Interactive Causal Inference Lab

20,000 synthetic accounts; half are at risk. Without a call, 80% of healthy and 40% of at-risk accounts renew; a call adds 8 percentage points in both segments. The slider sets how strongly calls depend on the segment: at 0% every account has a 50% chance of a call, at 100% it is 90% for at-risk and 10% for healthy accounts. The adjusted figure is the within-segment difference averaged over the two segments by size. Each account keeps the same random draws at every slider position, and the data is fixed by a seed, so the same settings always give the same numbers.

50,000 synthetic customers with a prior propensity score; the chance of buying without the campaign is a logistic function of it. The campaign adds the chosen lift to every customer’s purchase probability. The randomised test assigns the campaign by coin flip. The observational version sends it with a probability that rises with prior propensity; the slider sets how steeply. The interval is a normal-approximation 95% interval for a difference of two proportions. The adjusted estimate compares recipients and non-recipients within ten equal-sized propensity bands and averages by band size, skipping any band with fewer than 30 customers on either side. Fixed seed: the same settings always give the same numbers.

40,000 synthetic customers with two observed features, usage decline and past response to offers. Churn risk without the offer rises with usage decline. The offer’s effect grows with past response; with the box ticked it is largest at middling risk and smaller at the extremes, and unticked it grows with risk. Customers with little past response become slightly more likely to churn when contacted. 20,000 customers form a randomised pilot (offer by coin flip); in a 5 × 5 grid of segments the churn score is the churn rate without the offer and the uplift score is that rate minus the churn rate with the offer. The other 20,000 are ranked by each score, ties in simulation order. Extra customers retained counts customers who churn without the offer and stay with it, minus those who do the reverse; the simulation holds both outcomes for every customer. Fixed seed.

Two synthetic regions, 36 weeks of orders, launch in one region after week 24. Both share a trend of +0.5 orders a week and independent week-to-week noise (standard deviation 3). The launch adds a constant number of orders a week. The extra trend applies to the launch region from week 1. Difference-in-differences is the change in the launch region’s mean (weeks 25–36 minus weeks 1–24) minus the same change in the comparison region. The placebo applies the same calculation to weeks 13–24 against weeks 1–12. The gap trend is the least-squares slope of the difference between the regions over weeks 1–24. The dashed line is the comparison region shifted by the average pre-launch gap. Fixed seed.

10,000 synthetic customers, 40% at risk. Without the offer 35% of at-risk and 80% of other customers renew; the offer adds 25 and 5 percentage points. 15% of other customers get the offer; the slider sets the share of at-risk customers who do. Every customer has both outcomes fixed in advance, and the offer never turns a renewal into a loss. Seeing is the difference in observed renewal rates. Doing is the difference between everyone’s outcome with the offer and without it; the estimate from the data is the within-group difference averaged over the two groups by size. Imagining counts offered customers who renewed and would not have without the offer; the estimate from the data uses, within each group, the ratio of renewal rates without and with the offer, which is valid only because the offer never hurts. Fixed seed.