Skip to the tool

🎭 The Illusion Gallery

Hall of Statistical Traps · Catalogue 05
Exhibit A · Survivorship bias — the planes that never came back

Armour the planes that returned

WW2, statistician Abraham Wald. Engineers counted bullet holes on the bombers that made it home and proposed armouring exactly where the holes were. Wald said: armour the places with the fewest holes — because planes hit there never came back to be counted. Run the sorties and watch the gallery lie to you.

0 planes have come home. Every plane in the gallery is a survivor.
Exhibit B · Simpson's paradox — the treatment that wins by losing

The kidney-stone study (real data, 1986)

Two treatments for kidney stones. Treatment B has a better overall success rate — and is worse in every single type of case. Both are true at once. Toggle the view and watch the winner flip. This is not a trick of rounding; it is arithmetic.

Why it happens. Treatment B was given mostly to the easy cases (small stones), so its good overall average just reflects an easier patient mix. When you compare like-for-like — small with small, large with large — A wins both. Whenever you see "our patients did better than theirs," ask: were the patients actually the same?
Exhibit C · Regression to the mean — the curse of the hot streak

Champions get worse. Mathematically.

Every sport has a "Sports Illustrated curse": great first halves are followed by disappointing ones. It isn't a curse, and it isn't pressure. It's arithmetic — any extreme result is part skill, part luck, and the luck doesn't repeat. Run the season:

The lesson. Judge the process, not the streak. The player whose first half was a fluke "crashes" back toward their true ability — the player whose second half regressed may have been the better one all along. Bookies, coaches and hospitals that forget this make real money and real mistakes.

Kidney-stone data: Charig, Webb, Payne & Wickham, British Medical Journal 1986. The plane story is the standard account of Abraham Wald's work at the Statistical Research Group 1943. Simulation mechanics on this page are intentionally simple so the arithmetic is visible — no black box.

More in Museum & Collection

💎 The Mohs Gallery Friedrich Mohs, 1812: a mineral of higher number scratches one of lower number. The steps are not equal — corundum to…
🏗️ The Stress Gallery Apply loads to a beam and watch stress propagate in real time. See shear force and bending moment diagrams update live…
🐫 Ancient Egypt Quiz Test your knowledge of ancient Egypt — pharaohs, pyramids, gods and everyday life — in ten-question rounds with streaks.
🏛️ The Orders Bench Vitruvius counted in modules: the lower diameter of the column. Doric is stocky, Corinthian tall and leafy, Ionic the…
🧠 The Bayes Workshop Conditional probability you can feel: what a positive test really means (Bayes' theorem), a 300-game Monty Hall…
👑 British Monarchs Quiz Name the kings and queens of England, Scotland and the UK from 1066 to today — ten questions per round with streaks.
🏛️ Deep Time Museum Walk 4.6 billion years of Earth's story in one scroll — Hadean to Holocene, an era per hall, with an Earth-in-one-day…
🛡️ The Blazon Workshop A teaching coat, not a grant. Choose a field, an ordinary and a charge. The plaque writes the blazon in the old…

All 29 tools in Museum & Collection →