Some Geographical Clusters Are Due to Chance (It Is Not Always a Miracle, When Good, Or the Environment, When Bad)

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David J. Hand. Source of photo: online version of the NYT article quoted and cited below.

(p. 12) Your latest book, “The Improbability Principle,” aims to prove that extremely improbable events are in fact commonplace. Can you explain that a bit? Things like roulette wheels coming up in strange configurations or the same lottery numbers hitting two weeks in a row are clearly very rare events, but if you look at the number of lotteries and the number of roulette wheels, then you realize that you should actually expect these sorts of things to happen. I think within the statistical community people accept this. They’re aware of the impact of the law of truly large numbers.
. . .
You also write that geographical clusters of people with diseases might not necessarily be a result of environmental issues. It could just be a coincidence. Well, they could be due to some sort of pollution or infectious disease or something like that, but you can expect clusters to occur just by chance as well. So it’s an interesting statistical problem to tease these things out. Is this a genuine cluster in the sense that there’s a cause behind it? Or is it a chance cluster?

For the full interview, see:
Chozick, Amy, interviewer. “‘The Wonder Is Still There’; The Statistician David J. Hand on Eerie Coincidences and Playing the Lottery.” The New York Times Magazine (Sun., FEB. 23, 2014): 12.
(Note: ellipsis added; bold in original.)
(Note: the online version of the interview has the date FEB. 21, 2014, and has the title “David J. Hand’s Lottery Tips.”)

Hand’s book is:
Hand, David J. The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day. New York: Scientific American/Farrar, Straus and Giroux, 2014.

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