Statistical Fallacy & Survivorship Explorer

1. Sanders Uniform Sizing Paradox

10 students at 4′ (48″) & 10 students at 6′ (72″). Mean height is 5′ (60″).

20 Students

Calculated Mean Height

60″ (5′0″)

Uniforms Fitting Zero Students

20 / 20 (100%)

Group A (Short Cohort): 10 students @ 48″ (4′0″)

Group B (Tall Cohort): 10 students @ 72″ (6′0″)

Ordered Uniform Size: 60″ (Tailored to Mean) Tolerance: ±2″

2. Abraham Wald Bomber Survivorship Workbench

Returning planes show flak damage everywhere except the engines. Where do we reinforce?

Sorties: 400

Observed Hits on Returning Planes

91.8% Fuselage/Wings

Optimal Armor Recommendation

Engine & Fuel

Bullet hole (Returned)

Engine/Cockpit (Fatal if hit)

Armor Recommended Target

Simulated Fleet Survival Rate: 94.5%

When armoring the Engine & Fuel System (Wald's insight), planes hit in vulnerable spots survive. If the military mistakenly armored the heavily hit fuselage, survival drops to 68.0% because missing planes never returned to be counted.

Averages and the observations you never see

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Read the explanation

The uniform example starts with ten students assigned a height of forty eight inches and ten assigned seventy two inches. Add the heights and divide by twenty: the mean is sixty inches. That is a correct mean, but none of these students has that height. The blue and amber bars use six pixels per inch, so forty eight inches is two hundred eighty eight pixels and seventy two inches is four hundred thirty two pixels. The third bar marks sixty inches at three hundred sixty pixels using exactly the same scale. A mean summarizes a distribution; it does not promise that any person is equal to the mean. The tool is an illustrative two height cohort, not real clothing measurement data. The page defines a uniform as fitting when its assigned size differs from a student height by at most two inches. At a sixty inch target, both groups differ by twelve inches. All twenty uniforms fail the rule. Move the target to forty eight inches: ten short students fit, and ten tall students do not. Now increase only the short group to twenty. The mean becomes fifty six inches, because twenty times forty eight plus ten times seventy two, divided by thirty, is fifty six. Keep the target at forty eight. Twenty of thirty fit, and ten of thirty fail: one third, about thirty three point three three percent. These count bars use ten pixels per student, so increasing the short group from ten to twenty doubles its bar length while the tall group stays at ten. The fitting result depends on the full groups and the selected rule, rather than the mean alone. The second panel illustrates survivorship bias. You observe damage on aircraft that returned. Returning is a selection condition. If damage to one location prevents return, that location can be missing from the observations even when it is important. Counted hits are therefore not automatically a map of where protection matters most. This page makes the distinction visible with selectable armor and added marks. Its displayed ninety four point five and sixty eight percent survival rates are fixed values chosen by the source code for the two modes. They are not computed from the hits, not a measured historical dataset, and not a reliable engineering prediction. The added hit and sortie counters are part of the illustration. Use all the controls, export the complete JSON and CSV, and inspect which numbers are cohort calculations and which values are assigned assumptions. Ask who is missing from your sample before drawing a conclusion from the observations that survived.