The association that reverses
One dataset. Two ways of grouping it. Two apparently contradictory answers.
The comparison that reverses
Explore published counts for two kidney-stone treatment methods from a historical nonrandomized comparison. The outcome is recorded treatment success; the grouping variable is stone size. The data come from Charig and colleagues' 1986 report and later analyses.
Open surgery success78.0%
Percutaneous procedure success82.6%
Higher observed ratePercutaneous
Complete numerical data, for comparison and accessibility
| Stone size | Open surgery (A) | Percutaneous (B) |
|---|---|---|
| Smaller than 2 cm | 81 / 87 (93.1%) | 234 / 270 (86.7%) |
| At least 2 cm | 192 / 263 (73.0%) | 55 / 80 (68.8%) |
| Both sizes | 273 / 350 (78.0%) | 289 / 350 (82.6%) |
Important: These are historical, observational outcomes from different time periods, not randomized causal effects. Reversal of observed success proportions does not establish which treatment should be chosen for a patient. Harvard Statistics discussion and primary-study citation · Review article.