A/B Test Design for a New Group Call Feature with Network Effects

You are designing an experiment for a Group Call feature where social network effects and interference are expected. Assume a social graph between users, and that the feature is delivered at the user level but can be constrained by design. Address the following:

(a) Define exposure and the estimand(s):

• Clearly define user exposure under interference (e.g., own treatment plus share of treated neighbors).
• Specify the primary estimand: intent-to-treat (ITT) at the cluster level vs a per-user average treatment effect (ATE) under interference. Be explicit about the population and exposure mapping.

(b) Construct clusters from the social graph:

• Describe how to build edge weights for "strong ties" (which signals to include and how to combine them).
• Propose a clustering rule (e.g., threshold strong ties then take connected components, or community detection) that yields disjoint clusters of reasonable size.
• Explain how you will prevent cluster overlap and cap cluster size.

(c) Randomize at the cluster level and handle cross-cluster edges:

• Describe the randomization scheme (stratification, balance criteria).
• Define "frontier" users (those with cross-cluster edges) and how you’ll mitigate contamination (e.g., holdout buffers, gating cross-cluster invitations, or partial saturation). Clarify analysis vs exclusion rules for frontier users.

(d) Choose metrics:

• Pick one primary metric and two guardrail metrics.
• Critically assess "time spent per user per day" as a success metric (pros, cons, manipulation risks).
• Propose at least one viable alternative primary metric with a rationale.

(e) Compute design effect (DE) and sample-size inflation for cluster randomization:

• Given average cluster size m = 20 and intracluster correlation ICC = 0.05, compute DE.
• Recompute DE if m doubles but ICC halves.
• Explain implications for required sample size.

(f) Bias from ignoring network effects:

• If you randomize by user and ignore interference, under what conditions is the naïve difference-in-means biased downward vs upward?
• Provide intuition for positive vs negative spillovers and one real-world example for each direction.