is present. Under no interference, the estimator targets the usual ATE regardless of group formation. With interference and fixed groups, it converges to a Total Effect (TOT) that aggregates both direct and within-group spillover effects. With interference and random group formation, it converges instead to an Average Marginal Effect (AME)—an estimand that averages outcomes over all possible group compositions. We derive consistent variance estimators for each case, showing when cluster-robust estimators are valid and when individual-level heteroskedasticity-robust estimators suffice. We argue that clustering must be done at the level of potential-outcome input indices and establish central limit theorems using a novel coupling technique, enabling asymptotically valid hypothesis tests. Simulations confirm the theory, and a reanalysis of Mendelberg et al. (2013) and Iacovone et al. (2022) illustrates how the framework correctly interprets spillover-contaminated group interaction experiments. Together, the results provide the first unified blueprint for valid inference in group interaction experiments where interference and group formation are integral features rather than nuisances.