Friday miscellany

Thank you for continuing to share such interesting links! The airplane-design story is great. And the alternative medicine link made me laugh for a moment. If they’re all worthless, you should *expect* about 5% of them to look better than placebo at significance level alpha=0.05…

In the “wisdom of crowds” article, I was trying to understand why the author (Nick Carr) seems to think that the arithmetic mean is a natural measure to use while the median and geometric mean are “arcane” statistical inventions which “massage” the answers. It seems to me that the median and geometric mean are, in fact, the more “natural” approaches for questions where responses vary across many orders of magnitude, but commenters haven’t been able to convince him yet and he seems to have had enough of the discussion… Too bad.
Can you think of some simple examples that would clearly illustrate when geometric means might be more natural? For example, perhaps if we asked the crowd “How many zeros are there in a trillion?” we’d take the arithmetic mean, while if we asked them to “Write down a trillion” we’d take the geometric mean…

And that got me wondering if the arithmetic mean is so common in statistics largely because it’s easy to use in proofs: you can take derivatives of the mean (and the variance, as a sum of squared errors) but not of the median (or the sum of absolute errors). If not for this analytical simplicity, might medians be more commonly used than means?