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

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

#91

The concept of no members of a group fitting into the average range for all observations is reminiscent of the 'curse of dimensionality'. Can anyone with a data science background make the connection here? Secondly, this seems to explain why everyone hates autocorrect.

It doesn't have to be a high-dimensional space. 0% of a donut is near the average.

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

#92

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 tha…

"Out of 4,063 pilots, not a single airman fit within the average range on all 10 dimensions."

"If you’ve designed a cockpit to fit the average pilot, you’ve actually designed it to fit no one."

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

#93
post #69
post #64

Earlier quoted context omitted.

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.

I can't tell what you mean. In some sense (not a very good one), the data must follow a normal distribution, as the sum of normal distributions is itself a normal distribution. But that would imply that you could sensibly add values like "circumference of upper arm" and "length, ankle to knee", which you really shouldn't be doing.

- If you measure values from a 10-dimensional space, what would it mean for them to be "normally distributed"? Do we norm them by distance to the center of the space, or what? Does that approach preserve the nice properties of normals?

- If this concept exists, did Daniels or anyone related to the project know that? Is it really what they were looking for?

- If this concept exists, were the pilots in fact normally distributed?

Saying "the data should follow a normal distribution" without having a definition of "normal distribution" that allows for multidimensional points immediately implies that all body measurements are correlated with all other body measurements at plus or minus 1, which I'm certain nobody believed. And the individual measurements are normally distributed.

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

#94
post #49
post #46

The thing that strikes me here is how much we repeat the mistake of Norma (taking the mythical average body and assuming that differences mean problems) today in talking about people's minds. I started using computers before it was fashionable, before my fellow nerds started being worth billions and ending up on magazine covers. It's hard to describe now how much our difference was seen as wrong, as the sign of a pro…

Modern psychology does not care about average it cares about capable of functioning in society. If you can't avoid say screaming in public that's a problem not just a non issue. Arguably the tolerances might be low, but it's hard to argue with the basic premise. Granted doctors assume if your talking to them you have a problem. But that's arguably a reasonable prior. PS: The extremes of behavior get very far out ther…

[deleted]

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

#95
post #49
post #46

The thing that strikes me here is how much we repeat the mistake of Norma (taking the mythical average body and assuming that differences mean problems) today in talking about people's minds. I started using computers before it was fashionable, before my fellow nerds started being worth billions and ending up on magazine covers. It's hard to describe now how much our difference was seen as wrong, as the sign of a pro…

Modern psychology does not care about average it cares about capable of functioning in society. If you can't avoid say screaming in public that's a problem not just a non issue. Arguably the tolerances might be low, but it's hard to argue with the basic premise. Granted doctors assume if your talking to them you have a problem. But that's arguably a reasonable prior. PS: The extremes of behavior get very far out ther…

[deleted]

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

#96
post #46

The thing that strikes me here is how much we repeat the mistake of Norma (taking the mythical average body and assuming that differences mean problems) today in talking about people's minds. I started using computers before it was fashionable, before my fellow nerds started being worth billions and ending up on magazine covers. It's hard to describe now how much our difference was seen as wrong, as the sign of a pro…

>How much we repeat the mistake of Norma (taking the mythical average body and assuming that differences mean problems) today in talking about people's minds.

Makes me wonder which is the perfect text editor that everyone should use, is it emacs or vim?

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

#97
post #69

Earlier quoted context omitted.

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.

I can't tell what you mean. In some sense (not a very good one), the data must follow a normal distribution, as the sum of normal distributions is itself a normal distribution. But that would imply that you could sensibly add values like "circumference of upper arm" and "length, ankle to knee", which you really shouldn't be doing. - If you measure values from a 10-dimensional space, what would it mean for them to be…

I this case they may not have been. Given the US Airforce was selecting pilots with measurements within certain bounds their measurements were probably a truncated normal.

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

#98
My company Treemetrics has been challenging the forest industry for method used for measuring forests. They use the average tree size as the method for valuing a standing forest. From our data we see forests with thousands of trees where only a handful of average trees actually exist. Very helpful article for me to explain the flaw of averages.

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

#99
post #69

Earlier quoted context omitted.

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.

I can't tell what you mean. In some sense (not a very good one), the data must follow a normal distribution, as the sum of normal distributions is itself a normal distribution. But that would imply that you could sensibly add values like "circumference of upper arm" and "length, ankle to knee", which you really shouldn't be doing. - If you measure values from a 10-dimensional space, what would it mean for them to be…

You are looking for https://en.wikipedia.org/wiki/Multivariate_normal_distributi...

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

#100
post #75

Earlier quoted context omitted.

Weirdly enough, even the proportion of points within a distance of 1/2 to the midpoint becomes really small for higher dimensions.

takeaway: With enough dimensions everyone is weird

Or -- if you think everybody is the same -- then you aren't looking hard enough!
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