[10] http://www.nytimes.com/health/guides/disease/pneumonia/prognosis.html.
[11] Bayes’ s rule is: P(A|B)=(P(B|A)×P(A))/P(B)
[12] This paragraph, and this discussion, quotes nearly verbatim from Kramer, W. and Gigerenzer, G. (2005). How to confuse with statistics or: The use and misuse of conditional probabilities. Statistical Science, 20 (3), 223–230.
[13] How do you know what number to choose? Sometimes it takes trial and error. But it’s also possible to figure it out. Because the probability is .8 percent, or eight people per thousand, if you chose to build a table for 1,000 women you’d end up with eight in one of the squares, and that’s okay, but later on we’re going to be multiplying that by 90 percent, which will give us a decimal. There’s nothing wrong with that, it’s just less convenient for most people to work with decimals. Increasing our population by an order of magnitude to 100 gives us all whole numbers, but then we’re looking at larger numbers than we need. It doesn’t really matter because all we’re looking for is probabilities and we’ll be dividing one number by another anyway for the result.
[14] Still confused? If there were eight times as many cars on the road at seven p.m. than at seven a.m., the raw number of accidents could be higher at seven p.m., but that does not necessarily mean that the proportion of accidents to cars is greater. And that is the relevant statistic to you: not how many accidents happen at seven p.m., but how many accidents occur per thousand cars on the road. This latter formulation quantifies your risk. This example is modified from one in Huff, op. cit. p. 78, and discussed by Kr?mer & Gigerenzer (2005).
[15] Cited in Spirer, Spirer & Jaffe, op. cit., p. 197: Thompson, W. C. & Schumann, E. L. (1987). Interpretation of statistical evidence in criminal trials, Law and Human Behavior, 11 (167).
[16] From Spirer, Spirer & Jaffee, op. cit., first reported in Hastie, R. & Dawes, R. M. (1988). Rational Choice in an Uncertain World, New York: Harcourt Brace Jovanovich. The original report of the surgeon’s work appeared in McGee, G. (1979, February 6). Breast surgery before cancer. Ann Arbor News, p. B1 (reprinted from the Bay City News).
[17] Best, op. cit., p. 184.
第二部分
猜不透的文字游戏
真假参半的谎言最为凶险。
——阿尔弗雷德·丁尼生勋爵
