Two banana vendors. On Monday, Ana sells a higher fraction of her stock than Bo. On Tuesday, Ana again beats Bo. So Ana is the better seller… except when you add both days together, Bo wins. This isn’t a trick of arithmetic gone wrong — it’s real, it’s called Simpson’s paradox, and it has flipped conclusions in medicine and hiring lawsuits. The culprit is a hidden variable: how much stock each had each day. Toggle between the days and the total.
Simpson’s paradox: a trend that holds in every subgroup can REVERSE when the groups are combined. Classic figures — group 1: Ana 81/87 (93%) vs Bo 234/270 (87%); group 2: Ana 192/263 (73%) vs Bo 55/80 (69%). Ana wins BOTH, yet pooled Ana is 273/350 (78%) vs Bo 289/350 (83%) — Bo wins. The reversal comes from a confounding variable (the group sizes / base rates) correlated with both the grouping and the outcome. It is why aggregated data can mislead and why you must ask what was held constant. A fail-loud self-check throws unless Ana leads in both groups yet loses the pooled total. ◆ real statistics, node-verified.
The numbers are the standard textbook (Berkeley-style) reversal; the point is structural — whether to trust the pooled or the split answer depends on the causal story (is the confounder a cause or a mediator?), which the data alone can’t settle.