https://plus.maths.org/content/reckoning-risk
This is what most people struggle with:
> 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?
That can be reworded to something much easier:
> 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?
It's a good book and covers cases of misdiagnosed HIV.
That becomes scary when you're talking to a doctor about a test that returned a positive result. Does that doctor know how likely it is you actually have what you tested positive for? Are you going to get treatment for this thing?
Gerd Gigerenzer has a nice book about this: http://www.amazon.com/Reckoning-Risk-Learning-Live-Uncertain...
Here's one example about breast cancer testing: http://imgur.com/zO4zkl4
I agree that presenting risks as percentages instead of real numbers is misleading.
But they say this device is better than primary care doctors so I'm not sure what that says about primary care.
Gerd Gigerenzer wrote a book in 2002 about clinicians inability to understand percentages and screening tests.
http://www.amazon.co.uk/gp/aw/d/0140297863?pc_redir=13991465...
http://plus.maths.org/content/reckoning-risk
http://www.amazon.com/gp/aw/d/0140297863?pc_redir=1399339535...
Look at Morgellon's; Mercury Chelation; Anti-vaccination; etc etc etc.
There are very many people willing to sell tests, and very many people happy to sell quack cures based on those tests. (I'm not saying that 23andMe are quacks!)
> "Man, is there anything worse than being told you have something terrible wrong with you, living with that, then finding out it was a false alarm". Uhm, yeah. How about finding out it wasn't?
That's happened to a few people. You get told you're HIV+ (in the late 90s, when this means it's a death sentence.) You lose your job (because people are arseholes), you stop showing your 8 year old son affection (because you're scared of the infection), you have unprotected sex with people with HIV (you're already +, so what does it matter?) and then you get told that there was a mistake with the original test and you're actually negative.
http://www.amazon.com/Reckoning-Risk-Learning-Live-Uncertain...
I really hope she had more information than a 23andme result.
As I understand it she has a strong family history, and the mutated gene. Prophylactic surgery can reduce risk in those cases.
Most people don't understand what "risk reduction means" so I hope she had doctors who were able to explain it to her.
This website http://www.cancer.gov/cancertopics/factsheet/Therapy/risk-re... describes it as a 95% reduction in risk.
Very very few people are going to understand what that means for them. Gerd Gigerenzer has a book that's a useful discussion of why presenting risks as percentages is bad.
http://www.amazon.com/Reckoning-Risk-Learning-Live-Uncertain...
And here's an example from the book http://imgur.com/zO4zkl4
> The problem isn't just that such a system is wrong, it's that the mathematics of testing makes this sort of thing pretty ineffective in practice. It's called the "base rate fallacy." Suppose you have a test that's 90% accurate in identifying both sociopaths and non-sociopaths. If you assume that 4% of people are sociopaths, then the chance of someone who tests positive actually being a sociopath is 26%. (For every thousand people tested, 90% of the 40 sociopaths will test positive, but so will 10% of the 960 non-sociopaths.) You have postulate a test with an amazing 99% accuracy -- only a 1% false positive rate -- even to have an 80% chance of someone testing positive actually being a sociopath.
Interestingly here he uses percentages to describe base rates and risk. Gerd Gigerenzer has a nice book, Reckoning with Risk, where he explains with many examples the problems of this approach. Gerd asks people to use real numbers instead, which are much easier to understand for most people.
Thus, Schneier's example becomes:
> Out of 1,000 people about 40 of will be sociopaths. You have a test that will tell you if someone is, or is not, a sociopath. The test will be correct 9 times out of 10. Bob has taken the test, and has been identified as a possible sociopath. The chance that Bob is actually a sociopath are actually about 1 in 4. This is because the test will tell you that 36 of the 40 sociopaths are sociopaths, but it will also incorrectly tell you that 96 non-sociopaths are sociopaths.
My writing is lousy, and other people will be able to clean this up, but even with my poor writing style it's easier for most people to follow and understand than the percentages.
This is alarmingly important when you're making a health decision - "Should I remove my breasts to reduce my risk of breast cancer?" for example.
(http://www.amazon.com/Reckoning-Risk-Learning-Live-Uncertain...)
EDIT: I use "sociopath" because it's in the source article. I agree with NNQ that it's very troubling to bandy around diagnostic labels like this, and deem people to be dangerous, just because of a tentative probabilistic diagnosis.
Or read Gerd Gigerenzer's book Reckoning with Risk http://www.amazon.com/Reckoning-Risk-Learning-Live-Uncertain...
https://plus.maths.org/content/reckoning-risk
And, as Temporal says, without knowing the base rate (am I raising my risk from 1 in 100,000 or from 1 in 1,000?) it provides very little useful information.