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This reminds of this article, Useless Medical Disclaimers. It's about how medical disclaimers are useless because they don't include probabilities, but they can

This reminds of this article, Useless Medical Disclaimers. It's about how medical disclaimers are useless because they don't include probabilities, but they can't because most people don't understand probabilities: http://lesswrong.com/lw/h4/useless_medical_disclaimers/ http://lesswrong.com/lw/h4/useless_medical_disclaimers/ >innumeracy being so widespread, no one would dare put numbers on that sheet of paper. If "amputation" is listed as a consequence with a probability of 0.0001%, patients will run screaming out of the office, crying, "Not my toe! I don't want to lose my toe!"

DanBC 11y ago
See also Gerd Gigerenzer's book "Reckoning with Risk". https://plus.maths.org/content/reckoning-risk https://plus.maths.org/content/reckoning-risk >The probability that one of these women [asymptomatic, aged 40 to 50, from a particular region, participating in mammography screening] has breast cancer is 0.8 percent. If a woman has breast cancer, the probability is 90 percent that she will have a positive mammogram. If a woman does not have breast cancer, the probability is 7 percent that she will still have a positive mammogram. Imagine a woman who has a positive mammogram. What is the probability that she actually has breast cancer? > Eight out of every 1,000 women have breast cancer. Of these 8 women with breast cancer, 7 will have a positive mammogram. Of the remaining 992 women who don't have breast cancer, some 70 will still have a positive mammogram. Imagine a sample of women who have positive mammograms in screening. How many of these women actually have breast cancer? His point is that it's not just patients who don't know the numbers. Doctors and nurse, who use these numbers every day, also don't understand them.
- Houshalter 11y ago
  That's a classic problem to introduce Bayes theorem. However the more interesting fact is 95% of doctors get that question wrong.
  - incompatible 11y ago
    Surely doctors would learn to expect the numerous false positives after a while. Or does the question not really relate to reality?
- pjscott 11y ago
  The "imagine 1000 women..." formulation definitely sounds easier to understand, but doctors do very poorly on it as well. Some numbers: http://slatestarcodex.com/2013/12/17/statistical-literacy-among-doctors-now-lower-than-chance/ http://slatestarcodex.com/2013/12/17/statistical-literacy-am... In practice things are not quite as dire as you'd expect, thanks to diagnostic guidelines written with input from people who know about conditional probability.

DanBC 11y ago

See also Gerd Gigerenzer's book "Reckoning with Risk". https://plus.maths.org/content/reckoning-risk https://plus.maths.org/content/reckoning-risk >The probability that one of these women [asymptomatic, aged 40 to 50, from a particular region, participating in mammography screening] has breast cancer is 0.8 percent. If a woman has breast cancer, the probability is 90 percent that she will have a positive mammogram. If a woman does not have breast cancer, the probability is 7 percent that she will still have a positive mammogram. Imagine a woman who has a positive mammogram. What is the probability that she actually has breast cancer? > Eight out of every 1,000 women have breast cancer. Of these 8 women with breast cancer, 7 will have a positive mammogram. Of the remaining 992 women who don't have breast cancer, some 70 will still have a positive mammogram. Imagine a sample of women who have positive mammograms in screening. How many of these women actually have breast cancer? His point is that it's not just patients who don't know the numbers. Doctors and nurse, who use these numbers every day, also don't understand them.

Houshalter 11y ago
That's a classic problem to introduce Bayes theorem. However the more interesting fact is 95% of doctors get that question wrong.
- incompatible 11y ago
  Surely doctors would learn to expect the numerous false positives after a while. Or does the question not really relate to reality?
pjscott 11y ago
The "imagine 1000 women..." formulation definitely sounds easier to understand, but doctors do very poorly on it as well. Some numbers: http://slatestarcodex.com/2013/12/17/statistical-literacy-among-doctors-now-lower-than-chance/ http://slatestarcodex.com/2013/12/17/statistical-literacy-am... In practice things are not quite as dire as you'd expect, thanks to diagnostic guidelines written with input from people who know about conditional probability.