I recently read an article about statistics. It was pretty eye-opening for me, because it really showed me 1) how illiterate we are in basic statistics, and 2) how easy it is to fool someone with important sounding facts.
Part of the problem about statistics, I think, is that they seem so readily accessible to the average person, but how tricky and counter-intuitive they actually can be.
One of the examples from the article was the OJ Simpson trial. The prosecution went to great lengths to show that OJ was a wife-abuser. The defense conceded the point, but said "Look, only 1 in 2500 men who beat their wives actually end up killing them." I could easily see myself sitting on the jury, and having that argument bear some weight. Yes, he might be a terrible person, but does that imply that he killed his wife? Just because he abused his wife doesn't mean he killed her. That's reasonable.
The real question that should be asked is "If he abused his wife, and she was murdered by someone, then what are the chances that it was the husband?" This is a much more accurate question, and changes the probabilities significantly.
Here's another fun one:
The probability that a woman 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?
Quick, what is your gut estimate?
From the article:
"When Gigerenzer asked 24 other German doctors the same question, their estimates whipsawed from 1 percent to 90 percent. Eight of them thought the chances were 10 percent or less, 8 more said 90 percent, and the remaining 8 guessed somewhere between 50 and 80 percent. Imagine how upsetting it would be as a patient to hear such divergent opinions. As for the American doctors, 95 out of 100 estimated the woman’s probability of having breast cancer to be somewhere around 75 percent. The right answer is 9 percent."
Amazing stuff. I guess the point is to be skeptical of what you believe, even if there is numerical data to back it up. (Did you know that 85% of all stomach cancer patients drank cow's milk for years as children?)
Read this article when you have a moment.
Part of the problem about statistics, I think, is that they seem so readily accessible to the average person, but how tricky and counter-intuitive they actually can be.
One of the examples from the article was the OJ Simpson trial. The prosecution went to great lengths to show that OJ was a wife-abuser. The defense conceded the point, but said "Look, only 1 in 2500 men who beat their wives actually end up killing them." I could easily see myself sitting on the jury, and having that argument bear some weight. Yes, he might be a terrible person, but does that imply that he killed his wife? Just because he abused his wife doesn't mean he killed her. That's reasonable.
The real question that should be asked is "If he abused his wife, and she was murdered by someone, then what are the chances that it was the husband?" This is a much more accurate question, and changes the probabilities significantly.
Here's another fun one:
The probability that a woman 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?
Quick, what is your gut estimate?
From the article:
"When Gigerenzer asked 24 other German doctors the same question, their estimates whipsawed from 1 percent to 90 percent. Eight of them thought the chances were 10 percent or less, 8 more said 90 percent, and the remaining 8 guessed somewhere between 50 and 80 percent. Imagine how upsetting it would be as a patient to hear such divergent opinions. As for the American doctors, 95 out of 100 estimated the woman’s probability of having breast cancer to be somewhere around 75 percent. The right answer is 9 percent."
Amazing stuff. I guess the point is to be skeptical of what you believe, even if there is numerical data to back it up. (Did you know that 85% of all stomach cancer patients drank cow's milk for years as children?)
Read this article when you have a moment.
3 comments:
If you like this stuff, you should read _The Drunkard's Walk_. Excellent book (for the layman).
I've heard of this book before... just ordered it.
Thanks!
Reminds me of the famous Mark Twain Quote:
"There are three kinds of lies: lies, damned lies and statistics."
Discostup
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