Diagnose and fix selection bias in experiments

Explain what selection bias is and identify it in the following setup: users may choose to see a discount banner (the treatment), and those who see it convert at a higher rate. (a) Give at least three plausible ways selection could operate and state the direction of bias each one creates. (b) Suggest two remedies that yield unbiased or less biased causal estimates—such as randomized encouragement, regression discontinuity based on a threshold for eligibility, front-door adjustment, or instrumental variables with an assignment instrument—and for each, list the required assumptions and how you would check them. (c) Give a small numeric example in which the naive treated-versus-untreated difference is biased, but a corrected approach recovers an unbiased or less biased estimate.

Overview: This item tests a data scientist's skill in causal inference and diagnosing selection bias, centered on recognizing plausible selection mechanisms in an opt-in discount-banner setup and knowing when observational comparisons between treated and untreated users are biased.