Bayes' Theorem — Positive Predictive Value
Slide prevalence, sensitivity, and specificity to see the positive predictive value jump around. A hands-on look at why false positives matter so much in screening tests.
P.05 / BAYES THEOREM
Bayes' Theorem
Distribution toolbox complete. Finally, Bayes' theorem flips the conditioning. You test positive — what's the chance you're actually sick? Intuition fails here; let's build it.
"The test has 99% sensitivity & 95% specificity, and you tested positive" — is there a 99% chance you're sick?
…Answer: only 16.7%. More than half of doctors get this classic quiz wrong.
The trick is that we forget how rare the disease actually is in the first place.
Play with the three sliders below and watch the "town of 1,000" — you'll see why.
Lower = rare disease. Drag right for "common disease".
Of 100 sick people, how many does the test flag as positive?
Of 100 healthy people, how many does the test correctly clear? The rest become false positives.
If you tested +, chance you're sick—
If you tested NEG, chance you're healthy—
True positives (sick & tested +)—
False positives (healthy but tested +)—