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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)

#41

Earlier quoted context omitted.

Enter bayes theorem

Bayes' Theorem should be getting taught with quite some emphasis in high school, imo.

I would argue that Bayes Theorem is taught in high school basically conditional probabilities and inferences. The issue is that applied Bayes Theorem is not taught. What do you do with information given with the data at hand?

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

#42

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…

> ...the 10% they are choosing to ignore is comprised of millions of people. I don't understand your point here. Is it that somehow, some people are more than 10% likely to run into the 10%? Well, that's obvious. Roughly speaking, you'd expect 10% of commenters to be in that 10%, unless we're talking about something that disproportionately does or does not affect people interested in technologies, startups, etc. .

The point is that people often have an opinion, cite one statistic to validate their opinion, miss the bigger picture (because summarizing anything complex with a single number, rarely tells the whole story), and in the face of additional evidence stick to that one statistic that validates their original opinion. I see it happen a lot. Both on HN and elsewhere too. Presenting multiple statistics that shine a different light on the same population, enriches the conversation, and gives a more complete characterization of the population/situation/phenomena etc.

I also personally found that combined set of statistics enlightening because I previously did not realize how large the population of female veterans is, since I had only read about the percentages not the absolute numbers.

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

#43
post #37
post #25

Earlier quoted context omitted.

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 (Techno…

Regardless of Spitfires, Alan Turing, anti-sub technology, RADAR etc, WW2 was won and lost on the Eastern front. The Normandy invasion would have been impossible without the Russians sacrificing between 8-11 million soldiers. This compares to about 400k each for the UK and US. I'm just saying, don't get carried away with the technological superiority argument, there was plenty of innovation on both sides. After all,…

No real disagreement there - the war was won on the back of Russian Bodies, American Trucks, and British Grit.

The germans did indeed have wonderful technology in labs, and had it made it into mass production, it would have made the war stretch out much much longer.

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

#44

Earlier quoted context omitted.

> ...the 10% they are choosing to ignore is comprised of millions of people. I don't understand your point here. Is it that somehow, some people are more than 10% likely to run into the 10%? Well, that's obvious. Roughly speaking, you'd expect 10% of commenters to be in that 10%, unless we're talking about something that disproportionately does or does not affect people interested in technologies, startups, etc. .

The point is that people often have an opinion, cite one statistic to validate their opinion, miss the bigger picture (because summarizing anything complex with a single number, rarely tells the whole story), and in the face of additional evidence stick to that one statistic that validates their original opinion. I see it happen a lot. Both on HN and elsewhere too. Presenting multiple statistics that shine a differen…

It's a problem of lack of STEM education, unfortunately. More specifically, of metrology.

"90% of elementary school teachers" is not directly comparable to "90% of veterans". You have to multiply them by their respective populations to get numbers that can be compared. In general, a thing of the form "$amount of $something" is not comparable to "$amount of $somethingelse". That amount being a fraction with a '%' sign in front of it doesn't change anything.

Unfortunately, schools aren't beating people with sticks until they internalize that point, while at the same time a good part of sales and marketing relies on people not being formal enough in their thinking.

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

#45

Earlier quoted context omitted.

Bayes' Theorem should be getting taught with quite some emphasis in high school, imo.

I would argue that Bayes Theorem is taught in high school basically conditional probabilities and inferences. The issue is that applied Bayes Theorem is not taught. What do you do with information given with the data at hand?

Bayesian updates should be taught in schools, at least at the most coarse-grained level. Not to let people calculate anything; almost nobody is going to need that in life anyway. But so that some authority (which a school is) tells people they're allowed and supposed to update their beliefs on evidence. That evidence drags belief more in one direction than the other. That 0 and 1 are not probabilities in real life. That being certain of something is a rare thing, that they should embrace being more or less sure. That this is not someone's random worldview, but there is a proper (and rather fundamental) mathematical formalism behind it, it's just impossible to apply it fully in real life, so we have to approximate it.

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

#46

Earlier quoted context omitted.

The point is that people often have an opinion, cite one statistic to validate their opinion, miss the bigger picture (because summarizing anything complex with a single number, rarely tells the whole story), and in the face of additional evidence stick to that one statistic that validates their original opinion. I see it happen a lot. Both on HN and elsewhere too. Presenting multiple statistics that shine a differen…

It's a problem of lack of STEM education, unfortunately. More specifically, of metrology. "90% of elementary school teachers" is not directly comparable to "90% of veterans". You have to multiply them by their respective populations to get numbers that can be compared. In general, a thing of the form "$amount of $something" is not comparable to "$amount of $somethingelse". That amount being a fraction with a '%' sign…

Yes, I certainly wish schools would teach this better. I think showing different examples with surprising conclusions/outcomes helps people internalize that point.

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

#47
The referenced study of human dimensions was not the only thing done by the military to improve aviation safety. The discovery of human factors in user interfaces was also recognized. There had been some standardization of the cockpit controls of different aircraft during WWII and before, but not so much for the instruments and displays. That was no easy task, but the problem was recognized and addressed.

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

#48

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…

That's because you need to know that there are ~20 million veterans and ~1.87 million elementary school teachers, i.e. you need to know the base rate if I'm reversing the calculations properly.

Another flaw of averages is apparent when you realize that the average person has less than two eyes.

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

#49
Huh, the conventional story is that the UN forces won the air war in Korea because of better plane ergonomics despite Migs having better theoretical performance. But this report didn't come out until the war was mostly over. The conventional story emphasizes things like bubble canopies but still.

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

#50

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…

>Why would a government build an expensive, high tech piece of equipment, then not ensure it could X

Maybe short design periods in some cases too. Either way it was not too uncommon. There were bombers with escape hatches big enough for the crew, provided they didn't wear parachutes[1]. Fighter bomb releases that required ducking down to reach them[2] and fighter planes who's fuel feed stopped when pulling negative Gs [3]

[1] Lancaster bombers

[2] P-26 or F2A I think

[3] https://en.wikipedia.org/wiki/Miss_Shilling%27s_orifice

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