Bayes Theorem can help well informed patients too. They just need to
know how good their doctors are!
1. After reading the NYT you know that 1/3 of the time your doctor is
going to tell you that you have better than a 90% chance of breast
cancer if you have a positive mammogram.
2. After reading the NYT, you know that 0.8% of women your age get
breast cancer.
2. After a chat at the hair salon, you were surprised to learn that
about 2.5% of women who had mammograms and don't have breast cancer
were needlessly scared shitless when their doctors told them they had
a 90% chance of having breast cancer.
3. You take a mammogram and your doctor tells you that you have a 90%
chance of breast cancer.
What is your real chance of breast cancer after this mammogram?
p(H|E) = (pH * pE|H) / pE = (pH * pE|H) / (pH * pE|H + pE|H' * pH')
= (0.008 * 1/3) / ((0.008 * 1/3) + (0.025 * 0.992))
= 9.4%
Who needs an MD?
James
On Apr 26, 2010, at 12:30 PM, Jim Pflugrath wrote:
I'm always on the lookout for good ways to teach
Bayes's theorem.
