When statisticians forget how to do statistics

A great example of how statistical analysis is not always immediately intuitive comes from testing statisticians. As Nassim Taleb notes in “The Black Swan:”

“In 1971, the psychologists Danny Kahneman and Amos Tversky plied professors of statistics with statistical questions not phrased as statistical questions. One was similar to the following (changing the example for clarity): Assume that you live in a town with two hospitals – one large, the other small. On a given day 60 percent of those born in one of the two hospitals are boys. Which hospital is it likely to be? Many statisticians made the equivalent of the mistake (during a casual conversation) of choosing a larger hospital, when in fact the very basis of statistics is that large samples are more stable and should fluctuate less from the long-term average – here, 50 percent for each of the sexes – than smaller samples. These statisticians would have flunked their own exams.”

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