Even with just one dimension, the average may not be characteristic of the population.
When U.S. air force discovered the flaw of averages (2016)
11–20 of 116 posts
Re: When U.S. air force discovered the flaw of averages (2016)
#12This interesting but all a bit wordy and meandering.
Tldr: The air force was using the average dimensions of their pilots to design aircraft. Coincident to this, there was a large number of downed planes questionably attributed to "pilot error" but that many believed to be from an unknown cause. A recruit from Harvard charged with collecting data on pilots realized few people were close to the average, and recommending cockpits be fit to each individual. The AF took the recommendation and eventually companies produced aircraft with adjustable seating and cockpits.
Tldr tldr: dont just reach for the average
Re: When U.S. air force discovered the flaw of averages (2016)
#13Note that this is not some sort of unexpected effect due to humans not behaving mathematically ideally; this is what happens when your intuitions about 1, 2 and 3 dimensions are applied to higher dimensional spaces. Consider the goal of being in the middle 50% of a random value on one dimension; you have a 50% chance. But if you have two dimensions, and you want to be in the middle 50% for both of them, it's a 25% ch…
I find it more intuitive to to discard the spatial intuition and think in terms of events. You want something in the X% norm? Think about it like a X%-heads biased coin flip. If you flip it enough times, it'd be shocking to get all heads. Even if the coin flips (dimensions) are correlated, many coin flips (dimensions) means at least some tails (dimension outside the norm).
Re: When U.S. air force discovered the flaw of averages (2016)
#14This is a really interesting article. The most fascinating part is to learn that the AF actually listened to the man and changed their policies. This kind of thing can happen even when only measuring a single dimension, if the distribution is multimodal. If everyone is either really short or really tall, then nobody will be near the average height.
I realize that the audience is quite different, but it’s interesting to compare the response to “no woman matches our expectations” (means they’re fundamentally broken) vs “no man matches our expectations” (means the model is fundamentally broken).
Re: When U.S. air force discovered the flaw of averages (2016)
#15This is a duplicate, see https://news.ycombinator.com/item?id=11230287, https://news.ycombinator.com/item?id=16220499 and more.
Re: When U.S. air force discovered the flaw of averages (2016)
#16Note that this is not some sort of unexpected effect due to humans not behaving mathematically ideally; this is what happens when your intuitions about 1, 2 and 3 dimensions are applied to higher dimensional spaces. Consider the goal of being in the middle 50% of a random value on one dimension; you have a 50% chance. But if you have two dimensions, and you want to be in the middle 50% for both of them, it's a 25% ch…
That last bit seems to be the Crux of why this is so surprising -- being in the middle 50% on some dimension correlates positively with being in the middle 50% on the other dimensions, rather than each dimension being independent as in your calculation. It's difficult for me to reconcile that, for the 400 in the study within 5% of average height, each was a standard deviation away from the mean in some other measurement.
Re: When U.S. air force discovered the flaw of averages (2016)
#17> Out of 4,063 pilots, not a single airman fit within the average range on all 10 dimensions. > Less than 40 of the 3,864 contestants were average size on just five of the nine dimensions and none of the contestants — not even Martha Skidmore — came close on all nine dimensions. This seems more an issue of the "curse of dimensionality"[0] more than the "flaw of averages". Be very wary when you are trying to draw conc…
I don’t think so. They also said:
> Even more astonishing, Daniels discovered that if you picked out just three of the ten dimensions of size ... less than 3.5 per cent of pilots would be average sized on all three dimensions.
Re: When U.S. air force discovered the flaw of averages (2016)
#18This reminds me of an old math joke. A statistician and a mathematician went duck hunting. From a blind, the mathematician shot and hit a duck. Their retriever went and got the duck. Then the statistician spotted and shot at another duck but shot too high. Quickly the statistician shot again but too low. The statistician then beamed with pride, on average, that's a dead duck.
Re: When U.S. air force discovered the flaw of averages (2016)
#19The USAF employs averages in all kinds of interesting ways!
"How US nuclear force modernization is undermining strategic stability: The burst-height compensating super-fuze" (or: How I Learned to Stop Worrying About Undershoot and Love Terminal Detonation Timing)
Re: When U.S. air force discovered the flaw of averages (2016)
#20>The Aero Medical Laboratory hired Daniels because he had majored in physical anthropology, a field that specialized in the anatomy of humans, as an undergraduate at Harvard. During the first half of the 20th century, this field focused heavily on trying to classify the personalities of groups of people according to their average body shapes — a practice known as “typing.” For example, many physical anthropologists believed a short and heavy body was indicative of a merry and fun-loving personality, while receding hairlines and fleshy lips reflected a “criminal type.”
Can anyone point me in the direction of more information on this? Curious to learn more but my searches didn't turn up anything related.