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When U.S. air force discovered the flaw of averages (2016)

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Re: When U.S. air force discovered the flaw of averages (2016)

#21

Post by stcredzero »

I remember when this idea came around Hacker News the last time. I mentioned this over lunch, and one of my (highly respected and deservedly considered intelligent) younger coworkers called BS on it. His object was: "Why would a government build an expensive, high tech piece of equipment, then not ensure it could fit the operator?" He just couldn't imagine it.

Between 2020 and WWII, there is a huge difference in available technology and scale. There were a lot more planes and a lot more pilots back then. It's practically a WWII trope: Arguably "inferior" weapons systems win out because they can be produced in larger numbers with better maintainability and support logistics. (1)

Depending on how you evaluate it, the amount of firepower and capability embodied in one WWII fighter is greatly dwarfed by that in one gen 4 or gen 5 fighter jet.

(1) (Though, in WWII, Allied planes often had a tremendous advantage in performance, largely because they had access to far better fuel. This allowed for much higher compression ratios and higher pressure superchargers, so they could produce more power, more efficiently, for less weight. "Greg's Airplanes and Automobiles" on YouTube covers this.)

Re: When U.S. air force discovered the flaw of averages (2016)

#22

Post by Someone »

ken wrote: post #17
RcouF1uZ4gsC wrote: post #10

> 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.

FTA: ”These formed the dimensions of the “average pilot,” which Daniels generously defined as someone whose measurements were within the middle 30 per cent of the range of values for each dimension.“

0.3³ = 0.0027 = 2.7%, so if those measurements are independent of each other, it isn’t surprising that he found “less than 3.5 percent”.

Re: When U.S. air force discovered the flaw of averages (2016)

#23

Post by user5994461 »

lalaithion wrote: post #7

Note 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…

Should note that the study seems to be working on an extremely narrow range, the 30% in middle to quote the article. So measurements in the 35-65% percentile from what I understand.

In layman's term. It's so narrow that there are more people 1 inch off than there are people within the expected height. It's crazy.

Probability is talking in terms of standard deviations nowadays. They are selecting less than half a standard deviation, it's hyper selective. I'm curious how many people would fit the norm if the study was looking at 1 standard deviation. Surely a lot more.

For reference. Selecting the 30% on six metrics is keeping less than 0.01% of participants. Selecting the 68% (one deviation) on six metrics is keeping 10% of participants. It's night and day. Should be even more in practice because measurements are correlated.

Re: When U.S. air force discovered the flaw of averages (2016)

#25

Post by Aloha »

stcredzero wrote: post #21

I remember when this idea came around Hacker News the last time. I mentioned this over lunch, and one of my (highly respected and deservedly considered intelligent) younger coworkers called BS on it. His object was: "Why would a government build an expensive, high tech piece of equipment, then not ensure it could fit the operator?" He just couldn't imagine it. Between 2020 and WWII, there is a huge difference in avai…

Our technology also continued to evolve throughout the war, updated fighters, better engines, even whole new designs. The Germans as far as mass produced designs went were effectively frozen in 1939. A lot of this was the complete inefficiency of the Reich Air Ministry at project management, as well as the political supremacy of the Heer over the Luftwaffe. In addition to the political whims of a dictatorship (Technological choices were often driven by ideology, and perception, much more than in the other dictatorship at the time (the Soviet Union, where for the most part, the technocrat reigned supreme))

All this said, from purely a material point of view the war in europe was won by the allies in 1941 when the US joined the conflict, but the Axis could have dragged the conflict out much longer had they had an effective strategic bombing program, and more modern fighters.

Re: When U.S. air force discovered the flaw of averages (2016)

#26

Post by MyHypatia »

Consider this set of statistics: 90% of elementary school teachers are female [1]. 90% of veterans are male [2].

Unsurprising.

But, there are 2 million female veterans in the US, and only 1.7 million female elementary school teachers. That means if you talk to a random American female, it is more likely that she is a veteran than an elementary school teacher. I think a lot of disagreements on Hacker News and elsewhere stem from people saying "Well 90% of the time, X is true" without realizing that the 10% they are choosing to ignore is comprised of millions of people.

[1] https://nces.ed.gov/programs/coe/indicator_clr.asp [2] https://www.google.com/url?sa=t&source=web&rct=j&url=https:/...

Re: When U.S. air force discovered the flaw of averages (2016)

#27

Post by krenzo »

def8cefe wrote: post #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 b…

I think they're referring to this: https://en.wikipedia.org/wiki/Somatotype_and_constitutional_...

Re: When U.S. air force discovered the flaw of averages (2016)

#28

Post by Retric »

clintonc wrote: post #16
lalaithion wrote: post #7

Note 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 measurem…

It’s two different effects. First being within a range is not the same as being at the center of the range. Someone 4% above average height should have ~50% of their dimensions larger than that. Similarly someone at 4% below average should have around 50% of their dimensions below that. At best someone in the exact middle of the range only has so much buffer to work with.

Second the correlation is less significant than your assuming. My legs are the same length as some people a full foot shorter than I am.

Re: When U.S. air force discovered the flaw of averages (2016)

#29

Post by abrahamneben »

MyHypatia wrote: post #26

Consider this set of statistics: 90% of elementary school teachers are female [1]. 90% of veterans are male [2]. Unsurprising. But, there are 2 million female veterans in the US, and only 1.7 million female elementary school teachers. That means if you talk to a random American female, it is more likely that she is a veteran than an elementary school teacher. I think a lot of disagreements on Hacker News and elsewher…

Enter bayes theorem

Re: When U.S. air force discovered the flaw of averages (2016)

#30

Post by Retric »

Someone wrote: post #22
ken wrote: post #17

Earlier quoted context omitted.

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.

FTA: ”These formed the dimensions of the “average pilot,” which Daniels generously defined as someone whose measurements were within the middle 30 per cent of the range of values for each dimension.“ 0.3³ = 0.0027 = 2.7%, so if those measurements are independent of each other, it isn’t surprising that he found “less than 3.5 percent”.

I think the general assumption is arm length and height for example are strongly correlated.
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