Bayes' Theorem and the Medical Test You Probably Misunderstand
You test positive for a rare disease. The test is 99% accurate. How worried should you be? In many real scenarios, the answer is: not very. Here is the exact math.
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You test positive for a rare disease. The test is 99% accurate. How worried should you be? In many real scenarios, the answer is: not very. Here is the exact math.
Expected value is the average outcome of a random process over many repetitions. It is arguably the single most useful concept in decision-making under uncertainty.
A 95% confidence interval does not mean a 95% chance the true value lies inside it. This subtle distinction matters enormously — and almost everyone gets it wrong.
The 0.05 significance threshold has governed scientific publishing for 80 years. It was never meant for that purpose — and the resulting crisis is reshaping statistics.
Francis Galton discovered it in pea plants. It explains why the Sports Illustrated cover curse is real, why bad students improve after punishment, and why no hot streak lasts.