California Lawyer's review
Huffington Post review (great one!)
Scientific American
Notices of the American Mathematical Society review (likes the book but is not sure that the questions addressed are really all that important! Doesn't mind people unjustly convicted to years in prison? Hm, we'll need to respond to this one.)
Science News review
Mathematical Association of America review
Washington Independent review
Newsletter of the London Mathematical Society review by Ray Hill (p. 16)
And then there are some interviews:
Leila's online radio interview with "Science for the People"
Coralie in The Economist
Coralie's BBC interview (reached number one most-read article on the whole BBC website!)
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ReplyDeleteHi Leila and Coralie,
ReplyDeleteCongrats on the great reviews! I just finished reading the book, and found it tremendously entertaining and thought-provoking.
I did find however what I believe is a series of math errors (on the authors’ part) in the book. On page 139, you refer to Nurse N, who is "a little more careless or perhaps less trained than most", and rank her at position 500 out of 250,000 nurses, concluding that her record has a “p-value” of 1/250. But this is not a p-value at all; it is merely a percentile ranking. To conclude that a percentile ranking is a “p-value” would require that all other 249,999 nurses are each objectively ordinary in their skills, and work precisely the same number of shifts as N, thus creating a perfect binomial distribution of outcomes.
Furthermore, multiplying two p-values (e.g. to construct the 1 / 62,500 probability from N working at two hospitals) is perfectly legitimate, _if_ the inputs are actual p-values. In other words, the statement “p-values cannot be multiplied as a general rule” is not true. They can be. It might be more accurate to say: ‘values that superficially resemble but are not really p-values’ (e.g. percentile rankings) cannot be multiplied as a general rule.
Then: “Suppose that nurse N works at two hospitals. If two separate p-values are calculated.. both will be close to 1/250”. This statement underscores the fact that the values being “calculated” are not actually p-values. If they were, then both would be closer to 1/30. (E.g. if a coin lands heads 64/100 times overall, the p-value is about 1/250. If it turns out that half were flipped at one place and half at another, then each place would likely have measured about 32/50 heads, a p-value of about 1/30 each, not 1/250 each.)
Finally: the statement “…you get a p-value of 1/62,500, meaning that N must be one of the very worst nurses in the country”, is simply the wrong conclusion to draw no matter what, even if true p-values are involved. A p-value of 1/62,500 merely means that nurse N is almost certainly _worse than average_, but the number has no intrinsic bearing on _how much_ worse that is. For example, suppose you flip a coin one million times and it comes up heads 50.21% of the time. The p-value for this is also roughly 1/62,500, but clearly the coin itself is only marginally biased (if at all), and unlikely one of the worst coins in the coin jar, let alone the country.
To draw a parallel: I’m certain that if you did a study of open-heart surgeons, you would quickly find many with p-values below 1/62,500 in terms of surviving patients, relative to national averages. Suppose the national survival rate is 50%, and that surgeon S has performed 1000 surgeries over a career, and 43.4% survived. (p-value ~1/62,500.) The conclusion should not be that S has deliberately murdered 66 patients, but rather that his skill set was probably somewhat lacking, absent some other confounding factor. Similarly, a doctor for whom 56.6% of patients survived (also p=1/62,500) might be rightly praised, but probably not canonized.
Apologies for rambling; I’m overanalyzing this to make sure I’m not in error myself, which is entirely possible :-) Reposting just with some edits.
Best,
Ben