Statistical Fallacy & Survivorship Explorer Wald & Sanders Workshop

Hands-on empirical proof: why averages mislead bimodal cohorts, and why surviving samples deceive military armor design.

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″
The Average Human Fallacy: With an arithmetic mean of 60″, purchasing 20 size-60 uniforms leaves 0 students with a fitting uniform because nobody is average in a bimodal cohort.
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.
Abraham Wald's Breakthrough: "The bullets that bring down planes hit the engines. The ones we examine returned because they took hits where armor was least critical."
Enjoy this tool? Build your own with Super