THE FOLD / CHEAT / THE ROOT KIT / THE SIMPSON PARADOX
THE SIMPSON PARADOX
a treatment that wins twice and loses once
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Simpson’s paradox is the aggregation trap: a trend that holds in every subgroup can reverse when the groups are merged. The canonical real case is the 1986 kidney-stone study: Treatment A beats Treatment B on small stones (81/87 = 93% vs 234/270 = 87%) and on large stones (192/263 = 73% vs 55/80 = 69%) — yet in the combined table B appears to win, 289/350 = 83% against A’s 273/350 = 78%. No arithmetic error anywhere: A was simply assigned the harder cases, and the case-mix — a lurking variable — flips the headline. The paradox is why ‘adjusting for confounders’ is not statistical pedantry but the difference between a true claim and its opposite.
LIT verified live with exact integer cross-products — no floating point: A wins the small-stone comparison, A wins the large-stone comparison, and B wins the aggregate (window.__simpsonparadox). FIG no framing; the data are the published counts (Charig et al. 1986), credited as content, and every comparison is exact.
LIT verified live with exact integer cross-products — no floating point: A wins the small-stone comparison, A wins the large-stone comparison, and B wins the aggregate (window.__simpsonparadox). FIG no framing; the data are the published counts (Charig et al. 1986), credited as content, and every comparison is exact.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-root-kit — the cheat: the aggregate table is compromised at a level the surface numbers cannot see; the lurking variable is the rootkit. AVAN (AI) built the instrument: the exact subgroup and aggregate comparisons, integer arithmetic only.
Credit as content: E. H. Simpson (1951); Charig, Webb, Payne & Wickham (1986, the kidney-stone data). The weave: David names the hidden compromise; I confirm both subgroup wins and the aggregate reversal, exactly.
Credit as content: E. H. Simpson (1951); Charig, Webb, Payne & Wickham (1986, the kidney-stone data). The weave: David names the hidden compromise; I confirm both subgroup wins and the aggregate reversal, exactly.
3 ONE DIMENSION
The four success rates as bars — A above B in both panels, below B in the merged one.
4 TWO DIMENSIONS · INTERACTIVE
Walk the three comparisons; each is settled by exact integer cross-multiplication.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the subgroup truth — A wins twice.
AVAN’s addition (the inverse-companion): don’t read the merged table — ask who got the hard cases. The inverse of ‘B wins overall’ is ‘A won everywhere it fought, and fought where it was hardest’. Magenta is the aggregate reversal; green are the two subgroup wins it erases. The sum can contradict every one of its parts.
LIT Genuine Simpson's paradox on the published kidney-stone data (E. H. Simpson 1951; Charig, Webb, Payne & Wickham 1986, credited as content). Verified live with exact integer cross-products: A wins small stones (81·270 > 234·87), A wins large stones (192·80 > 55·263), yet B wins the aggregate (289/350 > 273/350) (window.__simpsonparadox.ok).
FIG No framing; the data are the published counts and every comparison is exact. The AVAN inverse is honest — don't read the merged table, ask who got the hard cases: the inverse of 'B wins overall' is 'A won everywhere it fought, and fought where it was hardest'. Magenta is the aggregate reversal; green are the two subgroup wins it erases. The sum can contradict every one of its parts.
FIG No framing; the data are the published counts and every comparison is exact. The AVAN inverse is honest — don't read the merged table, ask who got the hard cases: the inverse of 'B wins overall' is 'A won everywhere it fought, and fought where it was hardest'. Magenta is the aggregate reversal; green are the two subgroup wins it erases. The sum can contradict every one of its parts.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE ROOT KIT · David Lee Wise (ROOT0), with AVAN