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Inverse Probability Weighting by Hand
A retention email was sent by a rule-based system, more often to high-value customers. Data by customer value tier:
| Tier | Emailed: n, repurchase rate | Not emailed: n, repurchase rate |
|---|---|---|
| High | 600, 40% | 400, 34% |
| Low | 200, 16% | 800, 12% |
- Compute the naive difference in repurchase rate between emailed and non-emailed customers.
- Compute the propensity score for each tier and the IPW estimate of the average treatment effect. Compare with the stratum-specific effects.
- What assumption makes the IPW estimate causal, and what would you check about the propensity scores before trusting it?
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