By the way, this is also the reason why things like UI design have gotten so bad: Most Machine Learning algorithms fit averages. Combine them, and you learn surprisingly little!
When U.S. air force discovered the flaw of averages (2016)
81–90 of 116 posts
Re: When U.S. air force discovered the flaw of averages (2016)
#82Earlier quoted context omitted.
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 th…
Every time I get my height measured by a new doctor, they feel the need to tell me that my legs are short for my height.
Re: When U.S. air force discovered the flaw of averages (2016)
#83Note 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…
nit: 0.01% is 1 in ten thousand.
Re: When U.S. air force discovered the flaw of averages (2016)
#84[deleted]
Re: When U.S. air force discovered the flaw of averages (2016)
#85Earlier quoted context omitted.
There are about 2mm active and reserve military members and about 400mm Americans on the whole, so there are, at any time, 0.5% Americans in the military. Assuming the average enlistment is 1 term or 4 years, and people have about 80 year lifespans, then you get ~20 (80/4) "generations" of enlistments over a person's lifespan. 20 * 0.5% is 10%, so about what you would expect for "living veterans" if you had a constan…
Possibly, though I would think that many who serve do more than 1 enlistment. It's just that from my own personal experiences I've encountered few veterans in my life (except for older generation family members who served in WWII), that's why intuitively I find the number a bit surprising.
> It's just that from my own personal experiences I've encountered few veterans in my life
Lots of veterans don't advertise the fact that they are.
Re: When U.S. air force discovered the flaw of averages (2016)
#86Earlier quoted context omitted.
And half of the population is dumber than the average. :-)
Shouldn't it be: Half of the population is dumber than the median . ??
The median is an average, one of many (though the most common thing people mean when they say “average” is “arithmetic mean”.)
Re: When U.S. air force discovered the flaw of averages (2016)
#87Earlier quoted context omitted.
Shouldn't it be: Half of the population is dumber than the median . ??
>Shouldn't it be: >Half of the population is dumber than the median. >?? Probably not. Imagine a population of three people. The middle person is not dumber than themselves.
At least 50% must be at or under the median.
Exactly half under is correct only for if none is exactly at the median, which requires (but is not necessarily the case when) there are an even number of measures.
Re: When U.S. air force discovered the flaw of averages (2016)
#88Earlier quoted context omitted.
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”.
Human dimensions are closer to a normal distribution. (Not quite normal, but let's pretend.) In that distribution then 46% of subjects should be in the middle 30% of 3 dimensions. [0] [0] With 4000 subjects they presumably have all sizes within ~3.5 stddevs represented. The middle ~1.2 stddevs should hold ~77% of the population. 0.77^3 = ~46%
> Human dimensions are closer to a normal distribution
Human height is (it's the textbook example of a real, intuitive_that is, using the normal linear scale—physical measure that is a good fit for a normal distribution) plenty of other human dimensions are not.
Re: When U.S. air force discovered the flaw of averages (2016)
#89Earlier quoted context omitted.
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,…
And the Eastern Front was largely won and lost on the Atlantic Ocean.
And the Arctic Ocean etc etc
The Soviets won out eventually, but without the west they could very well have lost before they really got ready.
Re: When U.S. air force discovered the flaw of averages (2016)
#90Earlier quoted context omitted.
This is only true if each dimension is independent and identically distributed random variables, which is doubtfully true for humans. That said, the overall intuition is probably more correct than incorrect...
They are neither fully independent nor fully dependent. It falls somewhere in the middle. The same will apply, just in a slightly less dramatic effect.
But surely the engineers were who were inventing jets and rocket guidance systems and radar understood probabilities of independent events. The point, which the author almost misses completely, is that they dramatically overestimated how correlated the measurements were.
Beyond that, while there's no accounting for taste, I find it to be an appallingly bad article. It's poor man's Malcolm Gladwell.