All simulators
Balancing on the Propensity Score
Stratify on the estimated score: covariate imbalance vanishes within strata and the bias with it.
Day 43: The Propensity Score Theoremnaive difference
3.85
stratified estimate
2.10
truth
2.00
Strata are equal-size groups of the estimated (logit) propensity score. With K = 1 there is no adjustment; about five strata remove most of the bias (Cochran's 90% rule of thumb).
ageincome±0.1 balance threshold
A health programme targeted at older, lower-income adults. Balancing theorem: within groups of similar propensity score, treated and untreated have the same covariate distribution. Bars show normalised differences — huge overall, small within strata. True effect +2.