When the U.S. air force discovered the flaw of averages • Hacker News Board

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

#61

Post by douche » Sat, Mar 05, 2016, 10:56 PM UTC

danbruc wrote: post #34

harywilke wrote: post #28

Earlier quoted context omitted.

Why is it certainly false?

The simplest example I can come up with is the weight - the density of humans is probably constant for practical purposes and therefore the weight must be positively correlated with your body dimensions. It is also pretty obvious that humans, or tissue for the matter, does not grow in a strongly directional manner. If you gain weight more or less all dimensions not constraint by your skeleton will increase, i.e. you…

I wouldn't say density is a constant. Muscle weighs more than fat for the same volume, as does bone. Same height, higher muscle or denser bone structure, and you can have wildly different weights. Makes simplistic measurements like BMI pretty laughable - look at pretty much any athlete, who would run high over-weight or obese according to BMI.

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

#62

Post by sparky_z » Sat, Mar 05, 2016, 10:56 PM UTC

keenerd wrote: post #59

While hindsight is 20:20, parts of this should have been more obvious. > Daniels generously defined as someone whose measurements were within the middle 30 per cent of the range of values > 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. 30% raised to the third power is 2.7%. Basic probability. I gu…

Assuming a normal distribution instead of a uniform one isn't that outlandishly unreasonable.

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

#63

Post by pbhjpbhj » Sat, Mar 05, 2016, 11:03 PM UTC

icodestuff wrote: post #50

danbruc wrote: post #34

Earlier quoted context omitted.

The simplest example I can come up with is the weight - the density of humans is probably constant for practical purposes and therefore the weight must be positively correlated with your body dimensions. It is also pretty obvious that humans, or tissue for the matter, does not grow in a strongly directional manner. If you gain weight more or less all dimensions not constraint by your skeleton will increase, i.e. you…

Sure, but weight gain in adulthood doesn't cause you to get taller.

>weight gain in adulthood doesn't cause you to get taller //

Not even a tiny bit, like because of fat feet or more fat on the head? Not trying to be facetious, just seems huge people have fat feet and that there's likely to be a little fat on the bottom of the foot. Mind you that's going to be countered by compression of the spine, so there could be a inverse correlation?

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

#64

Post by keenerd » Sat, Mar 05, 2016, 11:05 PM UTC

sparky_z wrote: post #62

keenerd wrote: post #59

While hindsight is 20:20, parts of this should have been more obvious. > Daniels generously defined as someone whose measurements were within the middle 30 per cent of the range of values > 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. 30% raised to the third power is 2.7%. Basic probability. I gu…

Assuming a normal distribution instead of a uniform one isn't that outlandishly unreasonable.

He didn't assume a normal distribution. It wasn't "within ±15% of the mean". It was "the middle 30% of the range". This means excluding 70% of the population for each factor, regardless of the distribution. Finding a "normal person" was impossible from the beginning with that approach.

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

#65

Post by sandworm101 » Sat, Mar 05, 2016, 11:10 PM UTC

I don't see the problem. The fact that no person fit the model perfectly doesn't mean that the model was a poor choice.

The question shouldn't be whether any customers fit the cockpit perfectly, but how many customers do and do not fit absolutely. You build the legroom so that most legs will fit, and headroom so that most heads will fit. Then as many people as possible shall fit. Everyone will have some dimension that isn't perfectly accommodated, but few should be rejected. The fact that nobody fits perfectly doesn't take away from a design that reasonably accommodates as many people as possible.

A cockpit is not a suit. It's a communal chair/workspace meant to be used by various persons over many years. The metric of a good design should be how many/few people are so out of standards that they cannot work properly in the space. This is a perfect metaphor for hiring. Look only for that 'prefect fit' and you won't hire anyone, or you end up with hiring the only applicant to get past the roboreader. Seek a broader standard and you'll find plenty of good people even though mr perfect never appears.

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

#66

Post by Gibbon1 » Sat, Mar 05, 2016, 11:13 PM UTC

danbruc wrote: post #12

gefh wrote: post #8

Earlier quoted context omitted.

But you might naturally assume a strong correlation between the middle range of each dimension - the interesting conclusion is that it's not nearly as strong as our intuition suggests.

But even if they are correlated that does not necessarily imply that being average on one dimension makes it likely to be average on other dimensions. I can well imagine that correlations conspire against you, i.e. that being average in one dimension makes it likely to be non-average in another dimension.

I assume there are developmental genetics that apply to a whole organism. Everything on an elephant has to be big and everything on a mouse has to be small. But then there probably is little correlation between localized development genetics. The result is that within the 5% to 95% range the correlation between the size and shape of developmental features is pretty much zippo and simple non-correlated probability dominates.

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

#67

Post by tomjen3 » Sat, Mar 05, 2016, 11:15 PM UTC

keenerd wrote: post #59

While hindsight is 20:20, parts of this should have been more obvious. > Daniels generously defined as someone whose measurements were within the middle 30 per cent of the range of values > 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. 30% raised to the third power is 2.7%. Basic probability. I gu…

Only if the variables are independent, right? Because I would expect a tall guy to have longer arms than I have.

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

#68

Post by andrewfong » Sat, Mar 05, 2016, 11:16 PM UTC

keenerd wrote: post #59

While hindsight is 20:20, parts of this should have been more obvious. > Daniels generously defined as someone whose measurements were within the middle 30 per cent of the range of values > 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. 30% raised to the third power is 2.7%. Basic probability. I gu…

> 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.”

Also, for what's it worth, this was during (or at least not too far removed from) a time period where researchers were trying to ascribe all sorts of random characteristics to people based on whether they were "Negroids", "Caucasoids", or "Mongoloids".

This says a lot to me about how people thought about physical characteristics back then. If researchers assumed male-pattern baldness was associated with a "criminal type", then it's not a huge stretch to imagine that researchers assumed there was a "pilot type" with a large number of clustered or heavily correlated characteristics.

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

#69

Post by dgemm » Sat, Mar 05, 2016, 11:19 PM UTC

keenerd wrote: post #64

sparky_z wrote: post #62

Earlier quoted context omitted.

Assuming a normal distribution instead of a uniform one isn't that outlandishly unreasonable.

He didn't assume a normal distribution. It wasn't "within ±15% of the mean". It was "the middle 30% of the range". This means excluding 70% of the population for each factor, regardless of the distribution. Finding a "normal person" was impossible from the beginning with that approach.

The original assumption before Daniels was that the data would follow a normal distribution and so there was an "average" pilot.

He showed that was wrong.

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

#70

Post by danbruc » Sat, Mar 05, 2016, 11:21 PM UTC

douche wrote: post #61

danbruc wrote: post #34

Earlier quoted context omitted.

The simplest example I can come up with is the weight - the density of humans is probably constant for practical purposes and therefore the weight must be positively correlated with your body dimensions. It is also pretty obvious that humans, or tissue for the matter, does not grow in a strongly directional manner. If you gain weight more or less all dimensions not constraint by your skeleton will increase, i.e. you…

I wouldn't say density is a constant. Muscle weighs more than fat for the same volume, as does bone. Same height, higher muscle or denser bone structure, and you can have wildly different weights. Makes simplistic measurements like BMI pretty laughable - look at pretty much any athlete, who would run high over-weight or obese according to BMI.

That doesn't matter, humans are a lot of water and the density of humans seems - after a quick search - to be essentially within the density of water plus or minus ten percent. In this context that's constant enough for me and definitely way to small to possibly offset the variability in body weight.